Quantum algorithmic information theory
Svozil, Karl
1995-01-01
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capa...
Nielsen, M. A.
2000-01-01
Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent quantum information, and entanglement. Exploring the rich variety of capabilities allowed by these types of information is the subject of quantum information theory, and of this Dissertation. In particular, I demonstrate several novel limits to the informa...
Quantum biological information theory
Djordjevic, Ivan B
2016-01-01
This book is a self-contained, tutorial-based introduction to quantum information theory and quantum biology. It serves as a single-source reference to the topic for researchers in bioengineering, communications engineering, electrical engineering, applied mathematics, biology, computer science, and physics. The book provides all the essential principles of the quantum biological information theory required to describe the quantum information transfer from DNA to proteins, the sources of genetic noise and genetic errors as well as their effects. Integrates quantum information and quantum biology concepts; Assumes only knowledge of basic concepts of vector algebra at undergraduate level; Provides a thorough introduction to basic concepts of quantum information processing, quantum information theory, and quantum biology; Includes in-depth discussion of the quantum biological channel modelling, quantum biological channel capacity calculation, quantum models of aging, quantum models of evolution, quantum models o...
Nielsen, M A
1998-01-01
Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent quantum information, and entanglement. Exploring the rich variety of capabilities allowed by these types of information is the subject of quantum information theory, and of this Dissertation. In particular, I demonstrate several novel limits to the information processing ability of quantum mechanics. Results of especial interest include: the demonstration of limitations to the class of measurements which may be performed in quantum mechanics; a capacity theorem giving achievable limits to the transmission of classical information through a two-way noiseless quantum channel; resource bounds on distributed quantum computation; a new proof of the quantum noiseless channel coding theorem; an information-theoretic characterization of the conditions under which quantum error-cor...
Wilde, Mark M
2017-01-01
Developing many of the major, exciting, pre- and post-millennium developments from the ground up, this book is an ideal entry point for graduate students into quantum information theory. Significant attention is given to quantum mechanics for quantum information theory, and careful studies of the important protocols of teleportation, superdense coding, and entanglement distribution are presented. In this new edition, readers can expect to find over 100 pages of new material, including detailed discussions of Bell's theorem, the CHSH game, Tsirelson's theorem, the axiomatic approach to quantum channels, the definition of the diamond norm and its interpretation, and a proof of the Choi–Kraus theorem. Discussion of the importance of the quantum dynamic capacity formula has been completely revised, and many new exercises and references have been added. This new edition will be welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theo...
Quantum information theory mathematical foundation
Hayashi, Masahito
2017-01-01
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an impro...
Quantum Information Theory - an Invitation
Werner, R. F.
2001-01-01
We give a non-technical introduction of the basic concepts of Quantum Information Theory along the distinction between possible and impossible machines. We then proceed to describe the mathematical framework of Quantum Information Theory. The capacities of a quantum channel for classical and for quantum information are defined in a unified scheme, and a mathematical characterization of all teleportation and dense coding schemes is given.
Recoverability in quantum information theory
Wilde, Mark M
2015-01-01
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information...
Introduction to quantum information theory
Nielsen, M. A.
2000-01-01
This is an expanded and revised text for a fifteen minute talk given at the University of Queensland Physics Camp, September 2000. The focus is on the goals and motivations for studying quantum information theory, rather than on technical results.
Studies in quantum information theory
Menicucci, Nicolas C.
Quantum information theory started as the backdrop for quantum computing and is often considered only in relation to this technology, which is still in its infancy. But quantum information theory is only partly about quantum computing. While much of the interest in this field is spurred by the possible use of quantum computers for code breaking using fast factoring algorithms, to a physicist interested in deeper issues, it presents an entirely new set of questions based on an entirely different way of looking at the quantum world. This thesis is an exploration of several topics in quantum information theory. But it is also more than this. This thesis explores the new paradigm brought about by quantum information theory---that of physics as the flow of information. The thesis consists of three main parts. The first part describes my work on continuous-variable cluster states, a new platform for quantum computation. This begins with background material discussing classical and quantum computation and emphasizing the physical underpinnings of each, followed by a discussion of two recent unorthodox models of quantum computation. These models are combined into an original proposal for quantum computation using continuous-variable cluster states, including a proposed optical implementation. These are followed by a mathematical result radically simplifying the optical construction. Subsequent work simplifies this connection even further and provides a constructive proposal for scalable generation of large-scale cluster states---necessary if there is to be any hope of using this method in practical quantum computation. Experimental implementation is currently underway by my collaborators at The University of Virginia. The second part describes my work related to the physics of trapped ions, starting with an overview of the basic theory of linear ion traps. Although ion traps are often discussed in terms of their potential use for quantum computation, my work looks at their
Recoverability in quantum information theory
Wilde, Mark
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This is based on arXiv:1505.04661, now accepted for publication in Proceedings of the Royal Society A. I acknowledge support from startup funds from the Department of Physics and Astronomy at LSU, the NSF under Award No. CCF-1350397, and the DARPA Quiness Program through US Army Research Office award W31P4Q-12-1-0019.
Quantum information theory and quantum statistics
Energy Technology Data Exchange (ETDEWEB)
Petz, D. [Alfred Renyi Institute of Mathematics, Budapest (Hungary)
2008-07-01
Based on lectures given by the author, this book focuses on providing reliable introductory explanations of key concepts of quantum information theory and quantum statistics - rather than on results. The mathematically rigorous presentation is supported by numerous examples and exercises and by an appendix summarizing the relevant aspects of linear analysis. Assuming that the reader is familiar with the content of standard undergraduate courses in quantum mechanics, probability theory, linear algebra and functional analysis, the book addresses graduate students of mathematics and physics as well as theoretical and mathematical physicists. Conceived as a primer to bridge the gap between statistical physics and quantum information, a field to which the author has contributed significantly himself, it emphasizes concepts and thorough discussions of the fundamental notions to prepare the reader for deeper studies, not least through the selection of well chosen exercises. (orig.)
Quantum Theory is an Information Theory
D'Ariano, Giacomo M.; Perinotti, Paolo
2016-03-01
In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.
The decoupling approach to quantum information theory
Dupuis, Frédéric
2010-01-01
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and ha...
Some Issues in Quantum Information Theory
Institute of Scientific and Technical Information of China (English)
Run-Yao Duan; Zheng-Feng Ji; Yuan Feng; Ming-Sheng Ying
2006-01-01
Quantum information theory is a new interdisciplinary research field related to quantum mechanics, computer science, information theory, and applied mathematics. It provides completely new paradigms to do information processing tasks by employing the principles of quantum mechanics. In this review, we first survey some of the significant advances in quantum information theory in the last twenty years. We then focus mainly on two special subjects: discrimination of quantum objects and transformations between entanglements. More specifically, we first discuss discrimination of quantum states and quantum apparatus in both global and local settings. Secondly, we present systematical characterizations and equivalence relations of several interesting entanglement transformation phenomena, namely entanglement catalysis,multiple-copy entanglement transformation, and partial entanglement recovery.
Foundations of quantum theory and quantum information applications
Galvão, E F
2002-01-01
This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement characterisation, and of a few quantum information protocols. Quantum non-locality and contextuality are shown to be essential for different implementations of quantum information protocols known as quantum random access codes and quantum communication complexity protocols. I derive sufficient experimental conditions for tests of these quantum properties. I also discuss how the distribution of quantum information through quantum cloning processes can be useful in quantum computing. Regarding entanglement characterisation, some results are obtained relating two problems, that of additivity of the relative entropy of entanglement, and that of identifying different types of tripartite entanglement in the asymptotic regime of manipulations of many copies of a given state. The thesis end...
Quantum theory informational foundations and foils
Spekkens, Robert
2016-01-01
This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information. Topics include: operational alternatives to quantum theory, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent features of the set of quantum correlations. Powered by the injection of fresh ideas from the field of Quantum Information and Computation, the foundations of Quantum Mechanics are in the midst of a renaissance. The last two decades have seen an explosion of new results and research directions, attracting broad interest in the scientific community. The variety and number of different approaches, however, makes it challenging for a newcomer to obtain a big picture of the field and of its high-level goals. Here, fourteen original contributions from leading experts in the field cover some of the most promising research directions that have emerged in the new wave of quant...
Relativistic quantum information theory and quantum reference frames
Palmer, Matthew C
2013-01-01
This thesis is a compilation of research in relativistic quantum information theory, and research in quantum reference frames. The research in the former category provides a fundamental construction of quantum information theory of localised qubits in curved spacetimes. For example, this concerns quantum experiments on free-space photons and electrons in the vicinity of the Earth. From field theory a description of localised qubits that traverse classical trajectories in curved spacetimes is obtained, for photons and massive spin-1/2 fermions. The equations governing the evolution of the two-dimensional quantum state and its absolute phase are determined. Quantum information theory of these qubits is then developed. The Stern-Gerlach measurement formalism for massive spin-1/2 fermions is also derived from field theory. In the latter category of research, the process of changing reference frames is considered for the case where the reference frames are quantum systems. As part of this process, it is shown that...
Holography, Quantum Geometry, and Quantum Information Theory
Directory of Open Access Journals (Sweden)
P. A. Zizzi
2000-03-01
Full Text Available Abstract: We interpret the Holographic Conjecture in terms of quantum bits (qubits. N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labelled by the spin-Ã‚Â½ representation of SU(2, which are in a superposed quantum state of spin "up" and spin "down". The formalism is applied in particular to de Sitter horizons, and leads to a picture of the early inflationary universe in terms of quantum computation. A discrete micro-causality emerges, where the time parameter is being defined by the discrete increase of entropy. Then, the model is analysed in the framework of the theory of presheaves (varying sets on a causal set and we get a quantum history. A (bosonic Fock space of the whole history is considered. The Fock space wavefunction, which resembles a Bose-Einstein condensate, undergoes decoherence at the end of inflation. This fact seems to be responsible for the rather low entropy of our universe.
Random subspaces in quantum information theory
Hayden, Patrick
2005-03-01
The selection of random unitary transformations plays a role in quantum information theory analogous to the role of random hash functions in classical information theory. Recent applications have included protocols achieving the quantum channel capacity and methods for extending superdense coding from bits to qubits. In addition, the corresponding random subspaces have proved useful for studying the structure of bipartite and multipartite entanglement. In quantum information theory, we're fond of saying that Hilbert space is a big place, the implication being that there's room for the unexpected to occur. The goal of this talk is to further bolster this homespun wisdowm. I'm going to present a number of results in quantum information theory that stem from the initially counterintuitive geometry of high-dimensional vector spaces, where subspaces with highly extremal properties are the norm rather than the exception. Peter Shor has shown, for example, that randomly selected subspaces can be used to send quantum information through a noisy quantum channel at the highest possible rate, that is, the quantum channel capacity. More recently, Debbie Leung, Andreas Winter and I demonstrated that a randomly chosen subspace of a bipartite quantum system will likely contain nothing but nearly maximally entangled states, even if the subspace is nearly as large as the original system in qubit terms. This observation has implications for communication, especially superdense coding.
Distinguishability and accessible information in quantum theory
Fuchs, C
1996-01-01
This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states. These measures should have important appli- cations in quantum cryptography and quantum computation theory. The results reported include the following. An exact expression for the quantum fidelity between two mixed states is derived. The optimal measurement that gives rise to it is studied in detail. Several upper and lower bounds on the quantum mutual information are derived via similar techniques and compared to each other. Of note is a simple derivation of the important upper bound first proved by Holevo and an explicit expression for another (tighter) upper bound that appears implicitly in the same derivation. Several upper and lower bounds to the quan- tum Kullback relative information are derived. The measures developed are also applied to ferreting out the extent to which quantum systems must be disturbed by information...
The decoupling approach to quantum information theory
Dupuis, Frédéric
2010-04-01
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and have as corollaries entanglement-assisted and unassisted asymptotic coding theorems. The entanglement-assisted asymptotic versions can, in both cases, be considered as quantum versions of the best coding theorems known for the classical versions of these problems. The last chapter deals with a purely quantum phenomenon called locking. We demonstrate that it is possible to encode a classical message into a quantum state such that, by removing a subsystem of logarithmic size with respect to its total size, no measurement can have significant correlations with the message. The message is therefore "locked" by a logarithmic-size key. This thesis presents the first locking protocol for which the success criterion is that the trace distance between the joint distribution of the message and the measurement result and the product of their marginals be sufficiently small.
The role of quantum discord in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Streltsov, Alexander [ICFO - The Institute of Photonic Sciences, Castelldefels (Spain)
2014-07-01
Quantum correlations beyond entanglement - in particular represented by quantum discord - have become a major research field in the last few years. In this talk we report on the role of quantum discord in several fundamental tasks in quantum information theory. Starting with the role of quantum discord in the quantum measurement process, we also discuss its role in the tasks of information sharing and entanglement distribution. Finally, we also show the limits of these results and present possible ways to go beyond these limits.
Random matrix techniques in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Collins, Benoît, E-mail: collins@math.kyoto-u.ac.jp [Department of Mathematics, Kyoto University, Kyoto 606-8502 (Japan); Département de Mathématique et Statistique, Université d’Ottawa, 585 King Edward, Ottawa, Ontario K1N6N5 (Canada); CNRS, Lyon (France); Nechita, Ion, E-mail: nechita@irsamc.ups-tlse.fr [Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching (Germany); Laboratoire de Physique Théorique, CNRS, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse (France)
2016-01-15
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Quantum information theory with Gaussian systems
Energy Technology Data Exchange (ETDEWEB)
Krueger, O.
2006-04-06
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Information and Entropy in Quantum Theory
Maroney, O J E
2004-01-01
We look at certain thought experiments based upon the 'delayed choice' and 'quantum eraser' interference experiments, which present a complementarity between information gathered from a quantum measurement and interference effects. It has been argued that these experiments show the Bohm interpretation of quantum theory is untenable. We demonstrate that these experiments depend critically upon the assumption that a quantum optics device can operate as a measuring device, and show that, in the context of these experiments, it cannot be consistently understood in this way. By contrast, we then show how the notion of 'active information' in the Bohm interpretation provides a coherent explanation of the phenomena shown in these experiments. We then examine the relationship between information and entropy. The thought experiment connecting these two quantities is the Szilard Engine version of Maxwell's Demon, and it has been suggested that quantum measurement plays a key role in this. We provide the first complete ...
Introduction to the theory of quantum information processing
Bergou, János A
2013-01-01
Introduction to the Theory of Quantum Information Processing provides the material for a one-semester graduate level course on quantum information theory and quantum computing for students who have had a one-year graduate course in quantum mechanics. Many standard subjects are treated, such as density matrices, entanglement, quantum maps, quantum cryptography, and quantum codes. Also included are discussions of quantum machines and quantum walks. In addition, the book provides detailed treatments of several underlying fundamental principles of quantum theory, such as quantum measurements, the no-cloning and no-signaling theorems, and their consequences. Problems of various levels of difficulty supplement the text, with the most challenging problems bringing the reader to the forefront of active research. This book provides a compact introduction to the fascinating and rapidly evolving interdisciplinary field of quantum information theory, and it prepares the reader for doing active research in this area.
Measuring orbital interaction using quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Rissler, Joerg [Fachbereich Physik, Philipps-Universitaet Marburg, AG Vielteilchentheorie, Renthof 6, D-35032 Marburg (Germany)], E-mail: rissler@staff.uni-marburg.de; Noack, Reinhard M. [Fachbereich Physik, Philipps-Universitaet Marburg, AG Vielteilchentheorie, Renthof 6, D-35032 Marburg (Germany); White, Steven R. [Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575 (United States)
2006-04-21
Quantum information theory gives rise to a straightforward definition of the interaction of electrons I {sub p,q} in two orbitals p,q for a given many-body wave function. A convenient way to calculate the von Neumann entropies needed is presented in this work, and the orbital interaction I {sub p,q} is successfully tested for different types of chemical bonds. As an example of an application of I {sub p,q} beyond the interpretation of wave functions, I {sub p,q} is then used to investigate the ordering problem in the density-matrix renormalization group.
From information geometry to quantum theory
Energy Technology Data Exchange (ETDEWEB)
Goyal, Philip [Perimeter Institute, Waterloo (Canada)], E-mail: pgoyal@perimeterinstitute.ca
2010-02-15
In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely complementarity, measurement simulability, and global gauge invariance. When these features are appropriately formalized within an information geometric framework, and combined with a novel information-theoretic principle, the central features of the finite-dimensional quantum formalism can be reconstructed.
Quantum: information theory: technological challenge; Computacion Cuantica: un reto tecnologico
Energy Technology Data Exchange (ETDEWEB)
Calixto, M.
2001-07-01
The new Quantum Information Theory augurs powerful machines that obey the entangled logic of the subatomic world. Parallelism, entanglement, teleportation, no-cloning and quantum cryptography are typical peculiarities of this novel way of understanding computation. (Author) 24 refs.
The black hole information problem beyond quantum theory
Mueller, Markus P; Dahlsten, Oscar C O
2012-01-01
The origin of black hole entropy and the black hole information problem provide important clues for trying to piece together a quantum theory of gravity. Thus far, discussions on this topic have mostly assumed that in a consistent theory of gravity and quantum mechanics, quantum theory will be unmodified. Here, we examine the black hole information problem in the context of generalisations of quantum theory. In particular, we examine black holes in the setting of generalised probabilistic theories, in which quantum theory and classical probability theory are special cases. We compute the time it takes information to escape a black hole, assuming that information is preserved. We find that under some very general assumptions, the arguments of Page (that information should escape the black hole after half the Hawking photons have been emitted), and the black-hole mirror result of Hayden and Preskill (that information can escape quickly) need to be modified. The modification is determined entirely by what we cal...
Complementarity and Entanglement in Quantum Information Theory
Tessier, T E
2004-01-01
The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems, and yield vital insights into the design of protocols for the quantum control of ensembles with potential applications in the field of quantum computing. We show how this entanglement sharing behavior may be studied in increasingly complex systems of both theoretical and experimental significance and demonstrate that entanglement sharing, as well as other unique features of entanglement, e.g. the fact that maximal information about a multipartite quantum system does not necessarily entail maximal information about its component subsystems, may be understood as specific consequences of the phenomenon of complementarity extended to composite quantum systems. We also present a local hidden-variable model supplemented by an efficient amount of classical communication that reproduces the quantum-mechanical predictions for the entire class of Gottesman-Kni...
Quantum theory from first principles an informational approach
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-01-01
Quantum theory is the soul of theoretical physics. It is not just a theory of specific physical systems, but rather a new framework with universal applicability. This book shows how we can reconstruct the theory from six information-theoretical principles, by rebuilding the quantum rules from the bottom up. Step by step, the reader will learn how to master the counterintuitive aspects of the quantum world, and how to efficiently reconstruct quantum information protocols from first principles. Using intuitive graphical notation to represent equations, and with shorter and more efficient derivations, the theory can be understood and assimilated with exceptional ease. Offering a radically new perspective on the field, the book contains an efficient course of quantum theory and quantum information for undergraduates. The book is aimed at researchers, professionals, and students in physics, computer science and philosophy, as well as the curious outsider seeking a deeper understanding of the theory.
What information theory can tell us about quantum reality
Adami, C
1998-01-01
An investigation of Einstein's ``physical'' reality and the concept of quantum reality in terms of information theory suggests a solution to quantum paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schroedinger-cat paradoxes. Quantum reality, the picture based on unitarily evolving wavefunctions, is complete, but appears incomplete from the observer's point of view for fundamental reasons arising from the quantum information theory of measurement. Physical reality, the picture based on classically accessible observables is, in the worst case of EPR experiments, unrelated to the quantum reality it purports to reflect. Thus, quantum information theory implies that only correlations, not the correlata, are physically accessible: the mantra of the Ithaca interpretation of quantum mechanics.
Quantum information theory of the Bell-state quantum eraser
Glick, Jennifer R.; Adami, Christoph
2017-01-01
Quantum systems can display particle- or wavelike properties, depending on the type of measurement that is performed on them. The Bell-state quantum eraser is an experiment that brings the duality to the forefront, as a single measurement can retroactively be made to measure particlelike or wavelike properties (or anything in between). Here we develop a unitary information-theoretic description of this and several related quantum measurement situations that sheds light on the trade-off between the quantum and classical features of the measurement. In particular, we show that both the coherence of the quantum state and the classical information obtained from it can be described using only quantum-information-theoretic tools and that those two measures satisfy an equality on account of the chain rule for entropies. The coherence information and the which-path information have simple interpretations in terms of state preparation and state determination and suggest ways to account for the relationship between the classical and the quantum world.
Realism and Antirealism in Informational Foundations of Quantum Theory
Directory of Open Access Journals (Sweden)
Tina Bilban
2014-08-01
Full Text Available Zeilinger-Brukner's informational foundations of quantum theory, a theory based on Zeilinger's foundational principle for quantum mechanics that an elementary system carried one bit of information, explains seemingly unintuitive quantum behavior with simple theoretical framework. It is based on the notion that distinction between reality and information cannot be made, therefore they are the same. As the critics of informational foundations of quantum theory show, this antirealistic move captures the theory in tautology, where information only refers to itself, while the relationships outside the information with the help of which the nature of information would be defined are lost and the questions "Whose information? Information about what?" cannot be answered. The critic's solution is a return to realism, where the observer's effects on the information are neglected. We show that radical antirealism of informational foundations of quantum theory is not necessary and that the return to realism is not the only way forward. A comprehensive approach that exceeds mere realism and antirealism is also possible: we can consider both sources of the constraints on the information, those coming from the observer and those coming from the observed system/nature/reality. The information is always the observer's information about the observed. Such a comprehensive philosophical approach can still support the theoretical framework of informational foundations of quantum theory: If we take that one bit is the smallest amount of information in the form of which the observed reality can be grasped by the observer, we can say that an elementary system (grasped and defined as such by the observer correlates to one bit of information. Our approach thus explains all the features of the quantum behavior explained by informational foundations of quantum theory: the wave function and its collapse, entanglement, complementarity and quantum randomness. However, it does
Entropy in quantum information theory - Communication and cryptography
DEFF Research Database (Denmark)
Majenz, Christian
to density matrices, the von Neumann entropy behaves dierently. The latter does not, for example, have the monotonicity property that the latter possesses: When adding another quantum system, the entropy can decrease. A long-standing open question is, whether there are quantum analogues of unconstrained non......Entropies have been immensely useful in information theory. In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. The rst one concerns the von Neumann entropy. While a direct generalization of the Shannon entropy...... in quantum Shannon theory. While immensely more entanglement-consuming, the variant of port based teleportation is interesting for applications like instantaneous non-local computation and attacks on quantum position-based cryptography. Port based teleportation cannot be implemented perfectly...
Quantum field theory, statistical physics, and information theory
Energy Technology Data Exchange (ETDEWEB)
Toyoda, Tadashi [Tokai Univ., Kanagawa (Japan)
2001-05-01
It is shown that the one-particle Matsubara temperature Green's function can be regarded as a Fisher information matrix on the basis of the quantum generalization of relative entropy due to Watanabe and Neumann.
Concepts of a quantum information theory of many letters
Boström, K J
2000-01-01
A theoretical framework is presented allowing the treatment of quantum messages with components of variable length. To this aim a many-letter space is constructed which turns out to be a natural space for quantum messages of this type, generalizing the usual fixed-length quantum information theory which is fully contained within this framework. An observable is defined measuring the amount of quantum information carried by a particular message, with the "qbit" obtaining a second meaning as its unit. A general characterization of quantum codes is given where compression codes are defined by their property of decreasing the average information content of a given a priori message ensemble. A lossless quantum coding scheme - analog to the classical Huffman scheme but different from the Braunstein scheme - is implemented, which not only ensures perfect fidelity in retrieving the original messages but also provides optimal compression.
Toolbox for reconstructing quantum theory from rules on information acquisition
Hoehn, Philipp A
2015-01-01
We develop a novel operational approach for reconstructing (qubit) quantum theory from elementary rules on information acquisition. The focus lies on an observer O interrogating a system S with binary questions and S's state is taken as O's `catalogue of knowledge' about S. The mathematical tools of the framework are simple and we attempt to highlight all underlying assumptions to provide a handle for future generalizations. Five principles are imposed, asserting (1) a limit on the amount of information available to O; (2) the mere existence of complementary information; (3) the possibility for O's information to be `in superposition'; (4) O's information to be preserved in between interrogations; and, (5) continuity of time evolution. This approach permits a constructive derivation of quantum theory, elucidating how the ensuing independence, complementarity and compatibility structure of O's questions matches that of projective measurements in quantum theory, how entanglement and monogamy of entanglement and...
Toward a fully relativistic theory of quantum information
Adami, Christoph
2011-01-01
Information theory is a statistical theory dealing with the relative state of detectors and physical systems. Because of this physicality of information, the classical framework of Shannon needs to be extended to deal with quantum detectors, perhaps moving at relativistic speeds, or even within curved space-time. Considerable progress toward such a theory has been achieved in the last fifteen years, while much is still not understood. This review recapitulates some milestones along this road, and speculates about future ones.
A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information
Plotnitsky, Arkady
2015-01-01
This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be be addressed as well in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation for the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall, however, also consider Heisenberg's derivation of quantum mechanics, which inspired Dirac. I argue that Heisenberg's and Dirac's work alike was guided by their adherence to and confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by G. M. D' Ariano and his coworkers on the principles of quantum information theory, which extends quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equation from these principles alone...
Algebraic geometry informs perturbative quantum field theory
Broadhurst, David
2014-01-01
Single-scale Feynman diagrams yield integrals that are periods, namely projective integrals of rational functions of Schwinger parameters. Algebraic geometry may therefore inform us of the types of number to which these integrals evaluate. We give examples at 3, 4 and 6 loops of massive Feynman diagrams that evaluate to Dirichlet $L$-series of modular forms and examples at 6, 7 and 8 loops of counterterms that evaluate to multiple zeta values or polylogarithms of the sixth root of unity. At 8 loops and beyond, algebraic geometry informs us that polylogs are insufficient for the evaluation of terms in the beta-function of $\\phi^4$ theory. Here, modular forms appear as obstructions to polylogarithmic evaluation.
Quantum correlations beyond entanglement and their role in quantum information theory
Streltsov, Alexander
2015-01-01
Quantum correlations are not restricted to the well known entanglement investigated in Bell-type experiments. Other forms of correlations, for example quantum discord, have recently been shown to play an important role in several aspects of quantum information theory. First experiments also support these findings. This book is an introduction into this up-and-coming research field and its likely impact on quantum technology. After giving a general introduction to the concept of quantum correlations and their role in quantum information theory, the author describes a number of pertinent results and their implications.
The future (and past) of quantum theory after the Higgs boson: a quantum-informational viewpoint.
Plotnitsky, Arkady
2016-05-28
Taking as its point of departure the discovery of the Higgs boson, this article considers quantum theory, including quantum field theory, which predicted the Higgs boson, through the combined perspective of quantum information theory and the idea of technology, while also adopting anon-realistinterpretation, in 'the spirit of Copenhagen', of quantum theory and quantum phenomena themselves. The article argues that the 'events' in question in fundamental physics, such as the discovery of the Higgs boson (a particularly complex and dramatic, but not essentially different, case), are made possible by the joint workings of three technologies: experimental technology, mathematical technology and, more recently, digital computer technology. The article will consider the role of and the relationships among these technologies, focusing on experimental and mathematical technologies, in quantum mechanics (QM), quantum field theory (QFT) and finite-dimensional quantum theory, with which quantum information theory has been primarily concerned thus far. It will do so, in part, by reassessing the history of quantum theory, beginning with Heisenberg's discovery of QM, in quantum-informational and technological terms. This history, the article argues, is defined by the discoveries of increasingly complex configurations of observed phenomena and the emergence of the increasingly complex mathematical formalism accounting for these phenomena, culminating in the standard model of elementary-particle physics, defining the current state of QFT.
Entropy in quantum information theory - Communication and cryptography
DEFF Research Database (Denmark)
Majenz, Christian
Entropies have been immensely useful in information theory. In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. The rst one concerns the von Neumann entropy. While a direct generalization of the Shannon entropy......-Shannon type inequalities. Here, a new constrained non-von-Neumann type inequality is proven, a step towards a conjectured unconstrained inequality by Linden and Winter. Like many other information-theoretic tasks, quantum source coding problems such as coherent state merging have recently been analyzed...... in the one-shot setting. While the case of many independent, identically distributed quantum states has been treated using the decoupling technique, the essentially optimal one-shot results in terms of the max-mutual information by Berta et al. and Anshu at al. had to bring in additional mathematical...
The g-theorem and quantum information theory
Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo
2016-10-01
We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.
Lattice gauge theory simulations in the quantum information era
Dalmonte, M.; Montangero, S.
2016-07-01
The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behaviour of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analysing the symmetric properties of Hamiltonian and states: the most striking examples are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realisation of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review, we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.
The g-theorem and quantum information theory
Casini, Horacio; Torroba, Gonzalo
2016-01-01
We study boundary renormalization group flows between boundary conformal field theories in $1+1$ dimensions using methods of quantum information theory. We define an entropic $g$-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this $g$-function decreases along boundary renormalization group flows. This entropic $g$-theorem is valid at zero temperature, and is independent from the $g$-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between vacuum states.
Semiclassical gravity from the perspective of quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Landulfo, Andre Gustavo Scagliusi [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil)
2012-07-01
Full text: Quantum field theory in curved spacetimes makes remarkable predictions about the behavior of quantum fields in the presence of strong gravitational fields. Nevertheless, these striking discoveries raises several issues. The development of a theory at the interface between relativity, quantum mechanics, and information theory could not only shed new light on such questions as well as allowing to uncover new low-energy quantum gravity effects. In this talk I will review several results in this new field. In particular it will be shown that the Bell inequalities can be satisfied rather than violated by quantum mechanics if the detectors making the measurements are set in relativistic motion. It will also be shown that the entanglement between a pair of quits can suffer a sudden death when one of the quits accelerates uniformly for a finite proper time. This result will be used to analyze the behavior of entanglement in the vicinity of a nonrotating chargeless black hole. I will end with a discussion about the prospects of the field, emphasizing the so called 'black hole information paradox' and the question of what is the microscopic origin of the black hole entropy. (author)
Decision theory and information propagation in quantum physics
Forrester, Alan
In recent papers, Zurek [(2005). Probabilities from entanglement, Born's rule p k =| ψ k | 2 from entanglement. Physical Review A, 71, 052105] has objected to the decision-theoretic approach of Deutsch [(1999) Quantum theory of probability and decisions. Proceedings of the Royal Society of London A, 455, 3129-3137] and Wallace [(2003). Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation. Studies in History and Philosophy of Modern Physics, 34, 415-438] to deriving the Born rule for quantum probabilities on the grounds that it courts circularity. Deutsch and Wallace assume that the many worlds theory is true and that decoherence gives rise to a preferred basis. However, decoherence arguments use the reduced density matrix, which relies upon the partial trace and hence upon the Born rule for its validity. Using the Heisenberg picture and quantum Darwinism-the notion that classical information is quantum information that can proliferate in the environment pioneered in Ollivier et al. [(2004). Objective properties from subjective quantum states: Environment as a witness. Physical Review Letters, 93, 220401 and (2005). Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe. Physical Review A, 72, 042113]-I show that measurement interactions between two systems only create correlations between a specific set of commuting observables of system 1 and a specific set of commuting observables of system 2. This argument picks out a unique basis in which information flows in the correlations between those sets of commuting observables. I then derive the Born rule for both pure and mixed states and answer some other criticisms of the decision theoretic approach to quantum probability.
Quantum Computation and Information From Theory to Experiment
Imai, Hiroshi
2006-01-01
Recently, the field of quantum computation and information has been developing through a fusion of results from various research fields in theoretical and practical areas. This book consists of the reviews of selected topics charterized by great progress and cover the field from theoretical areas to experimental ones. It contains fundamental areas, quantum query complexity, quantum statistical inference, quantum cloning, quantum entanglement, additivity. It treats three types of quantum security system, quantum public key cryptography, quantum key distribution, and quantum steganography. A photonic system is highlighted for the realization of quantum information processing.
Entanglement dynamics in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Cubitt, T.S.
2007-03-29
This thesis contributes to the theory of entanglement dynamics, that is, the behaviour of entanglement in systems that are evolving with time. Progressively more complex multipartite systems are considered, starting with low-dimensional tripartite systems, whose entanglement dynamics can nonetheless display surprising properties, progressing through larger networks of interacting particles, and finishing with infinitely large lattice models. Firstly, what is perhaps the most basic question in entanglement dynamics is considered: what resources are necessary in order to create entanglement between distant particles? The answer is surprising: sending separable states between the parties is sufficient; entanglement can be created without it being carried by a ''messenger'' particle. The analogous result also holds in the continuous-time case: two particles interacting indirectly via a common ancilla particle can be entangled without the ancilla ever itself becoming entangled. The latter result appears to discount any notion of entanglement flow. However, for pure states, this intuitive idea can be recovered, and even made quantitative. A ''bottleneck'' inequality is derived that relates the entanglement rate of the end particles in a tripartite chain to the entanglement of the middle one. In particular, no entanglement can be created if the middle particle is not entangled. However, although this result can be applied to general interaction networks, it does not capture the full entanglement dynamics of these more complex systems. This is remedied by the derivation of entanglement rate equations, loosely analogous to the rate equations describing a chemical reaction. A complete set of rate equations for a system reflects the full structure of its interaction network, and can be used to prove a lower bound on the scaling with chain length of the time required to entangle the ends of a chain. Finally, in contrast with these more
Quantum Information Biology: From Theory of Open Quantum Systems to Adaptive Dynamics
Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro
This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB re ects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.
Nambu-Goldstone Effective Theory of Information at Quantum Criticality
Dvali, Gia; Gomez, Cesar; Wintergerst, Nico
2015-01-01
We establish a fundamental connection between quantum criticality of a many-body system, such as Bose-Einstein condensates, and its capacity of information-storage and processing. For deriving the effective theory of modes in the vicinity of the quantum critical point we develop a new method by mapping a Bose-Einstein condensate of $N$-particles onto a sigma model with a continuous global (pseudo)symmetry that mixes bosons of different momenta. The Bogolyubov modes of the condensate are mapped onto the Goldstone modes of the sigma model, which become gapless at the critical point. These gapless Goldstone modes are the quantum carriers of information and entropy. Analyzing their effective theory, we observe the information-processing properties strikingly similar to the ones predicted by the black hole portrait. The energy cost per qubit of information-storage vanishes in the large-$N$ limit and the total information-storage capacity increases with $N$ either exponentially or as a power law. The longevity of i...
Characterizing quantum theory in terms of information-theoretic constraints
Clifton, R; Halvorson, H; Clifton, Rob; Bub, Jeffrey; Halvorson, Hans
2003-01-01
We show that three fundamental information-theoretic constraints--the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment--suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment.
A Framework for Non-Asymptotic Quantum Information Theory
Tomamichel, Marco
2012-01-01
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\\'enyi entropies. We introduce the purified distance, a novel metric for unnormalized quantum states and use it to define smooth entropies as optimizations of the min- and max-entropies over a ball of close states. We explore various properties of these entropies, including data-processing inequalities, chain rules and their classical limits. The most important property is an entropic formulation of the asymptotic equipartition property, which implies that the smooth entropies converge to the von Neumann entropy in the limit of many independent copies. The smooth entropies also satisfy duality and entropic uncertainty relations that provide limits on the power of two different observers to predict the outcome of a measurement on a quantum system. Finally, we discuss three example...
Correlations in complex nonlinear systems and quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Guehne, Otfried [Institut fuer Quantenoptik und Quanteninformation, Oesterreichische Akademie der Wissenschaften, Innsbruck (Austria); Galla, Tobias [School of Physics and Astronomy, University of Manchester (United Kingdom)
2010-07-01
The dynamical evolution of classical complex systems such as coupled logistic maps or simple models of lattice gases and cellular automata can result in correlations between distant parts of the system. For the understanding of these systems, it is crucial to develop methods to characterize and quantify these multi-party correlations. On the other hand, the study of correlations between distant particles is also a central problem in the field of quantum information theory. There, correlations are often viewed as a resource and many tools have been developed for their characterization. In this talk, we explore the extent to which the tools from quantum information can be applied to study classical complex systems and whether they allow to study complex systems from a different perspective.
EDITORIAL: Focus on Quantum Information and Many-Body Theory
Eisert, Jens; Plenio, Martin B.
2010-02-01
Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac
What Density Functional Theory could do for Quantum Information
Mattsson, Ann
2015-03-01
The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Role of information theoretic uncertainty relations in quantum theory
Energy Technology Data Exchange (ETDEWEB)
Jizba, Petr, E-mail: p.jizba@fjfi.cvut.cz [FNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1 (Czech Republic); ITP, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin (Germany); Dunningham, Jacob A., E-mail: J.Dunningham@sussex.ac.uk [Department of Physics and Astronomy, University of Sussex, Falmer, Brighton, BN1 9QH (United Kingdom); Joo, Jaewoo, E-mail: j.joo@surrey.ac.uk [Advanced Technology Institute and Department of Physics, University of Surrey, Guildford, GU2 7XH (United Kingdom)
2015-04-15
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson–Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson–Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.
Quantum entanglement in non-local games, graph parameters and zero-error information theory
Scarpa, G.
2013-01-01
We study quantum entanglement and some of its applications in graph theory and zero-error information theory. In Chapter 1 we introduce entanglement and other fundamental concepts of quantum theory. In Chapter 2 we address the question of how much quantum correlations generated by entanglement can d
Energy Technology Data Exchange (ETDEWEB)
Rodgers, P
1998-03-01
There is more to information than a string of ones and zeroes the ability of ''quantum bits'' to be in two states at the same time could revolutionize information technology. In the mid-1930s two influential but seemingly unrelated papers were published. In 1935 Einstein, Podolsky and Rosen proposed the famous EPR paradox that has come to symbolize the mysteries of quantum mechanics. Two years later, Alan Turing introduced the universal Turing machine in an enigmatically titled paper, On computable numbers, and laid the foundations of the computer industry one of the biggest industries in the world today. Although quantum physics is essential to understand the operation of transistors and other solid-state devices in computers, computation itself has remained a resolutely classical process. Indeed it seems only natural that computation and quantum theory should be kept as far apart as possible surely the uncertainty associated with quantum theory is anathema to the reliability expected from computers? Wrong. In 1985 David Deutsch introduced the universal quantum computer and showed that quantum theory can actually allow computers to do more rather than less. The ability of particles to be in a superposition of more than one quantum state naturally introduces a form of parallelism that can, in principle, perform some traditional computing tasks faster than is possible with classical computers. Moreover, quantum computers are capable of other tasks that are not conceivable with their classical counterparts. Similar breakthroughs in cryptography and communication followed. (author)
The geometrical structure of quantum theory as a natural generalization of information geometry
Energy Technology Data Exchange (ETDEWEB)
Reginatto, Marcel [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany)
2015-01-13
Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
Viola, Lorenza; Tannor, David
2011-08-01
Precisely characterizing and controlling the dynamics of realistic open quantum systems has emerged in recent years as a key challenge across contemporary quantum sciences and technologies, with implications ranging from physics, chemistry and applied mathematics to quantum information processing (QIP) and quantum engineering. Quantum control theory aims to provide both a general dynamical-system framework and a constructive toolbox to meet this challenge. The purpose of this special issue of Journal of Physics B: Atomic, Molecular and Optical Physics is to present a state-of-the-art account of recent advances and current trends in the field, as reflected in two international meetings that were held on the subject over the last summer and which motivated in part the compilation of this volume—the Topical Group: Frontiers in Open Quantum Systems and Quantum Control Theory, held at the Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP) in Cambridge, Massachusetts (USA), from 1-14 August 2010, and the Safed Workshop on Quantum Decoherence and Thermodynamics Control, held in Safed (Israel), from 22-27 August 2010. Initial developments in quantum control theory date back to (at least) the early 1980s, and have been largely inspired by the well-established mathematical framework for classical dynamical systems. As the above-mentioned meetings made clear, and as the burgeoning body of literature on the subject testifies, quantum control has grown since then well beyond its original boundaries, and has by now evolved into a highly cross-disciplinary field which, while still fast-moving, is also entering a new phase of maturity, sophistication, and integration. Two trends deserve special attention: on the one hand, a growing emphasis on control tasks and methodologies that are specifically motivated by QIP, in addition and in parallel to applications in more traditional areas where quantum coherence is nevertheless vital (such as, for instance
Concept of chemical bond and aromaticity based on quantum information theory
Szilvási, T; Legeza, Ö
2015-01-01
Quantum information theory (QIT) emerged in physics as standard technique to extract relevant information from quantum systems. It has already contributed to the development of novel fields like quantum computing, quantum cryptography, and quantum complexity. This arises the question what information is stored according to QIT in molecules which are inherently quantum systems as well. Rigorous analysis of the central quantities of QIT on systematic series of molecules offered the introduction of the concept of chemical bond and aromaticity directly from physical principles and notions. We identify covalent bond, donor-acceptor dative bond, multiple bond, charge-shift bond, and aromaticity indicating unified picture of fundamental chemical models from ab initio.
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective.
Bylicka, B; Chruściński, D; Maniscalco, S
2014-07-21
Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication.
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective
Bylicka, B.; Chruściński, D.; Maniscalco, S.
2014-01-01
Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication. PMID:25043763
Manning, Phillip
2011-01-01
The study of quantum theory allowed twentieth-century scientists to examine the world in a new way, one that was filled with uncertainties and probabilities. Further study also led to the development of lasers, the atomic bomb, and the computer. This exciting new book clearly explains quantum theory and its everyday uses in our world.
Finite-block-length analysis in classical and quantum information theory.
Hayashi, Masahito
2017-01-01
Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.
Quantum Theory, Active Information and the Mind-Matter Problem
Pylkkänen, Paavo
Bohm and Hiley suggest that a certain new type of active information plays a key objective role in quantum processes. This chapter discusses the implications of this suggestion to our understanding of the relation between the mental and the physical aspects of reality.
Fisher information and quantum-classical field theory: classical statistics similarity
Energy Technology Data Exchange (ETDEWEB)
Syska, J. [Department of Field Theory and Particle Physics, Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice (Poland)
2007-07-15
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self-consistent field theory, which joins the quantum theory and classical field theory, is proposed. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
An information theory model for dissipation in open quantum systems
Rogers, David M.
2017-08-01
This work presents a general model for open quantum systems using an information game along the lines of Jaynes’ original work. It is shown how an energy based reweighting of propagators provides a novel moment generating function at each time point in the process. Derivatives of the generating function give moments of the time derivatives of observables. Aside from the mathematically helpful properties, the ansatz reproduces key physics of stochastic quantum processes. At high temperature, the average density matrix follows the Caldeira-Leggett equation. Its associated Langevin equation clearly demonstrates the emergence of dissipation and decoherence time scales, as well as an additional diffusion due to quantum confinement. A consistent interpretation of these results is that decoherence and wavefunction collapse during measurement are directly related to the degree of environmental noise, and thus occur because of subjective uncertainty of an observer.
Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information
Yamamoto, Naoki
2014-10-01
To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information
Directory of Open Access Journals (Sweden)
Naoki Yamamoto
2014-11-01
Full Text Available To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
Topics in quantum information and the theory of open quantum systems
Oreshkov, Ognyan
This thesis examines seven topics in quantum information and the theory of open quantum systems. The first one concerns weak measurements and their universality as a means of generating quantum measurements. It is shown that every generalized measurement can be decomposed into a sequence of weak measurements which allows us to think of measurements as resulting form continuous stochastic processes. The second topic concerns an application of the decomposition into weak measurements to the theory of entanglement. Necessary and sufficient differential conditions for entanglement monotones are derived, and are used to find a new entanglement monotone for three-qubit states. The third topic examines the performance of different master equations for the description of non-Markovian dynamics. The system studied is a qubit coupled to a spin bath via the Ising interaction. The fourth topic studies continuous quantum error-correction in the case of non-Markovian decoherence. It is shown that due to the existence of a Zeno regime in non-Markovian dynamics, the performance of continuous quantum error correction may exhibit a quadratic improvement if the time resolution of the error-correcting operations is sufficiently high. The fifth topic concerns conditions for correctability of subsystem codes in the case of continuous decoherence. The obtained conditions on the Lindbladian and the system-environment Hamiltonian can be thought of as generalizations of the previously known conditions for noiseless subsystems to the case where the subsystem is time-dependent. The sixth topic examines the robustness of quantum error-correcting codes against initialization errors. It is shown that operator codes are robust against imperfect initialization without the need for restriction of the standard error-correction conditions. For this purpose, a new measure of fidelity for encoded information is introduced and its properties are discussed. The last topic concerns holonomic quantum
Mouloudakis, K; Kominis, I K
2017-02-01
Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields.
Determining the continuous family of quantum Fisher information from linear-response theory
Shitara, Tomohiro; Ueda, Masahito
2016-12-01
The quantum Fisher information represents a continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of quantum Fisher information can be determined from linear-response theory through generalized covariances. We derive the generalized fluctuation-dissipation theorem that relates linear-response functions to generalized covariances and hence allows us to determine the quantum Fisher information from linear-response functions, which are experimentally measurable quantities. As an application, we examine the skew information, which is a quantum Fisher information, of a harmonic oscillator in thermal equilibrium, and show that the equality of the skew-information-based uncertainty relation holds.
Lombardi, Olimpia; Fortin, Sebastian; Holik, Federico; López, Cristian
2017-04-01
Preface; Introduction; Part I. About the Concept of Information: 1. About the concept of information Sebastian Fortin and Olimpia Lombardi; 2. Representation, information, and theories of information Armond Duwell; 3. Information, communication, and manipulability Olimpia Lombardi and Cristian López; Part II. Information and quantum mechanics: 4. Quantum versus classical information Jeffrey Bub; 5. Quantum information and locality Dennis Dieks; 6. Pragmatic information in quantum mechanics Juan Roederer; 7. Interpretations of quantum theory: a map of madness Adán Cabello; Part III. Probability, Correlations, and Information: 8. On the tension between ontology and epistemology in quantum probabilities Amit Hagar; 9. Inferential versus dynamical conceptions of physics David Wallace; 10. Classical models for quantum information Federico Holik and Gustavo Martin Bosyk; 11. On the relative character of quantum correlations Guido Bellomo and Ángel Ricardo Plastino; Index.
Generalised squeezing and information theory approach to quantum entanglement
Vourdas, A.
1993-01-01
It is shown that the usual one- and two-mode squeezing are based on reducible representations of the SU(1,1) group. Generalized squeezing is introduced with the use of different SU(1,1) rotations on each irreducible sector. Two-mode squeezing entangles the modes and information theory methods are used to study this entanglement. The entanglement of three modes is also studied with the use of the strong subadditivity property of the entropy.
Quantum Information An Introduction
Hayashi, Masahito
2006-01-01
Recently, quantum information theory has been developing through a fusion of results from various research fields. This requires that understanding of basic results on diverse topics, and derived from different disciplinary perspectives, is required for appreciating the overall picture. Intended to merge key topics from both the information-theoretic and quantum- mechanical viewpoints, this graduate-level textbook provides a unified viewpoint of quantum information theory and lucid explanations of those basic results, so that the reader fundamentally grasps advances and challenges. For example, advanced topics in quantum communication such as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction), and quantum encryption especially benefit from this unified approach. Unlike earlier treatments, the text requires knowledge of only linear algebra, probability theory, and quantum mechanics, while it treats the topics of quantum hypothesis testing and the discrimination of q...
Existence of an information unit as a postulate of quantum theory.
Masanes, Lluís; Müller, Markus P; Augusiak, Remigiusz; Pérez-García, David
2013-10-08
Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work, we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information.
Existence of an information unit as a postulate of quantum theory
Masanes, Lluís; Müller, Markus P.; Augusiak, Remigiusz; Pérez-García, David
2013-01-01
Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work, we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information. PMID:24062431
Theory of Gaussian quantum information and correlations using Renyi-2 entropy
Adesso, Gerardo; Serafini, Alessio
2012-01-01
We demonstrate that the Renyi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy.
Information carriers and (reading them through) information theory in quantum chemistry.
Geerlings, Paul; Borgoo, Alex
2011-01-21
This Perspective discusses the reduction of the electronic wave function via the second-order reduced density matrix to the electron density ρ(r), which is the key ingredient in density functional theory (DFT) as a basic carrier of information. Simplifying further, the 1-normalized density function turns out to contain essentially the same information as ρ(r) and is even of preferred use as an information carrier when discussing the periodic properties along Mendeleev's table where essentially the valence electrons are at stake. The Kullback-Leibler information deficiency turns out to be the most interesting choice to obtain information on the differences in ρ(r) or σ(r) between two systems. To put it otherwise: when looking for the construction of a functional F(AB) = F[ζ(A)(r),ζ(B)(r)] for extracting differences in information from an information carrier ζ(r) (i.e. ρ(r), σ(r)) for two systems A and B the Kullback-Leibler information measure ΔS is a particularly adequate choice. Examples are given, varying from atoms, to molecules and molecular interactions. Quantum similarity of atoms indicates that the shape function based KL information deficiency is the most appropriate tool to retrieve periodicity in the Periodic Table. The dissimilarity of enantiomers for which different information measures are presented at global and local (i.e. molecular and atomic) level leads to an extension of Mezey's holographic density theorem and shows numerical evidence that in a chiral molecule the whole molecule is pervaded by chirality. Finally Kullback-Leibler information profiles are discussed for intra- and intermolecular proton transfer reactions and a simple S(N)2 reaction indicating that the theoretical information profile can be used as a companion to the energy based Hammond postulate to discuss the early or late transition state character of a reaction. All in all this Perspective's answer is positive to the question of whether an even simpler carrier of
A short course in quantum information theory. An approach from theoretical physics. 2. ed.
Energy Technology Data Exchange (ETDEWEB)
Diosi, Lajos [KFKI Research Institute for Particle and Nuclear Physics (RMKI), Budapest (Hungary). MTA Budapest
2011-07-01
This short and concise primer takes the vantage point of theoretical physics and the unity of physics. It sets out to strip the burgeoning field of quantum information science to its basics by linking it to universal concepts in physics. An extensive lecture rather than a comprehensive textbook, this volume is based on courses delivered over several years to advanced undergraduate and beginning graduate students, but essentially it addresses anyone with a working knowledge of basic quantum physics. Readers will find these lectures a most adequate entry point for theoretical studies in this field. For the second edition, the authors has succeeded in adding many new topics while sticking to the conciseness of the overall approach. A new chapter on qubit thermodynamics has been added, while new sections and subsections have been incorporated in various chapter to deal with weak and time-continuous measurements, period-finding quantum algorithms and quantum error corrections. From the reviews of the first edition: ''The best things about this book are its brevity and clarity. In around 100 pages it provides a tutorial introduction to quantum information theory, including problems and solutions.. it's worth a look if you want to quickly get up to speed with the language and central concepts of quantum information theory, including the background classical information theory.'' (Craig Savage, Australian Physics, Vol. 44 (2), 2007). (orig.)
Gagatsos, Christos N.; Karanikas, Alexandros I.; Kordas, Georgios; Cerf, Nicolas J.
2016-02-01
In spite of their simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations on bosonic modes remain poorly understood in terms of entropy production. For instance, determining the quantum entropy generated by a Bogoliubov transformation is notably a hard problem, with generally no known analytical solution, while it is vital to the characterisation of quantum communication via bosonic channels. Here we overcome this difficulty by adapting the replica method, a tool borrowed from statistical physics and quantum field theory. We exhibit a first application of this method to continuous-variable quantum information theory, where it enables accessing entropies in an optical parametric amplifier. As an illustration, we determine the entropy generated by amplifying a binary superposition of the vacuum and a Fock state, which yields a surprisingly simple, yet unknown analytical expression.
Weighted Graph Theory Representation of Quantum Information Inspired by Lie Algebras
Belhaj, Abdelilah; Machkouri, Larbi; Sedra, Moulay Brahim; Ziti, Soumia
2016-01-01
Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a signless Laplacian matrix of an associated graph. Using similarities with root systems of simply laced Lie algebras, one-qubit theory is analyzed in some details and is found to be linked to a non-oriented weighted graph having two vertices. Moreover, this one-qubit theory is generalized to n-qubits. In this representation, quantum gates correspond to graph weight operations preserving the probability condition. A speculation from string theory, via D-brane quivers, is also given.
Controlling Quantum Information
Landahl, A J
2002-01-01
Quantum information science explores ways in which quantum physical laws can be harnessed to control the acquisition, transmission, protection, and processing of information. This field has seen explosive growth in the past several years from progress on both theoretical and experimental fronts. Essential to this endeavor are methods for controlling quantum information. In this thesis, I present three new approaches for controlling quantum information. First, I present a new protocol for continuously protecting unknown quantum states from noise. This protocol combines and expands ideas from the theories of quantum error correction and quantum feedback control. The result can outperform either approach by itself. I generalize this protocol to all known quantum stabilizer codes, and study its application to the three-qubit repetition code in detail via Monte Carlo simulations. Next, I present several new protocols for controlling quantum information that are fault-tolerant. These protocols require only local qu...
Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory
Directory of Open Access Journals (Sweden)
Federico Holik
2015-10-01
Full Text Available In this article, we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and a new family of generalized entropic measures.
Bastin, Ted
2009-07-01
List of participants; Preface; Part I. Introduction: 1. The function of the colloquium - editorial; 2. The conceptual problem of quantum theory from the experimentalist's point of view O. R. Frisch; Part II. Niels Bohr and Complementarity: The Place of the Classical Language: 3. The Copenhagen interpretation C. F. von Weizsäcker; 4. On Bohr's views concerning the quantum theory D. Bohm; Part III. The Measurement Problem: 5. Quantal observation in statistical interpretation H. J. Groenewold; 6. Macroscopic physics, quantum mechanics and quantum theory of measurement G. M. Prosperi; 7. Comment on the Daneri-Loinger-Prosperi quantum theory of measurement Jeffrey Bub; 8. The phenomenology of observation and explanation in quantum theory J. H. M. Whiteman; 9. Measurement theory and complex systems M. A. Garstens; Part IV. New Directions within Quantum Theory: What does the Quantum Theoretical Formalism Really Tell Us?: 10. On the role of hidden variables in the fundamental structure of physics D. Bohm; 11. Beyond what? Discussion: space-time order within existing quantum theory C. W. Kilmister; 12. Definability and measurability in quantum theory Yakir Aharonov and Aage Petersen; 13. The bootstrap idea and the foundations of quantum theory Geoffrey F. Chew; Part V. A Fresh Start?: 14. Angular momentum: an approach to combinatorial space-time Roger Penrose; 15. A note on discreteness, phase space and cohomology theory B. J. Hiley; 16. Cohomology of observations R. H. Atkin; 17. The origin of half-integral spin in a discrete physical space Ted Bastin; Part VI. Philosophical Papers: 18. The unity of physics C. F. von Weizsäcker; 19. A philosophical obstacle to the rise of new theories in microphysics Mario Bunge; 20. The incompleteness of quantum mechanics or the emperor's missing clothes H. R. Post; 21. How does a particle get from A to B?; Ted Bastin; 22. Informational generalization of entropy in physics Jerome Rothstein; 23. Can life explain quantum mechanics? H. H
Fortin, Sebastian; Holik, Federico; López, Cristian
2017-01-01
Combining physics and philosophy, this is a uniquely interdisciplinary examination of quantum information science which provides an up-to-date examination of developments in this field. The authors provide coherent definitions and theories of information, taking clearly defined approaches to considering information in connection with quantum mechanics, probability, and correlations. Concepts addressed include entanglement of quantum states, the relation of quantum correlations to quantum information, and the meaning of the informational approach for the foundations of quantum mechanics. Furthermore, the mathematical concept of information in the communicational context, and the notion of pragmatic information are considered. Suitable as both a discussion of the conceptual and philosophical problems of this field and a comprehensive stand-alone introduction, this book will benefit both experienced and new researchers in quantum information and the philosophy of physics.
Quantum-information approach to dynamical diffraction theory
Nsofini, J.; Ghofrani, K.; Sarenac, D.; Cory, D. G.; Pushin, D. A.
2016-12-01
We present a simplified model for dynamical diffraction of particles through a periodic thick perfect crystal based on repeated application of a coherent beam-splitting unitary at coarse-grained lattice sites. By demanding translational invariance and a computationally tractable number of sites in the coarse graining, we show how this approach reproduces many results typical of dynamical diffraction theory and experiments. This approach has the benefit of being applicable in the thick, thin, and intermediate crystal regimes. The method is applied to a three-blade neutron interferometer to predict the output beam profiles, interference patterns, and contrast variation.
Introduction to quantum information science
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Hayashi, Masahito [Nagoya Univ. (Japan). Graduate School of Mathematics; Ishizaka, Satoshi [Hiroshima Univ., Higashi-Hiroshima (Japan). Graduate School of Integrated Arts and Sciences; Kawachi, Akinori [Tokyo Institute of Technology (Japan). Dept. of Mathematical and Computing Sciences; Kimura, Gen [Shibaura Institute of Technology, Saitama (Japan). College of Systems Engineering and Science; Ogawa, Tomohiro [Univ. of Electro-Communications, Tokyo (Japan). Graduate School of Information Systems
2015-04-01
Presents the mathematical foundation for quantum information in a very didactic way. Summarizes all required mathematical knowledge in linear algebra. Supports teaching and learning with more than 100 exercises with solutions. Includes brief descriptions to recent results with references. This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. The required knowledge is only elementary calculus and linear algebra. This way the book can be understood by undergraduate students. In order to study quantum information, one usually has to study the foundation of quantum theory. This book describes it from more an operational viewpoint which is suitable for quantum information while traditional textbooks of quantum theory lack this viewpoint. The current book bases on Shor's algorithm, Grover's algorithm, Deutsch-Jozsa's algorithm as basic algorithms. To treat several topics in quantum information, this book covers several kinds of information quantities in quantum systems including von Neumann entropy. The limits of several kinds of quantum information processing are given. As important quantum protocols,this book contains quantum teleportation, quantum dense coding, quantum data compression. In particular conversion theory of entanglement via local operation and classical communication are treated too. This theory provides the quantification of entanglement, which coincides with von Neumann entropy. The next part treats the quantum hypothesis testing. The decision problem of two candidates of the unknown state are given. The asymptotic performance of this problem is characterized by information quantities. Using this result, the optimal performance of classical information transmission via noisy quantum channel is derived. Quantum information transmission via noisy quantum channel by quantum error
On the Role of Information Theoretic Uncertainty Relations in Quantum Theory
Jizba, Petr; Dunningham, Jacob A.; Joo, Jaewoo
2014-01-01
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\\'{e}nyi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson-Schr\\"{o}ding...
Getting Beyond the State of the Art of Information Retrieval with Quantum Theory
Melucci, Massimo
2011-01-01
According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key point of this principle is the separation of the document set into two subsets with a given level of fallout and with the highest recall. If subsets of set measures are replaced by subspaces and space measures, we obtain an alternative theory stemming from Quantum Theory. That theory is named after vector probability because vectors represent event like sets do in classical probability. The paper shows that the separation into vector subspaces is more effective than the separation into subsets with the same available evidence. The result is proved mathematically and verified experimentally. In general, the paper suggests that quantum theory is not only a source of rhetoric inspiration, but is a sufficient condition to improve retrieval effectiveness in a principled way.
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Erol, V. [Department of Computer Engineering, Institute of Science, Okan University, Istanbul (Turkey); Netas Telecommunication Inc., Istanbul (Turkey)
2016-04-21
Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC) transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.
Erol, V.
2016-04-01
Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC) transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.
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Benatti, Fabio [Trieste Univ., Miramare (Italy). Dipt. Fisica Teorica; Fannes, Mark [Leuven Univ. (Belgium). Inst. voor Theoretische Fysica; Floreanini, Roberto [INFN, Trieste (Italy). Dipt. di Fisica Teorica; Petritis, Dimitri (eds.) [Rennes 1 Univ., 35 (France). Inst. de Recherche Mathematique de Rennes
2010-07-01
This multi-authored textbook addresses graduate students with a background in physics, mathematics or computer science. No research experience is necessary. Consequently, rather than comprehensively reviewing the vast body of knowledge and literature gathered in the past twenty years, this book concentrates on a number of carefully selected aspects of quantum information theory and technology. Given the highly interdisciplinary nature of the subject, the multi-authored approach brings together different points of view from various renowned experts, providing a coherent picture of the subject matter. The book consists of ten chapters and includes examples, problems, and exercises. The first five present the mathematical tools required for a full comprehension of various aspects of quantum mechanics, classical information, and coding theory. Chapter 6 deals with the manipulation and transmission of information in the quantum realm. Chapters 7 and 8 discuss experimental implementations of quantum information ideas using photons and atoms. Finally, chapters 9 and 10 address ground-breaking applications in cryptography and computation. (orig.)
Griffiths, Robert B.
2007-01-01
Quantum, in contrast to classical, information theory, allows for different incompatible types (or species) of information which cannot be combined with each other. Distinguishing these incompatible types is useful in understanding the role of the two classical bits in teleportation (or one bit in one-bit teleportation), for discussing decoherence in information-theoretic terms, and for giving a proper definition, in quantum terms, of ``classical information.'' Various examples (some updating...
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D' Ariano, Giacomo Mauro (University of Pavia)
2010-10-20
The experience from Quantum Information of the last twenty years has lead theorists to look at Quantum Theory and the whole of Physics from a different angle. A new information-theoretic paradigm is emerging, long time ago prophesied by John Archibald Wheeler with his popular coinage 'It from bit'. Theoretical groups are now addressing the problem of deriving Quantum Theory from informational principles, and similar lines are investigated in new approaches to Quantum Gravity. In my talk I will review some recent advances on these lines. The general idea synthesizing the new paradigm is that there is only Quantum Theory (without quantization rules): the whole Physics--including space-time and relativity--is emergent from quantum-information processing. And, since Quantum Theory itself is made with purely informational principles, the whole Physics must be reformulated in information-theoretical terms. The review is divided into the following parts: (a) The informational axiomatization of Quantum Theory; (b) How space-time and relativistic covariance emerge from the quantum computation; (c) What is the information-theoretical meaning of inertial mass and Planck constant, and how the quantum field emerges; (d) Observational consequences: mass-dependent refraction index of vacuum. I then conclude with some possible future research lines.
Raedt, Hans De; Binder, K; Ciccotti, G
1996-01-01
The purpose of this set of lectures is to introduce the general concepts that are at the basis of the computer simulation algorithms that are used to study the behavior of condensed matter quantum systems. The emphasis is on the underlying concepts rather than on specific applications. Topics treate
Quantum-Holographic Informational Consciousness
National Research Council Canada - National Science Library
Francisco Di Biase
2009-01-01
The author propose a quantum-informational holographic model of brain-consciousness-universe interactions based in the holonomic neural networks of Karl Pribram, in the holographic quantum theory...
Hoehn, Philipp A
2016-01-01
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S's state as O's `catalogue of knowledge' about S; no ontic assumptions are necessary. From the rules we derive the state spaces for N qubits and show that (a) they coincide with the set of density matrices over N qubit Hilbert spaces; (b) states evolve unitarily under the group $\\rm{PSU}(2^N)$ according to the von Neumann evolution equation; and (c) the binary questions by means of which O interrogates the systems corresponds to projective measurements on Pauli operators with outcome probabilities given by the Born rule. Besides offering a novel conceptual perspective on qubit quantum theory, the reconstruction also unravels new structural insights. Namely, we show that, in a quadratic information measure, (d) qubits satisfy informational complementarity inequalities...
Relativistic quantum information
Mann, R. B.; Ralph, T. C.
2012-11-01
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from
Banks, Tom
2008-09-01
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
Bates, David Robert
1962-01-01
Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear combinations, collisions, and transitions. The selection first elaborates on the fundamental principles of quantum mechanics, exactly soluble bound state problems, and continuum. Discussions focus on delta function normalization, spherically symmetric potentials, rectangular potential wells, harmonic oscillators, spherically symmetrical potentials, Coulomb potential, axiomatic basis, consequences of first three postula
Quantum information processing in nanostructures Quantum optics; Quantum computing
Reina-Estupinan, J H
2002-01-01
Since information has been regarded os a physical entity, the field of quantum information theory has blossomed. This brings novel applications, such as quantum computation. This field has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineering, to the physical sciences. Thus, we now have an interdisciplinary field where great efforts are being made in order to build devices that should allow for the processing of information at a quantum level, and also in the understanding of the complex structure of some physical processes at a more basic level. This thesis is devoted to the theoretical study of structures at the nanometer-scale, 'nanostructures', through physical processes that mainly involve the solid-state and quantum optics, in order to propose reliable schemes for the processing of quantum information. Initially, the main results of quantum information theory and quantum computation are briefly reviewed. Next, the state-of-the-art of ...
Quantum electronics basic theory
Fain, V M; Sanders, J H
1969-01-01
Quantum Electronics, Volume 1: Basic Theory is a condensed and generalized description of the many research and rapid progress done on the subject. It is translated from the Russian language. The volume describes the basic theory of quantum electronics, and shows how the concepts and equations followed in quantum electronics arise from the basic principles of theoretical physics. The book then briefly discusses the interaction of an electromagnetic field with matter. The text also covers the quantum theory of relaxation process when a quantum system approaches an equilibrium state, and explai
Unambiguous state discrimination of two density matrices in quantum information theory
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Raynal, P.
2008-07-01
Quantum state discrimination is a fundamental task in quantum information theory. The signals are usually nonorthogonal quantum states, which implies that they can not be perfectly distinguished. One possible discrimination strategy is the so-called Unambiguous State Discrimination (USD) where the states are successfully identified with non-unit probability, but without error. The optimal USD measurement has been extensively studied in the case of pure states, especially for any pair of pure states. Recently, the problem of unambiguously discriminating mixed quantum states has attracted much attention. In the case of a pair of generic mixed states, no complete solution is known. In this thesis, we first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank r in a 2r-dimensional Hilbert space. These reduction theorems also allow us to reduce USD problems to simpler ones for which the solution might be known. As an application, we consider the unambiguous comparison of n linearly independent pure states with a simple symmetry. Moreover, lower bounds on the optimal failure probability have been derived. For two mixed states they are given in terms of the fidelity. Here we give tighter bounds as well as necessary and sufficient conditions for two mixed states to reach these bounds. We also construct the corresponding optimal measurement. With this result, we provide analytical solutions for unambiguously discriminating a class of generic mixed states. This goes beyond known results which are all reducible to some pure state case. We however show that examples exist where the bounds cannot be reached. Next, we derive properties on the rank and the spectrum of an optimal USD measurement. This finally leads to a second class of exact solutions. Indeed we present the optimal failure probability as well as the optimal measurement for
Quantum information does not exist
Duwell, Armond
Some physicists seem to believe that quantum information theory requires a new concept of information (Jozsa, 1998, Quantum information and its properties. In: Hoi-Kwong Lo, S. Popescu, T. Spiller (Eds.), Introduction to Quantum Computation and Information, World Scientific, Singapore, (pp. 49-75); Deutsch & Hayden, 1999, Information flow in entangled quantum subsystems, preprint quant-ph/9906007). I will argue that no new concept is necessary. Shannon's concept of information is sufficient for quantum information theory. Properties that are cited to contrast quantum information and classical information (i.e., Shannon information) actually point to differences in our ability to manipulate, access, and transfer information depending on whether quantum systems, opposed to classical systems, are used in a communication system. I also demonstrate that conceptually puzzling phenomena in quantum information theory, such as dense coding, teleportation, and Schumacher coding, all of which are cited as evidence that a new concept of information is required, do not have to be regarded as such.
Quantum information and physics: Some future directions
Preskill, John
2000-01-01
I consider some promising future directions for quantum information theory that could influence the development of 21st century physics. Advances in the theory of the distinguishability of superoperators may lead to new strategies for improving the precision of quantum-limited measurements. A better grasp of the properties of multi-partite quantum entanglement may lead to deeper understanding of strongly-coupled dynamics in quantum many-body systems, quantum field theory, and quantum gravity.
Olendski, O.
2016-12-01
Information-theoretical concepts are employed for the analysis of the interplay between a transverse electric field $\\mathscr{E}$ applied to a one-dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length $\\Lambda$ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schr\\"{o}dinger equation are derived and used for calculating energies, dipole moments, position $S_x$ and momentum $S_k$ quantum information entropies and their Fisher information $I_x$ and $I_k$ and Onicescu information energies $O_x$ and $O_k$ counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, $\\Lambda=0$ (Neumann, $\\Lambda=\\infty$), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum-information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field-independent sum $S_x+S_k$. Analogously, at $\\Lambda=0$ and $\\Lambda=\\infty$ the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as $\\mathscr{E}^{2/3}$ ($\\mathscr{E}^{1/3}$) and its inverse, respectively, leading to the field-independent product $I_xI_k$ ($O_xO_k$). Peculiarities of their transformations at the finite nonzero $\\Lambda$ are discussed and similarities and differences between the three quantum-information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.
Lorentz covariant reduced-density-operator theory for relativistic quantum information processing
Ahn, D; Hwang, S W; Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo
2003-01-01
In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. The formulation presented in this work is general and might be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.
Unified meta-theory of information, consciousness, time and the classical-quantum universe
Green, Martin A
2013-01-01
As time advances in our perceived real world, existing information is preserved and new information is added to history. All the information that may ever be encoded in history must be about some fundamental, unique, atemporal and pre-physical structure: the bare world. Scientists invent model worlds to efficiently explain aspects of the real world. This paper explores the features of and relationships between the bare, real, and model worlds. Time -- past, present and future -- is naturally explained. Both quantum uncertainty and state reduction are needed for time to progress, since unpredictable new information must be added to history. Deterministic evolution preserves existing information. Finite, but steadily increasing, information about the bare world is jointly encoded in equally uncertain spacetime geometry and quantum matter. Because geometry holds no information independent of matter, there is no need to quantize gravity. At the origin of time, information goes to zero and geometry and matter fade...
Lectures on quantum field theory
Das, Ashok
2008-01-01
This book consists of the lectures for a two-semester course on quantum field theory, and as such is presented in a quite informal and personal manner. The course starts with relativistic one-particle systems, and develops the basics of quantum field theory with an analysis of the representations of the Poincaré group. Canonical quantization is carried out for scalar, fermion, Abelian and non-Abelian gauge theories. Covariant quantization of gauge theories is also carried out with a detailed description of the BRST symmetry. The Higgs phenomenon and the standard model of electroweak interactio
Catalytic Decoupling of Quantum Information
DEFF Research Database (Denmark)
Majenz, Christian; Berta, Mario; Dupuis, Frédéric
2017-01-01
of an uncorrelated ancilla system. This removes a restriction on the standard notion of decoupling, which becomes important for structureless resources, and yields a tight characterization in terms of the max-mutual information. Catalytic decoupling naturally unifies various tasks like the erasure of correlations......The decoupling technique is a fundamental tool in quantum information theory with applications ranging from quantum thermodynamics to quantum many body physics to the study of black hole radiation. In this work we introduce the notion of catalytic decoupling, that is, decoupling in the presence...... and quantum state merging, and leads to a resource theory of decoupling....
Pitalúa-García, Damián
2012-01-01
How much information can a transmitted physical system fundamentally communicate? We introduce the principle of quantum information causality, which states the maximum amount of quantum information that a quantum system can communicate as a function of its dimension, independently of any previously shared quantum physical resources. We present a new quantum information task, whose success probability is upper bounded by the new principle, and show that an optimal strategy to perform it combin...
Negative entropy and information in quantum mechanics
Cerf, N. J.; Adami, C.
1995-01-01
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum non-separability. The possibility that negative (virtual) information can be carried by entangled particles sug...
Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?
Directory of Open Access Journals (Sweden)
William K. Wootters
2013-08-01
Full Text Available A quantum measurement can be regarded as a communication channel, in which the parameters of the state are expressed only in the probabilities of the outcomes of the measurement. We begin this paper by considering, in a non-quantum-mechanical setting, the problem of communicating through probabilities. For example, a sender, Alice, wants to convey to a receiver, Bob, the value of a continuous variable, θ, but her only means of conveying this value is by sending Bob a coin in which the value of θ is encoded in the probability of heads. We ask what the optimal encoding is when Bob will be allowed to flip the coin only a finite number of times. As the number of tosses goes to infinity, we find that the optimal encoding is the same as what nature would do if we lived in a world governed by real-vector-space quantum theory. We then ask whether the problem might be modified, so that the optimal communication strategy would be consistent with standard, complex-vector-space quantum theory.
Zeh, H D
1999-01-01
This is a brief reply to Goldstein's article on ``Quantum Theory Without Observers'' in Physics Today. It is pointed out that Bohm's quantum mechanics is successful only because it keeps Schrödinger's (exact) wave mechanics unchanged, while the rest of it is observationally meaningless and solely based on classical prejudice.
Resource Letter QI-1: Quantum Information
Strauch, Frederick W.
2016-07-01
This Resource Letter surveys the history and modern developments in the field of quantum information. It is written to guide advanced undergraduates, beginning graduate students, and other new researchers to the theoretical and experimental aspects of this field. The topics covered include quantum states and processes, quantum coding and cryptography, quantum computation, the experimental implementation of quantum information processing, and the role of quantum information in the fundamental properties and foundations of physical theories.
Mandl, Franz
2010-01-01
Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics. The three main objectives of the book are to: Explain the basic physics and formalism of quantum field theory To make the reader proficient in theory calculations using Feynman diagrams To introduce the reader to gauge theories, which play a central role in elementary particle physic
A short course in quantum information theory. An approach from theoretical physics
Energy Technology Data Exchange (ETDEWEB)
Diosi, L. [KFKI Research Institute for Partical and Nuclear Physics, Budapest (Hungary)
2007-07-01
This short and concise primer takes the vantage point of theoretical physics and the unity of physics. It sets out to strip the burgeoning field of quantum information science to its basics by linking it to universal concepts in physics. An extensive lecture rather than a comprehensive textbook, this volume is based on courses delivered over several years to advanced undergraduate and beginning graduate students, but essentially it addresses anyone with a working knowledge of basic quantum physics. Readers will find these lectures a most adequate entry point for theoretical studies in this field. (orig.)
Wentzel, Gregor
2003-01-01
A prominent figure in twentieth-century physics, Gregor Wentzel made major contributions to the development of quantum field theory, first in Europe and later at the University of Chicago. His Quantum Theory of Fields offers a knowledgeable view of the original literature of elementary quantum mechanics and helps make these works accessible to interested readers.An introductory volume rather than an all-inclusive account, the text opens with an examination of general principles, without specification of the field equations of the Lagrange function. The following chapters deal with particular
Bonitz, Michael
2016-01-01
This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.
Quantum information and convex optimization
Energy Technology Data Exchange (ETDEWEB)
Reimpell, Michael
2008-07-01
This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Holevo, A S [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation)
2006-04-30
The additivity problem is one of the most profound mathematical problems of quantum information theory. From an analytical point of view it is closely related to the multiplicative property, with respect to tensor products, of norms of maps on operator spaces equipped with the Schatten norms (non-commutative analogue of l{sub p}-norms). In this paper we survey the current state of the problem.
Quantum Cosmology: Effective Theory
Bojowald, Martin
2012-01-01
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge of specific properties of quantum states, it remained difficult to make testable predictions. For quantum cosmology to be part of empirical science, it must allow for a systematic framework in which corrections to well-tested classical equations can be derived, with any ambiguities and ignorance sufficiently parameterized. As in particle and condensed-matter physics, a successful viewpoint is one of effective theories, adapted to specific issues one encounters in quantum cosmology. This review presents such an effective framework of quantum cosmology, taking into account, among other things, space-time structures, covariance, the problem of time and the anomaly issue.
Quantum information causality.
Pitalúa-García, Damián
2013-05-24
How much information can a transmitted physical system fundamentally communicate? We introduce the principle of quantum information causality, which states the maximum amount of quantum information that a quantum system can communicate as a function of its dimension, independently of any previously shared quantum physical resources. We present a new quantum information task, whose success probability is upper bounded by the new principle, and show that an optimal strategy to perform it combines the quantum teleportation and superdense coding protocols with a task that has classical inputs.
Energy Technology Data Exchange (ETDEWEB)
Sadovskii, Michael V.
2013-06-01
This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The work illustrates the unity of modern theoretical physics by combining approaches and concepts of the quantum field theory and modern condensed matter theory. The inductive approach allows a deep understanding of ideas and methods used for solving problems in this field.
Zeh, H. D.
1998-01-01
This is a brief reply to Goldstein's article on ``Quantum Theory Without Observers'' in Physics Today. It is pointed out that Bohm's pilot wave theory is successful only because it keeps Schr\\"odinger's (exact) wave mechanics unchanged, while the rest of it is observationally meaningless and solely based on classical prejudice.
Zeh, H. D.
1999-04-01
This is a brief reply to S. Goldstein's article "Quantum theory without observers" in Physics Today. It is pointed out that Bohm's pilot wave theory is successful only because it keeps Schrödinger's (exact) wave mechanics unchanged, while the rest of it is observationally meaningless and solely based on classical prejudice.
Quantum information: primitive notions and quantum correlations
Scarani, Valerio
2009-01-01
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the field, like cloning, teleportation, state estimation...). The second part is devoted to a detailed introduction to the topic of quantum correlations, covering the evidence for failure of alternative theories, some aspects of the formalism of no-signaling probability distributions and some hints towards some current research topics in the field.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Friedberg, R; Hohenberg, P C
2014-09-01
Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call 'compatible quantum theory (CQT)', consists of a 'microscopic' part (MIQM), which applies to a closed quantum system of any size, and a 'macroscopic' part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths ('c-truths'), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory
Friedberg, R.; Hohenberg, P. C.
2014-09-01
Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call ‘compatible quantum theory (CQT)’, consists of a ‘microscopic’ part (MIQM), which applies to a closed quantum system of any size, and a ‘macroscopic’ part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths (‘c-truths’), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The
Reformulating and Reconstructing Quantum Theory
Hardy, Lucien
2011-01-01
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following: [Axiom 1] Operations correspond to operators. [Axiom 2] Every complete set of positive operators corresponds to a complete set of operations. The following operational postulates are shown to be equivalent to these mathematical axioms: [P1] Definiteness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state. [P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components. [P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components. [P4] Compound permutatability. There exis...
Quantum information and coherence
Öhberg, Patrik
2014-01-01
This book offers an introduction to ten key topics in quantum information science and quantum coherent phenomena, aimed at graduate-student level. The chapters cover some of the most recent developments in this dynamic research field where theoretical and experimental physics, combined with computer science, provide a fascinating arena for groundbreaking new concepts in information processing. The book addresses both the theoretical and experimental aspects of the subject, and clearly demonstrates how progress in experimental techniques has stimulated a great deal of theoretical effort and vice versa. Experiments are shifting from simply preparing and measuring quantum states to controlling and manipulating them, and the book outlines how the first real applications, notably quantum key distribution for secure communication, are starting to emerge. The chapters cover quantum retrodiction, ultracold quantum gases in optical lattices, optomechanics, quantum algorithms, quantum key distribution, quantum cont...
Are Quantum Theory Questions Epistemic?
Directory of Open Access Journals (Sweden)
Viviana Yaccuzzi Polisena
2013-12-01
Full Text Available How to displace-move quantum theory [Ǭ] questions-problems to philosophy? Seeing the collapse of our society’s cultural-intellectual-morals, the philosophy of the 21st century has to contribute to the formation of new principles-formalisms: the big task of the contemporary philosophy ©] is to innovate, to transform the building of the knowledge! Which is the role of the contemporary philosopher? (Noam Chomsky. Building science so that it is more human, out of the scientific mercantilism so that it does not continue transgressing that which is most precious: the thought-life. The ideas that I propose demand a deep cultural-epistemiologicscientific-philosophical-ethical rethinking that goes from quantum entities up to life in society. The starting idea is «the quantum [Ǭ], the paradigm of the contemporary science ©]» (Bernard D’Espagnat. I propose to displace-move questions of the quantum theory [Ǭ]: spin, measure, layering to the field of philosophy (φ to build generic symbols. Can the contemporary episteme model the collapse of the ? For a philosopher, can understanding the importance and the behaviour of the spin bring something new to philosophy ? Can information of the states of the spin be used to observe in a holographic way the pattern energy-information contained in the quantum entities? Is quantum [Ǭ] physics mechanical?
Quantum Information in Space and Time
Volovich, I V
2001-01-01
Many important results in modern quantum information theory have been obtained for an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime. Therefore such basic notions in quantum information theory as the notions of composite systems, entangled states and the channel should be formulated in space and time. We emphasize the importance of the investigation of quantum information in space and time. Entangled states in space and time are considered. A modification of Bell`s equation which includes the spacetime variables is suggested. A general relation between quantum theory and theory of classical stochastic processes is proposed. It expresses the condition of local realism in the form of a {\\it noncommutative spectral theorem}. Applications of this relation to the security of quantum key distribution in quantum cryptography are considered.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
Energy Technology Data Exchange (ETDEWEB)
Aastrup, Johannes; Moeller Grimstrup, Jesper
2016-10-15
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeo-morphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi-classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost-commutative algebra emerges from the holonomy-diffeomorphism algebra in the same limit. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Experimental quantum field theory
Bell, J S
1977-01-01
Presented here, is, in the opinion of the author, the essential minimum of quantum field theory that should be known to cultivated experimental particle physicists. The word experimental describes not only the audience aimed at but also the level of mathematical rigour aspired to. (0 refs).
Gupta, Ved Prakash; Sunder, V S
2015-01-01
This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator space...
Catalytic Decoupling of Quantum Information
DEFF Research Database (Denmark)
Majenz, Christian; Berta, Mario; Dupuis, Frédéric
2017-01-01
of an uncorrelated ancilla system. This removes a restriction on the standard notion of decoupling, which becomes important for structureless resources, and yields a tight characterization in terms of the max-mutual information. Catalytic decoupling naturally unifies various tasks like the erasure of correlations......The decoupling technique is a fundamental tool in quantum information theory with applications ranging from quantum thermodynamics to quantum many body physics to the study of black hole radiation. In this work we introduce the notion of catalytic decoupling, that is, decoupling in the presence...
Zeidler, Eberhard
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction). From the reviews: "… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from othe...
Von Weizsäcker, Carl Friedrich
1988-01-01
1- presentation of quantum theory in present-day physics. 2- a flash-back on the history : from Planck to Copenhagen. 3- the Copenhagen interpretation. 4- reconstrucction of Abstract Quantum Theory. 5- recent interpretations. 6- the philosophy of the mind. 7- concrete quantum theory. 8- the non-locality. This second tape contains the debate following the talk of the professor.
Ion trapping for quantum information processing
Institute of Scientific and Technical Information of China (English)
WAN Jin-yin; WANG Yu-zhu; LIU Liang
2007-01-01
In this paper we have reviewed the recent pro-gresses on the ion trapping for quantum information process-ing and quantum computation. We have first discussed the basic principle of quantum information theory and then fo-cused on ion trapping for quantum information processing.Many variations, especially the techniques of ion chips, have been investigated since the original ion trap quantum compu-tation scheme was proposed. Full two-dimensional control of multiple ions on an ion chip is promising for the realization of scalable ion trap quantum computation and the implemen-tation of quantum networks.
Quantum cellular automata and free quantum field theory
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-02-01
In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.
Energy Technology Data Exchange (ETDEWEB)
Green, H.S. [Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, SA (Australia)
1998-12-31
It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles. Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation. From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry. The algebraic method is extended to obtain solutions of Einstein`s gravitational field equations for empty space, with a cosmological term. General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein`s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) SO(4; 2). There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation. Copyright (1998) CSIRO Australia 33 refs.
Quantum States as Ordinary Information
Directory of Open Access Journals (Sweden)
Ken Wharton
2014-03-01
Full Text Available Despite various parallels between quantum states and ordinary information, quantum no-go-theorems have convinced many that there is no realistic framework that might underly quantum theory, no reality that quantum states can represent knowledge about. This paper develops the case that there is a plausible underlying reality: one actual spacetime-based history, although with behavior that appears strange when analyzed dynamically (one time-slice at a time. By using a simple model with no dynamical laws, it becomes evident that this behavior is actually quite natural when analyzed “all-at-once” (as in classical action principles. From this perspective, traditional quantum states would represent incomplete information about possible spacetime histories, conditional on the future measurement geometry. Without dynamical laws imposing additional restrictions, those histories can have a classical probability distribution, where exactly one history can be said to represent an underlying reality.
The operational meaning of quantum conditional information
Devetak, I; Devetak, Igor; Yard, Jon
2006-01-01
With a statistical view towards information and noise, information theory derives ultimate limitations on information processing tasks. These limits are generally expressed in terms of entropic measures of information and correlations. Here we answer the quantum information-theoretic question: ``How correlated are two quantum systems from the perspective of a third?" by solving the following `quantum state redistribution' problem. Given an arbitrary quantum state of three systems, where Alice holds two and Bob holds one, what is the cost, in terms of quantum communication and entanglement, for Alice to give one of her parts to Bob? The communication cost gives the first operational interpretation to quantum conditional mutual information. The optimal procedure is self-dual under time reversal and is perfectly composable. This generalizes known protocols such as the state merging and fully quantum Slepian-Wolf protocols, from which almost every known protocol in quantum Shannon theory can be derived.
Information Processing Structure of Quantum Gravity
Gyongyosi, Laszlo; Imre, Sandor
2014-05-01
The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework. Quantum gravity provides both the non-fixed causality of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity scenario, the causal structure is indefinite and the processes are causally non-separable. We provide a model for the information processing structure of quantum gravity. We show that the quantum gravity environment is an information resource-pool from which valuable information can be extracted. We analyze the structure of the quantum gravity space and the entanglement of the space-time geometry. We study the information transfer capabilities of quantum gravity space and define the quantum gravity channel. We characterize the information transfer of the gravity space and the correlation measure functions of the gravity channel. We investigate the process of stimulated storage for quantum gravity memories, a phenomenon that exploits the information resource-pool property of quantum gravity. The results confirm that the benefits of the quantum gravity space can be exploited in quantum computations, particularly in the development of quantum computers. The results are supported by the grant COST Action MP1006.
Hybrid quantum information processing
Energy Technology Data Exchange (ETDEWEB)
Furusawa, Akira [Department of Applied Physics, School of Engineering, The University of Tokyo (Japan)
2014-12-04
I will briefly explain the definition and advantage of hybrid quantum information processing, which is hybridization of qubit and continuous-variable technologies. The final goal would be realization of universal gate sets both for qubit and continuous-variable quantum information processing with the hybrid technologies. For that purpose, qubit teleportation with a continuousvariable teleporter is one of the most important ingredients.
Aastrup, Johannes
2015-01-01
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the...
Quantum information and general relativity
Peres, A
2004-01-01
The Einstein-Podolsky-Rosen paradox (1935) is reexamined in the light of Shannon's information theory (1948). The EPR argument did not take into account that the observers' information was localized, like any other physical object. General relativity introduces new problems: there are horizons which act as one-way membranes for the propagation of quantum information, in particular black holes which act like sinks.
Gurau, R; Rivasseau, V
2008-01-01
We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and Bosonic theories. It is compatible with the renormalization group, and it allows to define non-perturbatively {\\it differential} renormalization group equations. It accommodates any general stable polynomial Lagrangian. It can equally well treat noncommutative models or matrix models such as the Grosse-Wulkenhaar model. Perhaps most importantly it removes the space-time background from its central place in QFT, paving the way for a nonperturbative definition of field theory in noninteger dimension.
Quantum mechanics theory and experiment
Beck, Mark
2012-01-01
This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...
Gripaios, Ben
2014-01-01
The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is `freer', in the sense that the non-interacting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree- and loop-level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behaviour is radically different to both classical fluids and quantum fields, with interesting physical consequences for fluids in the low temperature regime.
Constructor theory of information.
Deutsch, David; Marletto, Chiara
2015-02-08
We propose a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible-i.e. in constructor-theoretic terms. It includes conjectured, exact laws of physics expressing the regularities that allow information to be physically instantiated. Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. This theory solves a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other. It also explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and locally inaccessible information (as in entangled systems).
Information transfer through quantum channels
Energy Technology Data Exchange (ETDEWEB)
Kretschmann, D.
2007-03-12
This PhD thesis represents work done between Aug. 2003 and Dec. 2006 in Reinhard F. Werner's quantum information theory group at Technische Universitaet Braunschweig, and Artur Ekert's Centre for Quantum Computation at the University of Cambridge. My thesis falls into the field of abstract quantum information theory. This work investigates both fundamental properties of quantum channels and their asymptotic capacities for classical as well as quantum information transfer. Stinespring's theorem is the basic structure theorem for quantum channels. It implies that every quantum channel can be represented as a unitary evolution on an enlarged system. In Ch. 3 we present a continuity theorem for Stinespring's representation: two quantum channels are similar if and only if it is possible to find unitary implementations that are likewise similar, with dimension-independent norm bounds. The continuity theorem allows to derive a formulation of the information-disturbance tradeoff in terms of quantum channels, and a continuity estimate for the no-broadcasting principle. In Ch. 4 we then apply the continuity theorem to give a strengthened no-go proof for quantum bit commitment, an important cryptographic primitive. This result also provides a natural characterization of those protocols that fall outside the standard setting of unconditional security, and thus may allow secure bit commitment. We present a new such protocol whose security relies on decoherence in the receiver's lab. Ch. 5 reviews the capacities of quantum channels for the transfer of both classical and quantum information, and investigates several variations in the notion of channel capacity. Memory effects are then investigated in detail in Ch. 6. We advertise a model which is sufficiently general to encompass all causal automata: every quantum process in which the outputs up to any given time t do not depend on the inputs at times t'>t can be represented as a concatenated memory
Theory of interacting quantum fields
Rebenko, Alexei L
2012-01-01
This monograph is devoted to the systematic and encyclopedic presentation of the foundations of quantum field theory. It represents mathematical problems of the quantum field theory with regardto the new methods of the constructive and Euclidean field theory formed for the last thirty years of the 20th century on the basis of rigorous mathematical tools of the functional analysis, the theory of operators, and the theory of generalized functions. The book is useful for young scientists who desire to understand not only the formal structure of the quantum field theory but also its basic concepts and connection with classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of functional integration.
Lombardi, Olimpia; Holik, Federico; Vanni, Leonardo
2016-11-01
In the present article we address the question 'What is quantum information?' from a conceptual viewpoint. In particular, we argue that there seems to be no sufficiently good reasons to accept that quantum information is qualitatively different from classical information. The view that, in the communicational context, there is only one kind of information, physically neutral, which can be encoded by means of classical or quantum states has, in turn, interesting conceptual advantages. First, it dissolves the widely discussed puzzles of teleportation without the need to assume a particular interpretation of information. Second, and from a more general viewpoint, it frees the attempts to reconstruct quantum mechanics on the basis of informational constraints from any risk of circularity; furthermore, it endows them with a strong conceptual appealing and, derivatively, opens the way to the possibility of a non-reductive unification of physics. Finally, in the light of the idea of the physical neutrality of information, the wide field of research about classical models for quantum information acquires a particular conceptual and philosophical interest.
Free Quantum Field Theory from Quantum Cellular Automata
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Quantum theory - essential from cosmos to consciousness
Energy Technology Data Exchange (ETDEWEB)
Goernitz, T, E-mail: goernitz@em.uni-frankfurt.d [Institut fuer Didaktik der Physik, FB Physik J. W. Goethe-Universitaet Frankfurt/Main Mail: Karl-Mangold-Str. 13, D-81245 Muenchen (Germany)
2010-06-01
Quantum theory is the most successful physical theory. About one third of the gross national product in the developed countries results from its applications. But very often quantum theory is still declared as 'crazy' or 'not understandable'. However, quantum theory has a clear mathematical structure that expresses well-known experiences from every day life: A whole is often more than the sum of its parts, and not only the facts also the possibilities can act. If such structures become important then the consequences differ from the models of classical physics which rests on the fundamental differences between matter and motion, material and force, localization and extension, fullness and emptiness. From quantum theory one can learn that all these differences are useful in many cases but are not fundamental. There are equivalences between them, and these can be extended even to the equivalence between matter, energy and abstract quantum information. It is cosmological funded and is denominated as 'Protyposis' to avoid the connotation of information and meaning. Protyposis enables a fundamentally new understanding of matter which can be seen as 'formed', 'condensed' or 'designed' abstract quantum information. One result of the Protyposis is a derivation of Einstein's equations from the abstract quantum information. Another consequence is the ontological reality of the mind and its connection to a brain which can be explained without any dualistic model.
Quantum paradoxes quantum theory for the perplexed
Aharonov, Yakir
2005-01-01
A Guide through the Mysteries of Quantum Physics!Yakir Aharonov is one of the pioneers in measuring theory, the nature of quantum correlations, superselection rules, and geometric phases and has been awarded numerous scientific honors. The author has contributed monumental concepts to theoretical physics, especially the Aharonov-Bohm effect and the Aharonov-Casher effect. Together with Daniel Rohrlich of the Weizmann Institute, Israel, he has written a pioneering work on the remaining mysteries of quantum mechanics. From the perspective of a preeminent researcher in the fundamental aspects of quantum mechanics, the text combines mathematical rigor with penetrating and concise language
Information, disturbance and Hamiltonian quantum feedback control
Doherty, A C; Jungman, G; Doherty, Andrew C.; Jacobs, Kurt; Jungman, Gerard
2001-01-01
We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the minimal constraint that the available strength of both is limited. This motivates concepts of information extraction and disturbance which are distinct from those usually considered in quantum information theory. Using these concepts we identify an information trade-off in quantum feedback control.
Introduction to quantum physics and information processing
Vathsan, Radhika
2016-01-01
An Elementary Guide to the State of the Art in the Quantum Information FieldIntroduction to Quantum Physics and Information Processing guides beginners in understanding the current state of research in the novel, interdisciplinary area of quantum information. Suitable for undergraduate and beginning graduate students in physics, mathematics, or engineering, the book goes deep into issues of quantum theory without raising the technical level too much.The text begins with the basics of quantum mechanics required to understand how two-level systems are used as qubits. It goes on to show how quant
Information Processing Structure of Quantum Gravity
Gyongyosi, Laszlo
2014-01-01
The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework. The space of quantum gravity provides both the non-fixed causality of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity scenario, the causal structure is indefinite and the processes are causally non-separable. In this work, we provide a model for the information processing structure of quantum gravity. We show that the quantum gravity environment is an information resource-pool from which valuable information can be extracted. We analyze the structure of the quantum gravity space and the entanglement of the space-time geometry. We study the information transfer capabilities of quantum gravity space and define the quantum gravity channel. We reveal that the quantum gravity space acts as a background noise on the local environment states. We characterize the properties of the noise of the quantum gravity space and show that it allows the separate local...
Illustrating the concept of quantum information
Jozsa, R
2003-01-01
Over the past decade quantum information theory has developed into a vigorous field of research despite the fact that quantum information, as a precise concept, is undefined. Indeed the very idea of viewing quantum states as carriers of some kind of information (albeit unknowable in classical terms), leads naturally to interesting questions that might otherwise never have been asked, and corresponding new insights. We will discuss some illustrative examples, including a strengthening of the well known no-cloning theorem leading to a property of permanence for quantum information, and considerations arising from information compression that reflect on fundamental issues.
Bayesian Intersubjectivity and Quantum Theory
Pérez-Suárez, Marcos; Santos, David J.
2005-02-01
Two of the major approaches to probability, namely, frequentism and (subjectivistic) Bayesian theory, are discussed, together with the replacement of frequentist objectivity for Bayesian intersubjectivity. This discussion is then expanded to Quantum Theory, as quantum states and operations can be seen as structural elements of a subjective nature.
Quantum Mechanics and Quantum Field Theory
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Quantum Information with Structured Light
Mirhosseini, Mohammad
Quantum information science promises dramatic progress in a variety of fields such as cryptography, computation, and metrology. Although the proof-of-principle attempts for implementing quantum protocols have often relied on only a few qubits, the utilization of more sophisticated quantum systems is required for practical applications. In this thesis, we investigate the emerging role of high-dimensional optical states as a resource for encoding quantum information. We begin the first chapter with a review of orbital angular momentum (OAM) as a prime candidate for realizing multilevel quantum states and follow with a brief introduction to the quantum measurement theory. The second and the third chapters are dedicated to the application of OAM modes in quantum cryptography. In the second chapter, we discuss the challenges of projective measurement of OAM at the single-photon level, a crucial task required for quantum information processing. We then present our development of an efficient and accurate mode-sorting device that is capable of projectively measuring the orbital angular momentum of single photons. In the third chapter, we discuss the role of OAM modes in increasing the information capacity of quantum cryptography. We start this chapter by establishing the merits of encoding information on the quantum index of OAM modes in a free-space link. We then generalizing the BB-84 QKD protocol to the Hilbert space spanned by a finite number of OAM modes and outline our experimental realization. The last two chapters are dedicated to the tomography of structured light fields. We start the fourth chapter by applying the recently found method of direct measurement to the characterization of OAM superpositions. We find the quantum state in the Hilbert space spanned by 27 OAM modes by performing a weak measurement of orbital angular momentum (OAM) followed by a strong measurement of azimuthal angle. We then introduce the concept of compressive direct measurement (CDM
Quantum Transition-State Theory
Hele, Timothy J H
2014-01-01
This dissertation unifies one of the central methods of classical rate calculation, `Transition-State Theory' (TST), with quantum mechanics, thereby deriving a rigorous `Quantum Transition-State Theory' (QTST). The resulting QTST is identical to ring polymer molecular dynamics transition-state theory (RPMD-TST), which was previously considered a heuristic method, and whose results we thereby validate. The key step in deriving a QTST is alignment of the flux and side dividing surfaces in path-integral space to obtain a quantum flux-side time-correlation function with a non-zero $t\\to 0_+$ limit. We then prove that this produces the exact quantum rate in the absence of recrossing by the exact quantum dynamics, fulfilling the requirements of a QTST. Furthermore, strong evidence is presented that this is the only QTST with positive-definite Boltzmann statistics and therefore the pre-eminent method for computation of thermal quantum rates in direct reactions.
Foundations of Information Theory
Burgin, Mark
2008-01-01
Information is the basic concept of information theory. However, there is no definition of this concept that can encompass all uses of the term information in information theories and beyond. Many question a possibility of such a definition. However, foundations of information theory developed in the context of the general theory of information made it possible to build such a relevant and at the same time, encompassing definition. Foundations of information theory are built in a form of onto...
Quantum Causality, Stochastics, Trajectories and Information
Belavkin, V P
2002-01-01
A history of the discovery of quantum mechanics and paradoxes of its interpretation is reconsidered from the modern point of view of quantum stochastics and information. It is argued that in the orthodox quantum mechanics there is no place for quantum phenomenology such as events. The development of quantum measurement theory, initiated by von Neumann, and Bell's conceptual critics of hidden variable theories indicated a possibility for resolution of this crisis. This can be done by divorcing the algebra of the dynamical generators and an extended algebra of the potential (quantum) and the actual (classical) observables. The latter, called beables, form the center of the algebra of all observables, as the only visible (macroscopic) observables must be compatible with any hidden (microscopic) observable. It is shown that within this approach quantum causality can be rehabilitated within an extended quantum mechanics (eventum mechanics) in the form of a superselection rule for compatibility of the consistent hi...
Quantum criticality from Fisher information
Song, Hongting; Luo, Shunlong; Fu, Shuangshuang
2017-04-01
Quantum phase transition is primarily characterized by a qualitative sudden change in the ground state of a quantum system when an external or internal parameter of the Hamiltonian is continuously varied. Investigating quantum criticality using information-theoretic methods has generated fruitful results. Quantum correlations and fidelity have been exploited to characterize the quantum critical phenomena. In this work, we employ quantum Fisher information to study quantum criticality. The singular or extremal point of the quantum Fisher information is adopted as the estimated thermal critical point. By a significant model constructed in Quan et al. (Phys Rev Lett 96: 140604, 2006), the effectiveness of this method is illustrated explicitly.
The quantum theory of measurement
Busch, Paul; Mittelstaedt, Peter
1996-01-01
The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement. Their approach includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations. The book addresses advanced students and researchers in physics and philosophy of science. In this second edition Chaps. II-IV have been substantially rewritten. In particular, an insolubility theorem for the objectification problem has been formulated in full generality, which includes unsharp object observables and unsharp pointers.
Amplification, Redundancy, and Quantum Chernoff Information
Zwolak, Michael; Riedel, C. Jess; Zurek, Wojciech H.
2014-04-01
Amplification was regarded, since the early days of quantum theory, as a mysterious ingredient that endows quantum microstates with macroscopic consequences, key to the "collapse of the wave packet," and a way to avoid embarrassing problems exemplified by Schrödinger's cat. Such a bridge between the quantum microworld and the classical world of our experience was postulated ad hoc in the Copenhagen interpretation. Quantum Darwinism views amplification as replication, in many copies, of the information about quantum states. We show that such amplification is a natural consequence of a broad class of models of decoherence, including the photon environment we use to obtain most of our information. This leads to objective reality via the presence of robust and widely accessible records of selected quantum states. The resulting redundancy (the number of copies deposited in the environment) follows from the quantum Chernoff information that quantifies the information transmitted by a typical elementary subsystem of the environment.
Cryptography from quantum uncertainty in the presence of quantum side information
Bouman, Niek Johannes
2012-01-01
The thesis starts with a high-level introduction into cryptography and quantum mechanics. Chapter 2 gives a theoretical foundation by introducing probability theory, information theory, functional analysis, quantum mechanics and quantum information theory. Chapter 3, 4 and 5 are editions of work
Cryptography from quantum uncertainty in the presence of quantum side information
Bouman, Niek Johannes
2012-01-01
The thesis starts with a high-level introduction into cryptography and quantum mechanics. Chapter 2 gives a theoretical foundation by introducing probability theory, information theory, functional analysis, quantum mechanics and quantum information theory. Chapter 3, 4 and 5 are editions of work pub
Elements of friction theory and nanotribology from statistical physics to quantum information
Gnecco, Enrico
2015-01-01
Combining the classical theories of contact mechanics and lubrication with the study of friction on the nanometer range, this multi-scale book for researchers and students alike guides the reader deftly through the mechanisms governing friction processes, based on state-of-the-art models and experimental results. The first book in the field to incorporate recent research on nanotribology with classical theories of contact mechanics, this unique text explores atomic scale scratches, non-contact friction and fishing of molecular nanowires as observed in the lab. Beginning with simple key concepts, the reader is guided through progressively more complex topics, such as contact of self-affine surfaces and nanomanipulation, in a consistent style, encompassing both macroscopic and atomistic descriptions of friction, and using unified notations to enable use by physicists and engineers across the scientific community.
Vargas, David L.
Emerging quantum simulator technologies provide a new challenge to quantum many body theory. Quantifying the emergent order in and predicting the dynamics of such complex quantum systems requires a new approach. We develop such an approach based on complex network analysis of quantum mutual information. First, we establish the usefulness of quantum mutual information complex networks by reproducing the phase diagrams of transverse Ising and Bose-Hubbard models. By quantifying the complexity of quantum cellular automata we then demonstrate the applicability of complex network theory to non-equilibrium quantum dynamics. We conclude with a study of student collaboration networks, correlating a student's role in a collaboration network with their grades. This work thus initiates a quantitative theory of quantum complexity and provides a new tool for physics education research. (Abstract shortened by ProQuest.).
Comments on quantum probability theory.
Sloman, Steven
2014-01-01
Quantum probability theory (QP) is the best formal representation available of the most common form of judgment involving attribute comparison (inside judgment). People are capable, however, of judgments that involve proportions over sets of instances (outside judgment). Here, the theory does not do so well. I discuss the theory both in terms of descriptive adequacy and normative appropriateness.
Time, chance and quantum theory
Sudbery, Anthony
2016-01-01
I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued logic for future statements, and a contextual theory of truth which gives objective and subjective perspectives equal validity.
Quantum Field Theory in (0 + 1) Dimensions
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
No extension of quantum theory can have improved predictive power.
Colbeck, Roger; Renner, Renato
2011-08-02
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography.
Elementary Concepts of Quantum Theory
Warren, J. W.
1974-01-01
Discusses the importance and difficulties of teaching basic quantum theory. Presents a discussion of wave-particle duality, indeterminacy, the nature of a quantized state of a system, and the exclusion principle. (MLH)
Quantum theory a wide spectrum
Manoukian, E B
2006-01-01
Suitable for instructors and graduate students in Physics, and researchers and professional scientists in Theoretical Physics, this textbook focuses on Quantum Theory. It includes traditional topics and contains numerous problems some of which are challenging enough for research
Quantum entanglement: theory and applications
Energy Technology Data Exchange (ETDEWEB)
Schuch, N.
2007-10-10
This thesis deals with various questions concerning the quantification, the creation, and the application of quantum entanglement. Entanglement arises due to the restriction to local operations and classical communication. We investigate how the notion of entanglement changes if additional restrictions in form of a superselection rule are imposed and show that they give rise to a new resource. We characterize this resource and demonstrate that it can be used to overcome the restrictions, very much as entanglement can overcome the restriction to local operations by teleportation. We next turn towards the optimal generation of resources. We show how squeezing can be generated as efficiently as possible from noisy squeezing operations supplemented by noiseless passive operations, and discuss the implications of this result to the optimal generation of entanglement. The difficulty in describing the behaviour of correlated quantum many-body systems is ultimately due to the complicated entanglement structure of multipartite states. Using quantum information techniques, we investigate the ground state properties of lattices of harmonic oscillators. We derive an exponential decay of correlations for gapped systems, compute the dependence of correlation length and gap, and investigate the notion of criticality by relating a vanishing energy gap to an algebraic decay of correlations. Recently, ideas from entanglement theory have been applied to the description of many-body systems. Matrix Product States (MPS), which have a particularly simple interpretation from the point of quantum information, perform extremely well in approximating the ground states of local Hamiltonians. It is generally believed that this is due to the fact that both ground states and MPS obey an entropic area law. We clarify the relation between entropy scaling laws and approximability by MPS, and in particular find that an area law does not necessarily imply approximability. Using the quantum
Black holes, quantum information, and unitary evolution
Giddings, Steven B
2012-01-01
The unitary crisis for black holes indicates an apparent need to modify local quantum field theory. This paper explores the idea that quantum mechanics and in particular unitarity are fundamental principles, but at the price of familiar locality. Thus, one should seek to parameterize unitary evolution, extending the field theory description of black holes, such that their quantum information is transferred to the external state. This discussion is set in a broader framework of unitary evolution acting on Hilbert spaces comprising subsystems. Here, various constraints can be placed on the dynamics, based on quantum information-theoretic and other general physical considerations, and one can seek to describe dynamics with "minimal" departure from field theory. While usual spacetime locality may not be a precise concept in quantum gravity, approximate locality seems an important ingredient in physics. In such a Hilbert space approach an apparently "coarser" form of localization can be described in terms of tenso...
Fractional statistics and quantum theory
Khare, Avinash
1997-01-01
This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f
Energy Technology Data Exchange (ETDEWEB)
Turner, Leaf [Los Alamos, New Mexico (United States)
2004-04-09
Time, Quantum and Information, a paean to Professor Carl Friedrich von Weizsaecker, commemorates his 90th birthday. The range of Professor Weizsaecker's endeavours is an exhilarating example of what can be accomplished by one freely-soaring human spirit, who is at the same time a physicist, a philosopher, and a humanitarian. The editors, Lutz Castell and Otfried Ischebeck, have assembled an admirable collection of essays and articles written by Weizsaecker?s past students, collaborators, colleagues and acquaintances. Time, Quantum and Information offers the reader a panoply of unique insights into twentieth century science and history. Entangled with the stories about Weizsaecker?s influence on the lives of some of the contributors are discussions of the activities of German scientists during and following World War II, emphasizing their reluctance to work on atomic weapons following the war. By outlining Weizsaecker?s role in the early development of numerous tributaries of physical science, the book gives us a new glimpse into the origins of some of its disparate domains, such as nuclear physics, the physics of stellar nucleosynthesis, cosmic ray physics, fluid turbulence, and the formation of the solar system. We physicists have all studied Weizsaecker?s semi-empirical mass formula describing the binding energy of nuclei. We are aware too that both he and Hans Bethe independently discovered the nuclear cycles that provide stars with their enduring energy output. We have studied the Weizsaecker--Williams technique of calculating the bremsstrahlung of relativistic electrons. But how many of us know of Weizsaecker's work in fluid turbulence that he, like Werner Heisenberg under whom he had earned his doctorate, pursued while holed up in Farm Hall? And how many of us are aware of his introduction of turbulent viscosity to account for the origin of planetary orbits, involving the migration of mass inwards and angular momentum outwards? Moreover, before
Energy Technology Data Exchange (ETDEWEB)
Vukmirovic, Nenad; Wang, Lin-Wang
2009-11-10
This review covers the description of the methodologies typically used for the calculation of the electronic structure of self-assembled and colloidal quantum dots. These are illustrated by the results of their application to a selected set of physical effects in quantum dots.
Preskill, John
2016-01-01
This is the 10th and final chapter of my book on Quantum Information, based on the course I have been teaching at Caltech since 1997. An early version of this chapter (originally Chapter 5) has been available on the course website since 1998, but this version is substantially revised and expanded. The level of detail is uneven, as I've aimed to provide a gentle introduction, but I've also tried to avoid statements that are incorrect or obscure. Generally speaking, I chose to include topics that are both useful to know and relatively easy to explain; I had to leave out a lot of good stuff, but on the other hand the chapter is already quite long. This is a working draft of Chapter 10, which I will continue to update. See the URL on the title page for further updates and drafts of other chapters, and please send me an email if you notice errors. Eventually, the complete book will be published by Cambridge University Press.
Quantum field theory competitive models
Tolksdorf, Jürgen; Zeidler, Eberhard
2009-01-01
For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. The present book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT. The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: 'To bring together outstanding experts working in...
Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
Wiese, U -J
2013-01-01
Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is non-perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should al...
Superconducting quantum circuits theory and application
Deng, Xiuhao
Superconducting quantum circuit models are widely used to understand superconducting devices. This thesis consists of four studies wherein the superconducting quantum circuit is used to illustrate challenges related to quantum information encoding and processing, quantum simulation, quantum signal detection and amplification. The existence of scalar Aharanov-Bohm phase has been a controversial topic for decades. Scalar AB phase, defined as time integral of electric potential, gives rises to an extra phase factor in wavefunction. We proposed a superconducting quantum Faraday cage to detect temporal interference effect as a consequence of scalar AB phase. Using the superconducting quantum circuit model, the physical system is solved and resulting AB effect is predicted. Further discussion in this chapter shows that treating the experimental apparatus quantum mechanically, spatial scalar AB effect, proposed by Aharanov-Bohm, can't be observed. Either a decoherent interference apparatus is used to observe spatial scalar AB effect, or a quantum Faraday cage is used to observe temporal scalar AB effect. The second study involves protecting a quantum system from losing coherence, which is crucial to any practical quantum computation scheme. We present a theory to encode any qubit, especially superconducting qubits, into a universal quantum degeneracy point (UQDP) where low frequency noise is suppressed significantly. Numerical simulations for superconducting charge qubit using experimental parameters show that its coherence time is prolong by two orders of magnitude using our universal degeneracy point approach. With this improvement, a set of universal quantum gates can be performed at high fidelity without losing too much quantum coherence. Starting in 2004, the use of circuit QED has enabled the manipulation of superconducting qubits with photons. We applied quantum optical approach to model coupled resonators and obtained a four-wave mixing toolbox to operate photons
Razavy, Mohsen
2014-01-01
In this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined. In addition by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and ...
Introduction to quantum Thurston theory
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L O [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation); Penner, R C [University of Southern California, Los Angeles (United States)
2003-12-31
This is a survey of the theory of quantum Teichmueller and Thurston spaces. The Thurston (or train track) theory is described and quantized using the quantization of coordinates for Teichmueller spaces of Riemann surfaces with holes. These surfaces admit a description by means of the fat graph construction proposed by Penner and Fock. In both theories the transformations in the quantum mapping class group that satisfy the pentagon relation play an important role. The space of canonical measured train tracks is interpreted as the completion of the space of observables in 3D gravity, which are the lengths of closed geodesics on a Riemann surface with holes. The existence of such a completion is proved in both the classical and the quantum cases, and a number of algebraic structures arising in the corresponding theories are discussed.
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
Algorithmic information theory
Grünwald, P.D.; Vitányi, P.M.B.; Adriaans, P.; van Benthem, J.
2008-01-01
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining 'information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are fundamentally different. We indicate how recent developments within the theory allow one to formally distinguish between 'structural' (meaningful) and 'random' information as measured by the Kolmo...
Algorithmic information theory
Grünwald, P.D.; Vitányi, P.M.B.
2008-01-01
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are fundamentally different. We indicate how recent developments within the theory allow one to formally distinguish between `structural' (meaningful) and `random' information as measured by the Kolmo...
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Propensity, Probability, and Quantum Theory
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
Algorithmic information theory
P.D. Grünwald; P.M.B. Vitányi
2008-01-01
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are
Algorithmic information theory
P.D. Grünwald; P.M.B. Vitányi
2008-01-01
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining 'information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are
Algorithmic information theory
Grünwald, P.D.; Vitányi, P.M.B.
2008-01-01
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are
Algorithmic information theory
Grünwald, P.D.; Vitányi, P.M.B.; Adriaans, P.; van Benthem, J.
2008-01-01
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining 'information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are
Quantum information, cognition, and music
Dalla Chiara, Maria L.; Giuntini, Roberto; Leporini, Roberto; Negri, Eleonora; Sergioli, Giuseppe
2015-01-01
Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: a comparison between classical probabilistic Turing machines and quantum Turing machines.possible applications of the quantum computational semantics to cognitive problems.parallelism in music. PMID:26539139
A Naturally Renormalized Quantum Field Theory
2006-01-01
It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space togeth...
Spacetime replication of continuous variable quantum information
Hayden, Patrick; Nezami, Sepehr; Salton, Grant; Sanders, Barry C.
2016-08-01
The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics.
Brady, Adam; Chapagain, Nirdosh; Simkhada, Prashanna
2011-10-01
Quantum Information (QI) is a relatively young science with exciting research opportunities. Nepal has an untapped reserve of motivated students with scientific research potential. Based on our educational experience in Nepal and in the US and based on our exposure to QI, we explore the possibility of developing QI research in Nepal. In this poster we lay out basic facts on physics and physics education in Nepal, report on an introductory QI class experiment at BYU, and use what we have learned to envision a QI future in Nepal.
Extraction of information from a single quantum
Paraoanu, G. S.
2011-01-01
We investigate the possibility of performing quantum tomography on a single qubit with generalized partial measurements and the technique of measurement reversal. Using concepts from statistical decision theory, we prove that, somewhat surprisingly, no information can be obtained using this scheme. It is shown that, irrespective of the measurement technique used, extraction of information from single quanta is at odds with other general principles of quantum physics.
Division Algebras and Quantum Theory
Baez, John C
2011-01-01
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way". It is perhaps easiest to see it in the study of irreducible unitary representations of groups on complex Hilbert spaces. These representations come in three kinds: those that are not isomorphic to their own dual (the truly "complex" representations), those that are self-dual thanks to a symmetric bilinear pairing (which are "real", in that they are the complexifications of representations on real Hilbert spaces), and those that are self-dual thanks to an antisymmetric bilinear pairing (which are...
The quantum field theory interpretation of quantum mechanics
de la Torre, Alberto C.
2015-01-01
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Arfi, Badredine
2007-02-01
Most game-theoretic studies of strategic interaction assume independent individual strategies as the basic unit of analysis. This paper explores the effects of non-independence on strategic interaction. Two types of non-independence effects are considered. First, the paper considers subjective non-independence at the level of the individual actor by looking at how choice ambivalence shapes the decision-making process. Specifically, how do alternative individual choices superpose with one another to “constructively/destructively” shape each other's role within an actor's decision-making process? This process is termed as quantum superposition of alternative choices. Second, the paper considers how inter-subjective non-independence across actors engenders collective strategies among two or more interacting actors. This is termed as quantum entanglement of strategies. Taking into account both types of non-independence effect makes possible the emergence of a new collective equilibrium, without assuming signaling, prior “contract” agreement or third-party moderation, or even “cheap talk”. I apply these ideas to analyze the equilibrium possibilities of a situation wherein N actors play a quantum social game of cooperation. I consider different configurations of large- N quantum entanglement using the approach of density operator. I specifically consider the following configurations: star-shaped, nearest-neighbors, and full entanglement.
Factorization algebras in quantum field theory
Costello, Kevin
2017-01-01
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
Quantum Field Theory, Revised Edition
Mandl, F.; Shaw, G.
1994-01-01
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical
Introduction to quantum field theory
Chang, Shau-Jin
1990-01-01
This book presents in a short volume the basics of quantum field theory and many body physics. The first part introduces the perturbative techniques without sophisticated apparatus and applies them to numerous problems including quantum electrodynamics (renormalization), Fermi and Bose gases, the Brueckner theory of nuclear system, liquid Helium and classical systems with noise. The material is clear, illustrative and the important points are stressed to help the reader get the understanding of what is crucial without overwhelming him with unnecessary detours or comments. The material in the s
de Wit, Bernard
1990-01-01
After a brief and practical introduction to field theory and the use of Feynman diagram, we discuss the main concept in gauge theories and their application in elementary particle physics. We present all the ingredients necessary for the construction of the standard model.
2013-02-15
Matthew James, Andre Carvalho and Michael Hush completed some work analyzing cross-phase modulation using single photon quantum filtering techniques...ANU Michael Hush January – June, 2012, Postdoc, ANU Matthew R. James Professor, Australian National University Ian R. Petersen Professor...appear, IEEE Trans. Aut. Control., 2013. A. R. R. Carvalho, M. R. Hush , and M. R. James, “Cavity driven by a single photon: Conditional dynamics and
Quantum information density and network
Institute of Scientific and Technical Information of China (English)
Qiao BI; Jin-qing FANG; Gui-ping LIU
2009-01-01
We present a quantum information network in which quantum information density is used for per- forming quantum computing or teleportation. The pho- tons are entangled in quantum channels and play a role of flying ebit to transmit interaction among the nodes. A particular quantum Gaussian channel is constructed; it permits photon-encoded information to transmit quan- tum signals with certain quantum parallelism. The cor- responding quantum dynamical mutual information is discussed, and the controlling nodes connectivity by driv- ing the network is studied. With regard to different driving functions, the connectivity distribution of the network is complicated. They obey positive or negative power law, and also influence the assortativity coefficient or the dynamical property of the network.
Information theory and Thermodynamics
Kafri, Oded
2006-01-01
A communication theory for a transmitter broadcasting to many receivers is presented. In this case energetic considerations cannot be neglected as in Shannon theory. It is shown that, when energy is assigned to the information bit, information theory complies with classical thermodynamic and is part of it. To provide a thermodynamic theory of communication it is necessary to define equilibrium for informatics systems that are not in thermal equilibrium and to calculate temperature, heat, and ...
Semiclassical and quantum Liouville theory
Menotti, P
2006-01-01
We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincare' accessory parameters. This provides the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the case of n finite charges and m infinitesimal. With the same technique we compute the exact Green function on the sphere on the background of three finite singularities. Turning to the full quantum problem we address the calculation of the quantum determinant on the background of three finite charges and of the further perturbative corrections. The zeta function regularization provides a theory which is not invariant under local conformal transformations. Instead by employing a regularization suggested in the case of the pseu...
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Interpreting quantum theory a therapeutic approach
Friederich, Simon
2014-01-01
Is it possible to approach quantum theory in a 'therapeutic' vein that sees its foundational problems as arising from mistaken conceptual presuppositions? The book explores the prospects for this project and, in doing so, discusses such fascinating issues as the nature of quantum states, explanation in quantum theory, and 'quantum non-locality'.
Interpreting quantum theory a therapeutic approach
Friederich, S
2014-01-01
Is it possible to approach quantum theory in a 'therapeutic' vein that sees its foundational problems as arising from mistaken conceptual presuppositions? The book explores the prospects for this project and, in doing so, discusses such fascinating issues as the nature of quantum states, explanation in quantum theory, and 'quantum non-locality'.
Interference and inequality in quantum decision theory
Energy Technology Data Exchange (ETDEWEB)
Cheon, Taksu, E-mail: taksu.cheon@kochi-tech.ac.j [Laboratory of Physics, Kochi University of Technology, Tosa Yamada, Kochi 782-8502 (Japan); Takahashi, Taiki, E-mail: ttakahashi@lynx.let.hokudai.ac.j [Laboratory of Social Psychology, Department of Behavioral Science, Faculty of Letters, Hokkaido University, N.10, W.7, Kita-ku, Sapporo 060-0810 (Japan)
2010-12-01
The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data indicating the breakdown of classical explanations are critically examined with quantum theory using the full set of quantum phases.
Inequalities for quantum skew information
DEFF Research Database (Denmark)
Audenaert, Koenraad; Cai, Liang; Hansen, Frank
2008-01-01
We study quantum information inequalities and show that the basic inequality between the quantum variance and the metric adjusted skew information generates all the multi-operator matrix inequalities or Robertson type determinant inequalities studied by a number of authors. We introduce an order...... relation on the set of functions representing quantum Fisher information that renders the set into a lattice with an involution. This order structure generates new inequalities for the metric adjusted skew informations. In particular, the Wigner-Yanase skew information is the maximal skew information...... with respect to this order structure in the set of Wigner-Yanase-Dyson skew informations....
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
Evolutionary Information Theory
Mark Burgin
2013-01-01
Evolutionary information theory is a constructive approach that studies information in the context of evolutionary processes, which are ubiquitous in nature and society. In this paper, we develop foundations of evolutionary information theory, building several measures of evolutionary information and obtaining their properties. These measures are based on mathematical models of evolutionary computations, machines and automata. To measure evolutionary information in an invariant form, we const...
Andrade, Eugenio
2014-06-01
I claim that Peirce's notion of information and sign iteration as an intermediation between potentialities that are actualized and actualities that are potentiated provides a suitable framework for interpretation of Zurek' Information gathering and using systems (IGUS). Moreover, this model can be extended to address the problem of quantum measurement (QM) since it allows exploring an alternative view based on IGUS understood as agents of internal measurement, beyond Copenhagen interpretation (CI) that invokes a classical observer that performs measurements and the "many worlds interpretation" (MWI) that rejects all sort of observers and measurements. This integrative view allows figuring out a hierarchy of IGUS-like systems of interpretation that explore new possibilities in the upper level analog boundary and consolidate actualized information in the lower level digital boundary.
Quantum Mechanics as Quantum Information (and only a little more)
Fuchs, C
2002-01-01
In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained application of the latest fad to a time-honored problem, this method holds promise precisely because a large part--but not all--of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. This paper, though taking quant-ph/0106166 as its core, corrects one mistake and offers several observations beyond the previous version. In particular, I identify one element of quantum mechanics that I would not label a subjective term in the theory--it is the in...
Pseudo-random unitary operators for quantum information processing.
Emerson, Joseph; Weinstein, Yaakov S; Saraceno, Marcos; Lloyd, Seth; Cory, David G
2003-12-19
In close analogy to the fundamental role of random numbers in classical information theory, random operators are a basic component of quantum information theory. Unfortunately, the implementation of random unitary operators on a quantum processor is exponentially hard. Here we introduce a method for generating pseudo-random unitary operators that can reproduce those statistical properties of random unitary operators most relevant to quantum information tasks. This method requires exponentially fewer resources, and hence enables the practical application of random unitary operators in quantum communication and information processing protocols. Using a nuclear magnetic resonance quantum processor, we were able to realize pseudorandom unitary operators that reproduce the expected random distribution of matrix elements.
Interpreting Quantum Theory : A Therapeutic Approach
Friederich, Simon
2014-01-01
Debates about the foundations of quantum theory usually circle around two main challenges: the so-called 'measurement problem' and a claimed tension between quantum theory and relativity theory that arises from the phenomena labelled 'quantum non-locality'. This work explores the possibility of a 't
Interpreting Quantum Theory : A Therapeutic Approach
Friederich, Simon
2014-01-01
Debates about the foundations of quantum theory usually circle around two main challenges: the so-called 'measurement problem' and a claimed tension between quantum theory and relativity theory that arises from the phenomena labelled 'quantum non-locality'. This work explores the possibility of a 't
Quantum metrology from a quantum information science perspective
Toth, Geza
2015-01-01
We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger-Horne-Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer-Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrela...
Quantum theory of acoustoelectric interaction
DEFF Research Database (Denmark)
Mosekilde, Erik
1974-01-01
term, significant in the classical-collision-dominated regime only, the dielectric response function and the acoustic gain factor for a piezoelectrically active sound wave are obtained for the quantum and semiclassical-microscopic regimes. The manner in which the theory can be extended to the collision......Within the self-consistent-field approximation, a quantum-mechanical derivation is given for the dielectric response function of an arbitrarily degenerate free-electron gas which is subjected to a drift field. Neglecting in the equation of motion for the one-electron density operator a convection...
Zitterbewegung in quantum field theory
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Yong; Xiong Cai-Dong
2008-01-01
Traditionally,the zitterbewegung (ZB) of the Dirac electron has just been studied at the level of quantum mechanics.Seeing the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic,graphene,and superconducting systems,etc.,this paper presents a quantum-field-theory investigation on ZB and obtains the con clusion that,the ZB of an electron arises from the influence of virtual electron-positron pairs (or vacuum fluctuations)on the electron.
BRICS and Quantum Information Processing
DEFF Research Database (Denmark)
Schmidt, Erik Meineche
1998-01-01
BRICS is a research centre and international PhD school in theoretical computer science, based at the University of Aarhus, Denmark. The centre has recently become engaged in quantum information processing in cooperation with the Department of Physics, also University of Aarhus. This extended...... abstract surveys activities at BRICS with special emphasis on the activities in quantum information processing....
Quantum Field Theory A Modern Perspective
Parameswaran Nair, V
2005-01-01
Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it gr...
Science and information theory
Brillouin, Leon
2013-01-01
A classic source for exploring the connections between information theory and physics, this text is geared toward upper-level undergraduates and graduate students. The author, a giant of 20th-century mathematics, applies the principles of information theory to a variety of issues, including Maxwell's demon, thermodynamics, and measurement problems. 1962 edition.
Science and information theory
Brillouin, Léon
1962-01-01
A classic source for exploring the connections between information theory and physics, this text is geared toward upper-level undergraduates and graduate students. The author, a giant of 20th-century mathematics, applies the principles of information theory to a variety of issues, including Maxwell's demon, thermodynamics, and measurement problems. 1962 edition.
Quantum information and computing
Ohya, M; Watanabe, N
2006-01-01
The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers. Contents: Coherent Quantum Control of ?-Atoms through the Stochastic Limit (L Accardi et al.); Recent Advances in Quantum White Noise Calculus (L Accardi & A Boukas); Joint Extension of States of Fermion Subsystems (H Araki); Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H Fichtner et al.); Quantum
Noncommutative quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Grosse, H. [Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Wien (Austria); Wulkenhaar, R. [Mathematisches Institut der Westfaelischen Wilhelms-Universitaet, Einsteinstrasse 62, 48149 Muenster (Germany)
2014-09-11
We summarize our recent construction of the φ{sup 4}-model on four-dimensional Moyal space. This is achieved by solving the quartic matrix model for a general external matrix in terms of the solution of a non-linear equation for the 2-point function and the eigenvalues of that matrix. The β-function vanishes identically. For the Moyal model, the theory of Carleman type singular integral equations reduces the construction to a fixed point problem. The resulting Schwinger functions in position space are symmetric and invariant under the full Euclidean group. The Schwinger 2-point function is reflection positive iff the diagonal matrix 2-point function is a Stieltjes function. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Jerusalem lectures on black holes and quantum information
Harlow, D.
2016-01-01
These lectures give an introduction to the quantum physics of black holes, including recent developments based on quantum information theory such as the firewall paradox and its various cousins. An introduction is also given to holography and the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, focusing on those aspects which are relevant for the black hole information problem.
Entropy, Topological Theories and Emergent Quantum Mechanics
Directory of Open Access Journals (Sweden)
D. Cabrera
2017-02-01
Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a ﬁnite dimensional Hilbert space of quantum states. Speciﬁcally, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological ﬁeld theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.
Lagrangian-Only Quantum Theory
Wharton, K B
2013-01-01
Despite the importance of the path integral, there have been relatively few attempts to look to the Lagrangian for a more realistic framework that might underlie quantum theory. While such realism is not available for the standard path integral or quantum field theory, a promising alternative is to only consider field histories for which the Lagrangian density is always zero. With this change, it appears possible to replace amplitudes with equally-weighted probabilities. This paper demonstrates a proof-of-principle for this approach, using a toy Lagrangian that corresponds to an arbitrary spin state. In this restricted framework one can derive both the Born rule and its limits of applicability. The fact that the Lagrangian obeys future boundary constraints also results in the first continuous, spacetime-based, hidden-variable description of a Bell-inequality-violating system.
Evolutionary Information Theory
Directory of Open Access Journals (Sweden)
Mark Burgin
2013-04-01
Full Text Available Evolutionary information theory is a constructive approach that studies information in the context of evolutionary processes, which are ubiquitous in nature and society. In this paper, we develop foundations of evolutionary information theory, building several measures of evolutionary information and obtaining their properties. These measures are based on mathematical models of evolutionary computations, machines and automata. To measure evolutionary information in an invariant form, we construct and study universal evolutionary machines and automata, which form the base for evolutionary information theory. The first class of measures introduced and studied in this paper is evolutionary information size of symbolic objects relative to classes of automata or machines. In particular, it is proved that there is an invariant and optimal evolutionary information size relative to different classes of evolutionary machines. As a rule, different classes of algorithms or automata determine different information size for the same object. The more powerful classes of algorithms or automata decrease the information size of an object in comparison with the information size of an object relative to weaker4 classes of algorithms or machines. The second class of measures for evolutionary information in symbolic objects is studied by introduction of the quantity of evolutionary information about symbolic objects relative to a class of automata or machines. To give an example of applications, we briefly describe a possibility of modeling physical evolution with evolutionary machines to demonstrate applicability of evolutionary information theory to all material processes. At the end of the paper, directions for future research are suggested.
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Mutual Entropy in Quantum Information and Information Genetics
Ohya, M
2004-01-01
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual entropy (information), information transmitted from an input system to an output system, by which communication processes could be analyzed on the stage of mathematical science. In this paper, first we review the quantum mutual entropy and discuss its uses in quantum information theory, and secondly we show how the classical mutual entropy can be used to analyze genomes, in particular, those of HIV.
Quantum theory of human communication
Slowikowski, Wojtek; Nielsen, Erik B.
2004-01-01
We use notions and techniques of Quantum Field Theory to formulate and investigate basic concepts and mechanisms of human communication. We start with attitudes which correspond to photons frequencies, then we introduce states-of-mind which correspond to wave functions. Finally, by way of the second quantization, we come to states-of-opinions which correspond to states of quantized radiation fields. In the present paper we shall only investigate superpositions of pairs of coherent states (e.g...
Semiclassical and quantum Liouville theory
Menotti, Pietro
2005-01-01
We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincare' accessory parameters. This provides the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the cas...
Quantum information with Rydberg atoms
DEFF Research Database (Denmark)
Saffman, Mark; Walker, T.G.; Mølmer, Klaus
2010-01-01
qubits. The availability of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding...... of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydberg-mediated quantum information processing.......Rydberg atoms with principal quantum number n»1 have exaggerated atomic properties including dipole-dipole interactions that scale as n4 and radiative lifetimes that scale as n3. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom...
High Information Capacity Quantum Imaging
2014-09-19
the quantum nature of light), and detector reset time. Algorithmic : We provide a method for spatiotemporally-regularized estimation of intensity and...High Information Capacity Quantum Imaging This is the final report for the DARPA InPho program. In reality, we finished this program in early 2013...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 Quantum Imaging, Photon Counting, LIDAR REPORT DOCUMENTATION PAGE 11
The development of elementary quantum theory
Capellmann, Herbert
2017-01-01
This book traces the evolution of the ideas that eventually resulted in the elementary quantum theory in 1925/26. Further, it discusses the essential differences between the fundamental equations of Quantum Theory derived by Born and Jordan, logically comprising Quantum Mechanics and Quantum Optics, and the traditional view of the development of Quantum Mechanics. Drawing on original publications and letters written by the main protagonists of that time, it shows that Einstein’s contributions from 1905 to 1924 laid the essential foundations for the development of Quantum Theory. Einstein introduced quantization of the radiation field; Born added quantized mechanical behavior. In addition, Born recognized that Quantum Mechanics necessarily required Quantum Optics; his radical concept of truly discontinuous and statistical quantum transitions (“quantum leaps”) was directly based on Einstein’s physical concepts.
Energy Technology Data Exchange (ETDEWEB)
Ranade, Kedar S.
2009-02-04
This PhD thesis deals with quantum-cryptographic protocols which allow general finite-dimensional quantum systems (qudits) as carriers of information in contrast to the predominantly used two-dimensional quantum systems (qubits). The main focus of investigations is the maximum tolerable error rate of such protocols and its behaviour as a function of the dimension of the information carriers. For this purpose, several concepts are introduced which allow the treatment of this problem. In particular, protocols are presented which work up to a maximum tolerate error rate, and it is shown that a wide class of protocols cannot be used for higher error rates. Among other things, it turns out that the maximum tolerable error rate for two-basis protocols increases up to 50% for high dimensions. Apart from the above-mentioned main subjects of this thesis, some other results from the field of quantum information theory are given, which were achieved during this PhD project. (orig.)
Nolting, Wolfgang
2009-01-01
Magnetism is one of the oldest and most fundamental problems of Solid State Physics although not being fully understood up to now. On the other hand it is one of the hottest topic of current research. Practically all branches of modern technological developments are based on ferromagnetism, especially what concerns information technology. The book, written in a tutorial style, starts from the fundamental features of atomic magnetism, discusses the essentially single-particle problems of dia- and paramagnetism, in order to provide the basis for the exclusively interesting collective magnetism (ferro, ferri, antiferro). Several types of exchange interactions, which take care under certain preconditions for a collective ordering of localized or itinerant permanent magnetic moments, are worked out. Under which conditions these exchange interactions are able to provoke a collective moment ordering for finite temperatures is investigated within a series of theoretical models, each of them considered for a very spec...
Gravity Dual of Quantum Information Metric
Miyaji, Masamichi; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento
2015-01-01
We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.
Pettersson, Rune
2014-01-01
Information design has practical and theoretical components. As an academic discipline we may view information design as a combined discipline, a practical theory, or as a theoretical practice. So far information design has incorporated facts, influences, methods, practices, principles, processes, strategies, and tools from a large number of…
Quantum principal bundles and corresponding gauge theories
Durdevic, M
1995-01-01
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge transformations, are introduced and investigated. A natural differential calculus on quantum gauge bundles is constructed and analyzed. Kinematical and dynamical properties of corresponding gauge theories are discussed.
Random Matrix theory approach to Quantum mechanics
Chaitanya, K. V. S. Shiv
2015-01-01
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of random matrix theory. This study helps in identify the potential appear in the joint probability distribution function in the random matrix theory as a super potential. This approach allows to extend the random matrix theory to the newly discovered exceptional ...
Energy Technology Data Exchange (ETDEWEB)
Hoerhammer, C.
2007-11-26
In this thesis, non-Markovian dynamics, decoherence and entanglement in dissipative quantum systems are studied. In particular, applications to quantum information theory of continuous variable systems are considered. The non-Markovian dynamics are described by the Hu-Paz-Zhang master equation of quantum Brownian motion. In this context the focus is on non-Markovian effects on decoherence and separability time scales of various single- mode and two-mode continuous variable states. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial recurrence of coherence can occur in case of non-Lindblad-type dynamics. The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir and two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian and non-Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Therefore, new quantum correlations may emerge between the two modes. Below a critical bath temperature entanglement is preserved even in the steady state. A separability criterion is derived, which depends
Quantum mechanics and quantum information a guide through the quantum world
Fayngold, Moses
2013-01-01
Alongside a thorough definition of the basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of the quantum information theory. It also deals with other important topics hardly found in the literature, including the Robertson-Schrodinger-relation, angle and angular momentum uncertainties, interaction-free measurements, and the limitations of the no-cloning theorem With its interpretations of quantum mechanics and its discussions of quantum computing, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and as an essential reference for physics students and physics professionals.
Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr
2015-01-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories
Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr
2016-11-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
Quantum theory allows for absolute maximal contextuality
Amaral, Barbara; Cunha, Marcelo Terra; Cabello, Adán
2015-12-01
Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality witnesses can be expressed as a sum S of n probabilities, and the independence number α and the Tsirelson-like number ϑ of the corresponding exclusivity graph are, respectively, the maximum of S for noncontextual theories and for the theory under consideration. A theory allows for absolute maximal contextuality if it has scenarios in which ϑ /α approaches n . Here we show that quantum theory allows for absolute maximal contextuality despite what is suggested by the examination of the quantum violations of Bell and noncontextuality inequalities considered in the past. Our proof is not constructive and does not single out explicit scenarios. Nevertheless, we identify scenarios in which quantum theory allows for almost-absolute-maximal contextuality.
On the realization of quantum Fisher information
Saha, Aparna; Talukdar, B.; Chatterjee, Supriya
2017-03-01
With special attention to the role of information theory in physical sciences we present analytical results for the coordinate- and momentum-space Fisher information of some important one-dimensional quantum systems which differ in spacing of their energy levels. The studies envisaged allow us to relate the coordinate-space information ({I}ρ ) with the familiar energy levels of the quantum system. The corresponding momentum-space information ({I}γ ) does not obey such a simple relationship with the energy spectrum. Our results for the product ({I}ρ {I}γ ) depend quadratically on the principal quantum number n and satisfy an appropriate uncertainty relation derived by Dehesa et al (2007 J. Phys. A: Math. Theor. 40 1845)
Quantum information to the home
Choi, Iris; Young, Robert J.; Townsend, Paul D.
2011-06-01
Information encoded on individual quanta will play an important role in our future lives, much as classically encoded digital information does today. Combining quantum information carried by single photons with classical signals encoded on strong laser pulses in modern fibre-to-the-home (FTTH) networks is a significant challenge, the solution to which will facilitate the global distribution of quantum information to the home and with it a quantum internet [1]. In real-world networks, spontaneous Raman scattering in the optical fibre would induce crosstalk between the high-power classical channels and a single-photon quantum channel, such that the latter is unable to operate. Here, we show that the integration of quantum and classical information on an FTTH network is possible by performing quantum key distribution (QKD) on a network while simultaneously transferring realistic levels of classical data. Our novel scheme involves synchronously interleaving a channel of quantum data with the Raman scattered photons from a classical channel, exploiting the periodic minima in the instantaneous crosstalk and thereby enabling secure QKD to be performed.
Quantum information to the home
Energy Technology Data Exchange (ETDEWEB)
Choi, Iris; Young, Robert J; Townsend, Paul D, E-mail: paul.townsend@tyndall.ie [Photonic Systems Group, Tyndall National Institute and Department of Physics, University College Cork, Cork (Ireland)
2011-06-15
Information encoded on individual quanta will play an important role in our future lives, much as classically encoded digital information does today. Combining quantum information carried by single photons with classical signals encoded on strong laser pulses in modern fibre-to-the-home (FTTH) networks is a significant challenge, the solution to which will facilitate the global distribution of quantum information to the home and with it a quantum internet. In real-world networks, spontaneous Raman scattering in the optical fibre would induce crosstalk between the high-power classical channels and a single-photon quantum channel, such that the latter is unable to operate. Here, we show that the integration of quantum and classical information on an FTTH network is possible by performing quantum key distribution (QKD) on a network while simultaneously transferring realistic levels of classical data. Our novel scheme involves synchronously interleaving a channel of quantum data with the Raman scattered photons from a classical channel, exploiting the periodic minima in the instantaneous crosstalk and thereby enabling secure QKD to be performed.
Quantum communication and information processing
Beals, Travis Roland
Quantum computers enable dramatically more efficient algorithms for solving certain classes of computational problems, but, in doing so, they create new problems. In particular, Shor's Algorithm allows for efficient cryptanalysis of many public-key cryptosystems. As public key cryptography is a critical component of present-day electronic commerce, it is crucial that a working, secure replacement be found. Quantum key distribution (QKD), first developed by C.H. Bennett and G. Brassard, offers a partial solution, but many challenges remain, both in terms of hardware limitations and in designing cryptographic protocols for a viable large-scale quantum communication infrastructure. In Part I, I investigate optical lattice-based approaches to quantum information processing. I look at details of a proposal for an optical lattice-based quantum computer, which could potentially be used for both quantum communications and for more sophisticated quantum information processing. In Part III, I propose a method for converting and storing photonic quantum bits in the internal state of periodically-spaced neutral atoms by generating and manipulating a photonic band gap and associated defect states. In Part II, I present a cryptographic protocol which allows for the extension of present-day QKD networks over much longer distances without the development of new hardware. I also present a second, related protocol which effectively solves the authentication problem faced by a large QKD network, thus making QKD a viable, information-theoretic secure replacement for public key cryptosystems.
Theories of information behavior
Erdelez, Sandra; McKechnie, Lynne
2005-01-01
This unique book presents authoritative overviews of more than 70 conceptual frameworks for understanding how people seek, manage, share, and use information in different contexts. A practical and readable reference to both well-established and newly proposed theories of information behavior, the book includes contributions from 85 scholars from 10 countries. Each theory description covers origins, propositions, methodological implications, usage, links to related conceptual frameworks, and listings of authoritative primary and secondary references. The introductory chapters explain key concepts, theory–method connections, and the process of theory development.
Isotope-based quantum information
G Plekhanov, Vladimir
2012-01-01
The present book provides to the main ideas and techniques of the rapid progressing field of quantum information and quantum computation using isotope - mixed materials. It starts with an introduction to the isotope physics and then describes of the isotope - based quantum information and quantum computation. The ability to manipulate and control electron and/or nucleus spin in semiconductor devices provides a new route to expand the capabilities of inorganic semiconductor-based electronics and to design innovative devices with potential application in quantum computing. One of the major challenges towards these objectives is to develop semiconductor-based systems and architectures in which the spatial distribution of spins and their properties can be controlled. For instance, to eliminate electron spin decoherence resulting from hyperfine interaction due to nuclear spin background, isotopically controlled devices are needed (i.e., nuclear spin-depleted). In other emerging concepts, the control of the spatial...
Mind, Matter, Information and Quantum Interpretations
Directory of Open Access Journals (Sweden)
Reza Maleeh
2015-07-01
Full Text Available In this paper I give a new information-theoretic analysis of the formalisms and interpretations of quantum mechanics (QM in general, and of two mainstream interpretations of quantum mechanics in particular: The Copenhagen interpretation and David Bohm’s interpretation of quantum mechanics. Adopting Juan G. Roederer’s reading of the notion of pragmatic information, I argue that pragmatic information is not applicable to the Copenhagen interpretation since the interpretation is primarily concerned with epistemology rather than ontology. However it perfectly fits Bohm’s ontological interpretation of quantum mechanics in the realms of biotic and artificial systems. Viewing Bohm’s interpretation of QM in the context of pragmatic information imposes serious limitations to the qualitative aspect of such an interpretation, making his extension of the notion active information to every level of reality illegitimate. Such limitations lead to the idea that, contrary to Bohm’s claim, mind is not a more subtle aspect of reality via the quantum potential as active information, but the quantum potential as it affects particles in the double-slit experiment represents the non-algorithmic aspect of the mind as a genuine information processing system. This will provide an information-based ground, firstly, for refreshing our views on quantum interpretations and secondly, for a novel qualitative theory of the relationship of mind and matter in which mind-like properties are exclusive attributes of living systems. To this end, I will also take an information-theoretic approach to the notion of intentionality as interpreted by John Searle.
Psychophysical Interpretation of Quantum theory
Pradhan, Rajat K
2013-01-01
It is shown that the formalism of quantum theory naturally incorporates the psychophysical parallelism and thereby interprets itself, if the subjective aspects are taken as equal partners alongside the objective aspects as determinants of Reality as a Whole. The inevitable interplay of the subject (observer) and the object (observed) in making up Reality is brought out succinctly through a comprehensive psychophysical interpretation which includes in its bosom the truths of many of the major interpretations proposed so far as essential ingredients. At the heart of this novel approach lies the interpretation of the complex conjugate quantities such as the conjugate wave function {\\Psi}*(r, t), the bra vector , and the observable A etc. respectively. This brings out the psycho-physical parallelism lying hidden in the quantum mechanical formalism in a quite straightforward manner. The measurement process is shown to be a two-step process comprising objective interaction through the retarded waves and subjective ...
Goyal, Philip; Skilling, John
2009-01-01
Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this paper, we show that it is possible to derive the complex nature of the quantum formalism directly from the assumption that a pair of real numbers is associated to each sequence of measurement outcomes, and that the probability of this sequence is a real-valued function of this number pair. By making use of elementary symmetry and consistency conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes.
Holographic computations of the Quantum Information Metric
Trivella, Andrea
2016-01-01
In this note we show how the Quantum Information Metric can be computed holographically using a perturbative approach. In particular when the deformation of the conformal field theory state is induced by a scalar operator the corresponding bulk configuration reduces to a scalar field perturbatively probing the unperturbed background. We study two concrete examples: a CFT ground state deformed by a primary operator and thermofield double state in $d=2$ deformed by a marginal operator. Finally, we generalize the bulk construction to the case of a multi dimensional parameter space and show that the Quantum Information Metric coincides with the metric of the non-linear sigma model for the corresponding scalar fields.
Quantum thermodynamic processes energy and information flow at the nanoscale
Mahler, Guenter
2015-01-01
The point of departure of this book is a triad of themes: information theory, thermodynamics, and quantum mechanics. These are related: thermodynamics and quantum mechanics form the basis of quantum thermodynamics; information and quantum mechanics underly, inter alia, the notorious quantum measurement problem; and information and thermodynamics have much to say about control limits in the tension between micro- and macro-descriptions.Why does the world around us typically look thermal-from cosmology down to individual embedded spins? Do informational measures constitute additional (independen
An Introduction to Quantum Field Theory
Peskin, Michael E
1995-01-01
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the sta
On the Possibility of Quantum Informational Structural Realism
Bynum, Terrell Ward
2013-01-01
In The Philosophy of Information (2011 book), Luciano Floridi presents an ontological theory of Being qua Being, which he calls "Informational Structural Realism", a theory which applies, he says, to every possible world. He identifies primordial information ("dedomena") as the foundation of any structure in any possible world. The present essay examines Floridi's defense of that theory, as well as his refutation of "Digital Ontology" (which some people might confuse with his own). Then, using Floridi's ontology as a starting point, the present essay adds quantum features to dedomena, yielding an ontological theory for our own universe, Quantum Informational Structural Realism, which provides a metaphysical interpretation of key quantum phenomena, and diminishes the "weirdness" or "spookiness" of quantum mechanics. Key Words: digital ontology, dedomena, structural realism, quantum information, primordial qubit
A first course in topos quantum theory
Energy Technology Data Exchange (ETDEWEB)
Flori, Cecilia [Perimeter Institute for Theoretical Studies, Waterloo, ON (Canada)
2013-06-01
Written by a leading researcher in the field. Concise course-tested textbook. Includes worked-out problems In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory's unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics - such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer - is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory. This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a ''neo-realist'' classical physics theory again.
Linear response theory for quantum open systems
Wei, J. H.; Yan, YiJing
2011-01-01
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
Quantum Theory of Continuum Optomechanics
Rakich, Peter
2016-01-01
We present the basic ingredients of continuum optomechanics, i.e. the suitable extension of cavity-optomechanical concepts to the interaction of photons and phonons in an extended waveguide. We introduce a real-space picture and argue which coupling terms may arise in leading order in the spatial derivatives. This picture allows us to discuss quantum noise, dissipation, and the correct boundary conditions at the waveguide entrance. The connections both to optomechanical arrays as well as to the theory of Brillouin scattering in waveguides are highlighted. We identify the 'strong coupling regime' of continuum optomechanics that may be accessible in future experiments.
Introduction to the quantum theory
Park, David
2005-01-01
More than a chance to gain new insights into physics, this book offers students the opportunity to look at what they already know about the subject in an improved way. Geared toward upper-level undergraduates and graduate students, this self-contained first course in quantum mechanics consists of two parts: the first covers basic theory, and the second part presents selected applications. Numerous problems of varying difficulty examine not only the steps of the proofs but also related ideas.Starting with an introduction that ventures beyond classical physics, the first part examines the physic
A quantum Rosetta Stone for the information paradox
Pando Zayas, Leopoldo A.
2014-11-01
The black hole information loss paradox epitomizes the contradictions between general relativity and quantum field theory. The AdS/conformal field theory (CFT) correspondence provides an implicit answer for the information loss paradox in black hole physics by equating a gravity theory with an explicitly unitary field theory. Gravitational collapse in asymptotically AdS spacetimes is generically turbulent. Given that the mechanism to read out the information about correlations functions in the field theory side is plagued by deterministic classical chaos, we argue that quantum chaos might provide the true Rosetta Stone for answering the information paradox in the context of the AdS/CFT correspondence.
A first course in topos quantum theory
Flori, Cecilia
2013-01-01
In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility o...
A mathematical theory for deterministic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, Gerard ' t [Institute for Theoretical Physics, Utrecht University (Netherlands); Spinoza Institute, Postbox 80.195, 3508 TD Utrecht (Netherlands)
2007-05-15
Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.
Dynamic statistical information theory
Institute of Scientific and Technical Information of China (English)
XING; Xiusan
2006-01-01
In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel
Quantum theory and the role of mind in nature
Stapp, Henry P
2001-01-01
Orthodox Copenhagen quantum theory renounces the quest to understand the reality in which we are imbedded, and settles for practical rules describing connections between our observations. Many physicist have regarded this renunciation of our effort to describe nature herself as premature, and John von Neumann reformulated quantum theory as a theory of an evolving objective universe interacting with human consciousness. This interaction is associated both in Copenhagen quantum theory and in von Neumann quantum theory with a sudden change that brings the objective physical state of a system in line with a subjectively felt psychical reality. The objective physical state is thereby converted from a material substrate to an informational and dispositional substrate that carries both the information incorporated into it by the psychical realities, and certain dispositions for the occurrence of future psychical realities. The present work examines and proposes solutions to two problems that have appeared to block t...
Ohya, Masanori
2011-01-01
This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.
Irreversibility, Information and Randomness in Quantum Measurements
Mayburov, S N
2012-01-01
Irreversibility in quantum measurements is considered from the point of quantum information theory. For that purpose the information transfer between the measured object S and measuring system O is analyzed. It's found that due to the principal constraints of quantum-mechanical origin, the information about the purity of S state isn't transferred to O during the measurement of arbitraryS observable V. Consequently O can't discriminate the pure and mixed S ensembles with the same . As the result, the random outcomes should be detected by O in V measurement for S pure ensemble of V eigenstate superposition. It's shown that the outcome probabilties obey to Born rule. The influence of O decoherence by its environment is studied, however the account of its effects doesn't change these results principally.
PREFACE: International Conference on Quantum Optics and Quantum Information (icQoQi) 2013
2014-11-01
Quantum Information can be understood as being naturally derived from a new understanding of information theory when quantum systems become information carriers and quantum effects become non negligible. Experiments and the realization of various interesting phenomena in quantum information within the established field of quantum optics have been reported, which has provided a very convenient framework for the former. Together, quantum optics and quantum information are among the most exciting areas of interdisciplinary research in modern day science which cover a broad spectrum of topics, from the foundations of quantum mechanics and quantum information science to the introduction of new types of quantum technologies and metrology. The International Conference on Quantum Optics and Quantum Information (icQoQi) 2013 was organized by the Faculty of Science, International Islamic University Malaysia with the objective of bringing together leading academic scientists, researchers and scholars in the domain of interest from around the world to share their experiences and research results about all aspects of quantum optics and quantum information. While the event was organized on a somewhat modest scale, it was in fact a rather fruitful meeting for established researchers and students as well, especially for the local scene where the field is relatively new. We would therefore, like to thank the organizing committee, our advisors and all parties for having made this event successful and last but not least would extend our sincerest gratitude to IOP for publishing these selected papers from icQoQi2013 in Journal of Physics: Conference Series.
Chaos and quantum Fisher information in the quantum kicked top
Institute of Scientific and Technical Information of China (English)
Wang Xiao-Qian; Ma Jian; Zhang Xi-He; Wang Xiao-Guang
2011-01-01
Quantum Fisher information is related to the problem of parameter estimation. Recently, a criterion has been proposed for entanglement in multipartite systems based on quantum Fisher information. This paper studies the behaviours of quantum Fisher information in the quantum kicked top model, whose classical correspondence can be chaotic. It finds that, first, detected by quantum Fisher information, the quantum kicked top is entangled whether the system is in chaotic or in regular case. Secondly, the quantum Fisher information is larger in chaotic case than that in regular case, which means, the system is more sensitive in the chaotic case.
Neutrix Calculus and Finite Quantum Field Theory
Ng, Y J
2004-01-01
In general, quantum field theories require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series in their interaction couplings. We propose to apply neutrix calculus, developed by van der Corput and Hadamard in connection with asymptotic series, to tackle divergent integrals, yielding finite renormalizations for the parameters in quantum field theories. We observe that quantum gravity theories are rendered more manageable, and that both renormalizable field theories and effective field theories can be accommodated in the framework of neutrix calculus.
Localisation in Quantum Field Theory
Balachandran, A P
2016-01-01
In nonrelativistic quantum mechanics , Born's principle of localisation is as follows: For a single particle, if a wave function $\\psi_K$ vanishes outside a spatial region $K$, it is said to be localised in $K$. In particular if a spatial region $K'$ is disjoint from $K$, a wave function $\\psi_{K'}$ localised in $K'$ is orthogonal to $\\psi_K$. Such a principle of localisation does not exist compatibly with relativity and causality in quantum field theory (Newton and Wigner) or interacting point particles (Currie,Jordan and Sudarshan).It is replaced by symplectic localisation of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localisation gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with `continuous' spin. This review outlines the basic principles underlying symplectic localisation and shows or mentions its deep implications. In particular, it has the potential to affect...
Interference Phenomena in Quantum Information
Stefanak, Martin
2010-01-01
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the description of quantum systems. In terms of physics we usually talk about the superposition principle valid for individual and composed quantum objects. So, while the source of interference is understandable it leads in fact to many counter-intuitive physical phenomena which puzzle physicists for almost hundred years. The present thesis studies interference in two seemingly disjoint fields of physics. However, both have strong links to quantum information processing and hence are related. In the first part we study the intriguing properties of quantum walks. In the second part we analyze a sophisticated application of wave packet dynamics in atoms and molecules for factorization of integers. The main body of the thesis is based on the original contributions listed separately...
Thermodynamics and the structure of quantum theory
Krumm, Marius; Barrett, Jonathan; Mueller, Markus P
2016-01-01
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Results in quantum gravity and general ideas of what a fundamental theory should look like suggest that thermodynamics plays a major role in the foundations of physics. In this paper, we address the question of which parts of quantum theory are already determined by compatibility with thermodynamics, and which aspects may still admit modification. We employ two postulates that any probabilistic theory with reasonable thermodynamic behavior should arguably satisfy. In the framework of generalized probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechan...
Unusual signs in quantum field theory
O'Connell, Donal
Quantum field theory is by now a mature field. Nevertheless, certain physical phenomena remain difficult to understand. This occurs in some cases because well-established quantum field theories are strongly coupled and therefore difficult to solve; in other cases, our current understanding of quantum field theory seems to be inadequate. In this thesis, we will discuss various modifications of quantum field theory which can help to alleviate certain of these problems, either in their own right or as a component of a greater computational scheme. The modified theories we will consider all include unusual signs in some aspect of the theory. We will also discuss limitations on what we might expect to see in experiments, imposed by sign constraints in the customary formulation of quantum field theory.
Enßlin, Torsten
2013-01-01
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms even for non-linear and non-Gaussian signal inference problems. IFT algorithms exploit spatial correlations of the signal fields and b...
Quartic quantum theory: an extension of the standard quantum mechanics
Zyczkowski, Karol
2008-01-01
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system ...
Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro
2015-10-01
We discuss foundational issues of quantum information biology (QIB)—one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from "traditional quantum biophysics". The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue that the information interpretation of quantum mechanics (its various forms were elaborated by Zeilinger and Brukner, Fuchs and Mermin, and D' Ariano) is the most natural interpretation of QIB. Biologically QIB is based on two principles: (a) adaptivity; (b) openness (bio-systems are fundamentally open). These principles are mathematically represented in the framework of a novel formalism— quantum adaptive dynamics which, in particular, contains the standard theory of open quantum systems.
Directory of Open Access Journals (Sweden)
Gift S.
2009-01-01
Full Text Available In this paper, a new Quantum Theory of Magnetic Interaction is proposed. This is done under a relaxation of the requirement of covariance for Lorentz Boost Transformations. A modified form of local gauge invariance in which fermion field phase is allowed to vary with each space point but not each time point, leads to the introduction of a new compensatory field different from the electromagnetic field associated with the photon. This new field is coupled to the magnetic flux of the fermions and has quanta called magnatons, which are massless spin 1 particles. The associated equation of motion yields the Poisson equation for magnetostatic potentials. The magnatons mediate the magnetic interaction between magnetic dipoles including magnets and provide plausi- ble explanations for the Pauli exclusion principle, Chemical Reactivity and Chemical Bonds. This new interaction has been confirmed by numerical experiments. It estab- lishes magnetism as a force entirely separate from the electromagnetic interaction and converts all of classical magnetism into a quantum theory.
Quantum Information Science: An Update
Kwek, L. C.; Zen, Freddy P.
2016-08-01
It is now roughly thirty years since the incipient ideas on quantum information science was concretely formalized. Over the last three decades, there has been much development in this field, and at least one technology, namely devices for quantum cryptography, is now commercialized. Yet, the holy grail of a workable quantum computing machine still lies faraway at the horizon. In any case, it took nearly several centuries before the vacuum tubes were invented after the first mechanical calculating were constructed, and several decades later, for the transistor to bring the current computer technology to fruition. In this review, we provide a short survey of the current development and progress in quantum information science. It clearly does not do justice to the amount of work in the past thirty years. Nevertheless, despite the modest attempt, this review hopes to induce younger researchers into this exciting field.
Quantum chemistry simulation on quantum computers: theories and experiments.
Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng
2012-07-14
It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.
Contract Signature Using Quantum Information
De Sousa, P B M; Ramos, Rubens Viana; Sousa, Paulo Benicio Melo de
2006-01-01
This paper describes how to perform contract signature in a fair way using quantum information. The protocol proposed permits two partners, users of a communication network, to exchange their signatures with non-repudiation. For this, we assume that there is a trustable arbitrator, responsible for the authentication of the signers and that performs a central task in a quantum teleportation protocol of the XOR function between two classical bits.
Quantum information, oscillations and the psyche
Martin, F; Carminati, G Galli
2010-01-01
In this paper, taking the theory of quantum information as a model, we consider the human unconscious, pre-consciousness and consciousness as sets of quantum bits (qubits). We view how there can be communication between these various qubit sets. In doing this we are inspired by the theory of nuclear magnetic resonance. In this way we build a model of handling a mental qubit with the help of pulses of a mental field. Starting with an elementary interaction between two qubits we build two-qubit quantum logic gates that allow information to be transferred from one qubit to the other. In this manner we build a quantum process that permits consciousness to ``read{''} the unconscious and vice versa. The elementary interaction, e.g. between a pre-consciousness qubit and a consciousness one, allows us to predict the time evolution of the pre-consciousness + consciousness system in which pre-consciousness and consciousness are quantum entangled. This time evolution exhibits Rabi oscillations that we name mental Rabi o...
Introductory Lectures on Quantum Field Theory
Alvarez-Gaumé, Luís
2014-01-01
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String Theory.
Einstein's strugges with quantum theory a reappraisal
Home, Dipankar
2007-01-01
Einstein’s Struggles with Quantum Theory: A Reappraisal by Dipankar Home and Andrew Whitaker provides a detailed account of Albert Einstein’s thinking in regard to quantum physics. Until recently, most of Einstein’s views on quantum physics were dismissed and even ridiculed; some critics even suggested that Einstein was not able to grasp the complexities of the formalism of quantum theory and subtleties of the standard interpretation of this theory known as the Copenhagen interpretation put forward by Niels Bohr and his colleagues. But was that true? Modern scholarship argues otherwise, insist Drs. Home and Whitaker, who painstakingly explain the questions Einstein raised as well as offer a detailed discussion of Einstein’s position and major contributions to quantum theory, connecting them with contemporary studies on fundamental aspects of this theory. This unique book presents a mathematical as well as a non-mathematical route through the theories, controversies, and investigations, making the disc...
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory
Jerusalem Lectures on Black Holes and Quantum Information
Harlow, Daniel
2014-01-01
In these lectures I give an introduction to the quantum physics of black holes, including recent developments based on quantum information theory such as the firewall paradox and its various cousins. I also give an introduction to holography and the AdS/CFT correspondence, focusing on those aspects which are relevant for the black hole information problem.
Quantum mechanics II a second course in quantum theory
Landau, Rubin H
2004-01-01
Here is a readable and intuitive quantum mechanics text that covers scattering theory, relativistic quantum mechanics, and field theory. This expanded and updated Second Edition - with five new chapters - emphasizes the concrete and calculable over the abstract and pure, and helps turn students into researchers without diminishing their sense of wonder at physics and nature.As a one-year graduate-level course, Quantum Mechanics II: A Second Course in Quantum Theory leads from quantum basics to basic field theory, and lays the foundation for research-oriented specialty courses. Used selectively, the material can be tailored to create a one-semester course in advanced topics. In either case, it addresses a broad audience of students in the physical sciences, as well as independent readers - whether advanced undergraduates or practicing scientists
A Quantum Rosetta Stone for the Information Paradox
Zayas, Leopoldo A Pando
2014-01-01
The black hole information loss paradox epitomizes the contradictions between general relativity and quantum field theory. The AdS/CFT correspondence provides an implicit answer for the information loss paradox in black hole physics by equating a gravity theory with an explicitly unitary field theory. Gravitational collapse in asymptotically AdS spacetimes is generically turbulent. Given that the mechanism to read out the information about correlations functions in the field theory side is plagued by deterministic classical chaos, we argue that quantum chaos might provide the true Rosetta Stone for answering the information paradox in the context of the AdS/CFT correspondence.
Theory of Quantum Loschmidt Echoes
Prosen, T.; Seligman, T. H.; Žnidarič, M.
In this paper we review our recent work on the theoretical approach to quantum Loschmidt echoes, i.e., various properties of the so-called echo dynamics -- the composition of forward and backward time evolutions generated by two slightly different Hamiltonians, such as the state autocorrelation function (fidelity) and the purity of a reduced density matrix traced over a subsystem (purity fidelity). Our main theoretical result is a linear response formalism, expressing the fidelity and purity fidelity in terms of integrated time autocorrelation function of the generator of the perturbation. Surprisingly, this relation predicts that the decay of fidelity is the slower the faster the decay of correlations. In particular for a static (time-independent) perturbation, and for non-ergodic and non-mixing dynamics where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a time scale ∝ 1/δ as opposed to mixing dynamics where the fidelity is found to decay exponentially on a time-scale ∝ 1/δ2, where δ is a strength of perturbation. A detailed discussion of a semi-classical regime of small effective values of Planck constant hbar is given where classical correlation functions can be used to predict quantum fidelity decay. Note that the correct and intuitively expected classical stability behavior is recovered in the classical limit hbarto 0, as the two limits δto 0 and hbarto 0 do not commute. The theoretical results are demonstrated numerically for two models, the quantized kicked top and the multi-level Jaynes Cummings model. Our method can for example be applied to the stability analysis of quantum computation and quantum information processing.
Quantum Mechanics as a Principle Theory
Bub, J
1999-01-01
I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the Quantum World (Cambridge: Cambridge University Press, 1999).
De Sitter Symmetry and Quantum Theory
Lev, Felix M
2011-01-01
De Sitter symmetry on quantum level implies that operators describing a given system satisfy commutation relations of the de Sitter algebra. This approach gives a new perspective on fundamental notions of quantum theory. We discuss applications of the approach to the cosmological constant problem, gravity and particle theory.
The conceptual basis of Quantum Field Theory
Hooft, G. 't
2007-01-01
Relativistic Quantum Field Theory is a mathematical scheme to describe the sub-atomic particles and forces. The basic starting point is that the axioms of Special Relativity on the one hand and those of Quantum Mechanics on the other, should be combined into one theory. The fundamental ingredients f
A nilpotent symmetry of quantum gauge theories
Lahiri, Amitabha
2001-09-01
For the Becchi-Rouet-Stora-Tyutin invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher-order ghost terms are also possible.
Quantum tunneling and field electron emission theories
Liang, Shi-Dong
2013-01-01
Quantum tunneling is an essential issue in quantum physics. Especially, the rapid development of nanotechnology in recent years promises a lot of applications in condensed matter physics, surface science and nanodevices, which are growing interests in fundamental issues, computational techniques and potential applications of quantum tunneling. The book involves two relevant topics. One is quantum tunneling theory in condensed matter physics, including the basic concepts and methods, especially for recent developments in mesoscopic physics and computational formulation. The second part is the f
Quantum Computers: A New Paradigm in Information Technology
Directory of Open Access Journals (Sweden)
Mahesh S. Raisinghani
2001-01-01
Full Text Available The word 'quantum' comes from the Latin word quantus meaning 'how much'. Quantum computing is a fundamentally new mode of information processing that can be performed only by harnessing physical phenomena unique to quantum mechanics (especially quantum interference. Paul Benioff of the Argonne National Laboratory first applied quantum theory to computers in 1981 and David Deutsch of Oxford proposed quantum parallel computers in 1985, years before the realization of qubits in 1995. However, it may be well into the 21st century before we see quantum computing used at a commercial level for a variety of reasons discussed in this paper. The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This paper discusses some of the current advances, applications, and chal-lenges of quantum computing as well as its impact on corporate computing and implications for management. It shows how quantum computing can be utilized to process and store information, as well as impact cryptography for perfectly secure communication, algorithmic searching, factorizing large numbers very rapidly, and simulating quantum-mechanical systems efficiently. A broad interdisciplinary effort will be needed if quantum com-puters are to fulfill their destiny as the world's fastest computing devices.
Dynamical Equations for Quantum Information and Application in Information Channel
Institute of Scientific and Technical Information of China (English)
BI Qiao; XING Xiu-San; H. E. Ruda
2005-01-01
@@ We establish several dynamical equations for quantum information density. It is demonstrated that quantum information density shares the same formalism of the Liouville equation, subdynamics kinetic equation and Fokker-Planck equation as the density operator and also possesses the superposition property. These allow one to use quantum information density directly to model quantum information. The kinetic equations for quantum information density reveal that the dynamical process of quantum information may be related to dissipative,Markovian, or diffusional information flows, together causing irreversibility. Finally, we discuss superposition of quantum information density, which allows us to construct a quantum information channel in the coherent state representation using harmonic oscillator based encoded quantum information, and obtain a formula for quantum dynamical mutual information.
Information processing in convex operational theories
Energy Technology Data Exchange (ETDEWEB)
Barnum, Howard Nelch [Los Alamos National Laboratory; Wilce, Alexander G [SUSQUEHANNA UNIV
2008-01-01
In order to understand the source and extent of the greater-than-classical information processing power of quantum systems, one wants to characterize both classical and quantum mechanics as points in a broader space of possible theories. One approach to doing this, pioneered by Abramsky and Coecke, is to abstract the essential categorical features of classical and quantum mechanics that support various information-theoretic constraints and possibilities, e.g., the impossibility of cloning in the latter, and the possibility of teleportation in both. Another approach, pursued by the authors and various collaborators, is to begin with a very conservative, and in a sense very concrete, generalization of classical probability theory--which is still sufficient to encompass quantum theory--and to ask which 'quantum' informational phenomena can be reproduced in this much looser setting. In this paper, we review the progress to date in this second programme, and offer some suggestions as to how to link it with the categorical semantics for quantum processes developed by Abramsky and Coecke.
Quantum Information from Graviton-Matter Gas
Directory of Open Access Journals (Sweden)
Lukasz-Andrzej Glinka
2007-09-01
Full Text Available We present basics of conceptually new-type way for explaining of the origin, evolution and current physical properties of our Universe from the graviton-matter gas viewpoint. Quantization method for the Friedmann-Lemaitre Universe based on the canonical Hamilton equations of motion is proposed and quantum information theory way to physics of the Universe is showed. The current contribution from the graviton-matter gas temperature in quintessence approximation is discussed.
Synchronicity, Quantum Information and the Psyche
Martin, Francois; Galli Carminati, Giuliana
2009-01-01
In this paper we describe synchronicity phenomena. As an explanation of these phenomena we propose quantum entanglement between the psychic realm known as the "unconscious" and also the classical illusion of the collapse of the wave-function. Then, taking the theory of quantum information as a model we consider the human unconscious, pre-consciousness and consciousness as sets of quantum bits (qu-bits). We analyze how there can be communication between these various qu-bit sets. In doing this we are inspired by the theory of nuclear magnetic resonance. In this manner we build quantum processes that permit consciousness to "read" the unconscious and vice-versa. The most elementary interaction, e.g. between a pre-consciousness qu-bit and a consciousness one, allows us to predict the time evolution of the pre-consciousness + consciousness system in which pre-consciousness and consciousness are quantum entangled. This time evolution exhibits Rabi oscillations that we name mental Rabi oscillations. This time evolu...
Haag's theorem in renormalised quantum field theories
Klaczynski, Lutz
2016-01-01
We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.
Reconstruction and Reinvention in Quantum Theory
Dickson, Michael
2015-10-01
I consider the fact that there are a number of interesting ways to `reconstruct' quantum theory, and suggest that, very broadly speaking, a form of `instrumentalism' makes good sense of the situation. This view runs against some common wisdom, which dismisses instrumentalism as `cheap'. In contrast, I consider how an instrumentalist might think about the reconstruction theorems, and, having made a distinction between `reconstructing' quantum theory and `reinventing' quantum theory, I suggest that there is an adequate (not `cheap') instrumentalist approach to the theory (and to these theorems) that invokes both.
The structure of states and maps in quantum theory
Indian Academy of Sciences (India)
Sudhavathani Simon; S P Rajagopalan; R Simon
2009-09-01
The structure of statistical state spaces in the classical and quantum theories are compared in an interesting and novel manner. Quantum state spaces and maps on them have rich convex structures arising from the superposition principle and consequent entanglement. Communication channels (physical processes) in the quantum scheme of things are in one-to-one correspondence with completely positive maps. Positive maps which are not completely positive do not correspond to physical processes. Nevertheless they prove to be invaluable mathematical tools in establishing or witnessing entanglement of mixed states. We consider some of the recent developments in our understanding of the convex structure of states and maps in quantum theory, particularly in the context of quantum information theory.
Problems and solutions in quantum computing and quantum information
Steeb, Willi-Hans
2012-01-01
Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book supplies a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. All the important concepts and topics such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, deportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, number states and Bose operators, coherent states, squeezed states, Gaussian states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton opera...
Quantum field theory for the gifted amateur
Lancaster, Tom
2014-01-01
Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in ...
Quantum Information Processing and Quantum Error Correction An Engineering Approach
Djordjevic, Ivan
2012-01-01
Quantum Information Processing and Quantum Error Correction is a self-contained, tutorial-based introduction to quantum information, quantum computation, and quantum error-correction. Assuming no knowledge of quantum mechanics and written at an intuitive level suitable for the engineer, the book gives all the essential principles needed to design and implement quantum electronic and photonic circuits. Numerous examples from a wide area of application are given to show how the principles can be implemented in practice. This book is ideal for the electronics, photonics and computer engineer
A group theoretic approach to quantum information
Hayashi, Masahito
2017-01-01
This textbook is the first one addressing quantum information from the viewpoint of group symmetry. Quantum systems have a group symmetrical structure. This structure enables to handle systematically quantum information processing. However, there is no other textbook focusing on group symmetry for quantum information although there exist many textbooks for group representation. After the mathematical preparation of quantum information, this book discusses quantum entanglement and its quantification by using group symmetry. Group symmetry drastically simplifies the calculation of several entanglement measures although their calculations are usually very difficult to handle. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc. Usually it is very difficult to derive the optimal quantum information processes without asymptotic setting of these topics. However, group symmetry allows to derive these optimal solu...
Dynamical symmetry breaking in quantum field theories
Miransky, Vladimir A
1993-01-01
The phenomenon of dynamical symmetry breaking (DSB) in quantum field theory is discussed in a detailed and comprehensive way. The deep connection between this phenomenon in condensed matter physics and particle physics is emphasized. The realizations of DSB in such realistic theories as quantum chromodynamics and electroweak theory are considered. Issues intimately connected with DSB such as critical phenomenona and effective lagrangian approach are also discussed.
Renormalizable Quantum Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WU Ning
2002-01-01
The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.
Quantum gravity from theory to experimental search
Kiefer, Claus; Lämmerzahl, Claus
2003-01-01
The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.
Quantum information processing with finite resources mathematical foundations
Tomamichel, Marco
2016-01-01
This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigation possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. F...
Quantum Yang-Mills theory: an overview of a programme
Milsted, Ashley
2016-01-01
We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for $\\mathbb{Z}/2\\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalisation ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalisations. ...
Quantum field theory a tourist guide for mathematicians
Folland, Gerald B
2008-01-01
Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theor...
Information Theory: a Multifaceted Model of Information
Directory of Open Access Journals (Sweden)
Mark Burgin
2003-06-01
Full Text Available A contradictory and paradoxical situation that currently exists in information studies can be improved by the introduction of a new information approach, which is called the general theory of information. The main achievement of the general theory of information is explication of a relevant and adequate definition of information. This theory is built as a system of two classes of principles (ontological and sociological and their consequences. Axiological principles, which explain how to measure and evaluate information and information processes, are presented in the second section of this paper. These principles systematize and unify different approaches, existing as well as possible, to construction and utilization of information measures. Examples of such measures are given by ShannonÃ¢Â€Â™s quantity of information, algorithmic quantity of information or volume of information. It is demonstrated that all other known directions of information theory may be treated inside general theory of information as its particular cases.
Quantum Limitations on the Storage and Transmission of Information
Bekenstein, J D; Bekenstein, Jacob D.; Schiffer, Marcelo
1990-01-01
Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are here described. Quantum channel capacity theory is reviewed for both steady state and burst communication. An analytic approximation is given for the maximum signal information possible with occupation number signal states as a function of mean signal energy. A theorem guaranteeing that these states are optimal for communication is proved. A heuristic "proof" of the linear bound on communication is given, followed by rigorous proofs for signals with specified mean energy, and for signals with given energy budget. And systems of many parallel quantum channels are shown to obey the linear bound for a natural channel architecture. The time--energy uncertainty principle is reformulated in information language by means of the linear bound. The quantum bound on information storage capacity of quantum mechanical and quantum field devices is reviewed. A sim...
Suhov, Y.
We begin with the definition of information gained by knowing that an event A has occurred: iota (A) = -log_2 {{P}}(A). (A dual point of view is also useful (although more evasive), where iota (A) is the amount of information needed to specify event A.) Here and below {{P}} stands for the underlying probability distribution. So the rarer an event A, the more information we gain if we know it has occurred. (More broadly, the rarer an event A, the more impact it will have. For example, the unlikely event that occurred in 1938 when fishermen caught a coelacanth - a prehistoric fish believed to be extinct - required a significant change to beliefs about evolution and biology. On the other hand, the likely event of catching a herring or a tuna would hardly imply any change in theories.)
Quantum Information Processing in the Radical-Pair Mechanism
Mouloudakis, K
2016-01-01
Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We here show that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering the quantum information extracted during the reaction we unravel new magnetic-field effects not conveyed by reaction yields.
The conceptual framework of quantum field theory
Duncan, Anthony
2012-01-01
The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "utilitarian" treatments of the subject. The book is divided into four parts, entitled respectively "Origins", "Dynamics", "Symmetries", and "Scales". The emphasis is conceptual - the aim is to build the theory up systematically from some clearly stated foundational concepts - and therefore to a large extent anti-historical, but two historical Chapters ("Origins") are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The "Dynamics" section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quan...
Quantum Field Theory in a Semiotic Perspective
Günter Dosch, Hans; Sieroka, Norman
2005-01-01
Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincaré, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly ac...
Supergeometry in locally covariant quantum field theory
Hack, Thomas-Paul; Schenkel, Alexander
2015-01-01
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the en...
Quartic quantum theory: an extension of the standard quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Zyczkowski, Karol [Institute of Physics, Jagiellonian University, Krakow (Poland); Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland)], E-mail: karol@tatry.if.uj.edu.pl
2008-09-05
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be embedded inside a higher-dimensional convex body M{sub N}{sup Q} of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in the N-dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory works for simple quantum systems and is shown to be a non-trivial generalization of the standard quantum theory for which K = N{sup 2}. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. By imposing even stronger constraints one arrives at the classical theory, for which K = N.
Emergent "Quantum" Theory in Complex Adaptive Systems.
Minic, Djordje; Pajevic, Sinisa
2016-04-30
Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.
Minimum-cost quantum measurements for quantum information
Wallden, Petros; Dunjko, Vedran; Andersson, Erika
2014-01-01
Knowing about optimal quantum measurements is important for many applications in quantum information and quantum communication. However, deriving optimal quantum measurements is often difficult. We present a collection of results for minimum-cost quantum measurements, and give examples of how they can be used. Among other results, we show that a minimum-cost measurement for a set of given pure states is formally equivalent to a minimum-error measurement for certain mixed states of those same ...
Multichannel Quantum Defect Theory a Quantum Poincaré Map
Leyvraz, F; Lombardi, M; Seligman, T H
1999-01-01
The multichannel quantum defect theory (MQDT) can be reinterpreted as a quantum Poincare map in representation of angular momentum. We chose a simplified model for Rydberg molecules where the limit classical map is known and MQDT delivers the exact quantization of this map, which is a finite unitary matrix by construction. The result has two important implications: On one hand we have a paradigm of a true quantum Poincare map without semi-classical input and on the other hand we get an entirely new insight into the significance of MQDT. We obtain a new signature of quantum chaos and a more reliable method to calculate eigenfunctions in MQDT.
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
Representation Theory of Algebraic Groups and Quantum Groups
Gyoja, A; Shinoda, K-I; Shoji, T; Tanisaki, Toshiyuki
2010-01-01
Invited articles by top notch expertsFocus is on topics in representation theory of algebraic groups and quantum groupsOf interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics
Quantum theory of Thomson scattering
Crowley, B. J. B.; Gregori, G.
2014-12-01
The general theory of the scattering of electromagnetic radiation in atomic plasmas and metals, in the non-relativistic regime, in which account is taken of the Kramers-Heisenberg polarization terms in the Hamiltonian, is described from a quantum mechanical viewpoint. As well as deriving the general formula for the double differential Thomson scattering cross section in an isotropic finite temperature multi-component system, this work also considers closely related phenomena such as absorption, refraction, Raman scattering, resonant (Rayleigh) scattering and Bragg scattering, and derives many essential relationships between these quantities. In particular, the work introduces the concept of scattering strength and the strength-density field which replaces the normal particle density field in the standard treatment of scattering by a collection of similar particles and it is the decomposition of the strength-density correlation function into more familiar-looking components that leads to the final result. Comparisons are made with previous work, in particular that of Chihara [1].
IS PT -SYMMETRIC QUANTUM THEORY FALSE AS A FUNDAMENTAL THEORY?
Directory of Open Access Journals (Sweden)
Miloslav Znojil
2016-06-01
Full Text Available Yi-Chan Lee et al. claim (cf. Phys. Rev. Lett. 112, 130404 (2014 that the “recent extension of quantum theory to non-Hermitian Hamiltonians” (which is widely known under the nickname of “PT-symmetric quantum theory” is “likely false as a fundamental theory”. By their opinion their results “essentially kill any hope of PT-symmetric quantum theory as a fundamental theory of nature”. In our present text we explain that their toy-model-based considerations are misleading and that they do not imply any similar conclusions.
Is quantum theory compatible with special relativity?
Indian Academy of Sciences (India)
M Bahrami; A Shafiee; M Saravani; M Golshani
2013-03-01
How a proposed quantum nonlocal phenomenon could be incompatible with the requirements of special relativity is studied. To show this, the least set of assumptions about the formalism and the interpretation of non-relativistic quantum theory is considered. Then, without any reference to the collapse assumption or any other stochastic processes, an experiment is proposed, involving two quantum systems, that interacted at an arbitrary time, with results which seem to be in conflict with requirements of special relativity.
An introduction to information theory
Reza, Fazlollah M
1994-01-01
Graduate-level study for engineering students presents elements of modern probability theory, information theory, coding theory, more. Emphasis on sample space, random variables, capacity, etc. Many reference tables and extensive bibliography. 1961 edition.
Pilot-wave theory and quantum fields
Struyve, Ward
2010-10-01
Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schrödinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.
Design Theory in Information Systems
Directory of Open Access Journals (Sweden)
Shirley Gregor
2002-11-01
Full Text Available The aim of this paper is to explore an important category of information systems knowledge that is termed “design theory”. This knowledge is distinguished as the fifth of five types of theory: (i theory for analysing and describing, (ii theory for understanding, (iii theory for predicting, (iv theory for explaining and predicting, and (v theory for design and action. Examples of design theory in information systems are provided, with associated research methods. The limited understanding and recognition of this type of theory in information systems indicates that further debate concerning its nature and role in our discipline is needed.
Maximum Information and Quantum Prediction Algorithms
McElwaine, J N
1997-01-01
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm uses a maximum information principle to select from among the consistent sets formed by projections defined by the Schmidt decomposition. The algorithm unconditionally predicts the possible events in closed quantum systems and ascribes probabilities to these events. A simple spin model is described and a complete classification of all exactly consistent sets of histories formed from Schmidt projections in the model is proved. This result is used to show that for this example the algorithm selects a physically realistic set. Other tentative suggestions in the literature for set selection algorithms using ideas from information theory are discussed.
Holism, Physical Theories and Quantum Mechanics
Seevinck, M P
2004-01-01
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. I propose an operational criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if some determination (measurement) of the global properties in the theory which can be determined by global measurements, can not be implemented by local operations and classical communication. This approach is contrasted with the well known approaches to holism in terms of supervenience. I will argue that the latter have a limited scope and need to be extended using the criterion for holism proposed here in order to satisfactory address the issue for physical theories. I formalize this criterion for classical particle physics and Bohmian mechanics as represented on a Cartesian phase and configuration space, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum ope...
"Scars" connect classical and quantum theory
Monteiro, T
1990-01-01
Chaotic systems are unstable and extremely sensitive to initial condititions. So far, scientists have been unable to demonstrate that the same kind of behaviour exists in quantum or microscopic systems. New connections have been discovered though between classical and quantum theory. One is the phenomena of 'scars' which cut through the wave function of a particle (1 page).
Designing quantum information processing via structural physical approximation
Bae, Joonwoo
2017-10-01
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.
Teaching Quantum Theory in the Introductory Course.
Hobson, Art
1996-01-01
Describes an approach to teaching quantum theory without math with emphasis on some innovative approaches and topics such as nonlocality and Bell's theorem. Written in the form of suggestions to prospective instructors. (JRH)
Parameterized quantum field theory without Haag's theorem
Seidewitz, Ed
2015-01-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that quantum field theory can be formulated, using an invariant, fifth path parameter in addition to the usual four position parameters, in such a way that Haag's theorem no longer applies, but such that the Dyson perturbation expansion for the sc...
Molecular quantum dynamics from theory to applications
Gatti, Fabien
2014-01-01
Emphasizing fundamental educational concepts, this book offers an accessible introduction that covers eigenstates, wave packets, quantum mechanical resonances and more. Examples show that high-level experiments and theory must work closely together.
Density functional theory in quantum chemistry
Tsuneda, Takao
2014-01-01
This book examines density functional theory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.
Field redefinition invariance in quantum field theory
Apfeldorf, K M; Apfeldorf, Karyn M; Ordonez, Carlos
1994-01-01
We investigate the consequences of field redefinition invariance in quantum field theory by carefully performing nonlinear transformations in the path integral. We first present a ``paradox'' whereby a 1+1 freemassless scalar theory on a Minkowskian cylinder is reduced to an effectively quantum mechanical theory. We perform field redefinitions both before and after reduction to suggest that one should not ignore operator ordering issues in quantum field theory. We next employ a discretized version of the path integral for a free massless scalar quantum field in d dimensions to show that beyond the usual jacobian term, an infinite series of divergent ``extra'' terms arises in the action whenever a nonlinear field redefinition is made. The explicit forms for the first couple of these terms are derived. We evaluate Feynman diagrams to illustrate the importance of retaining the extra terms, and conjecture that these extra terms are the exact counterterms necessary to render physical quantities invariant under fie...
Quantum dots for quantum information technologies
2017-01-01
This book highlights the most recent developments in quantum dot spin physics and the generation of deterministic superior non-classical light states with quantum dots. In particular, it addresses single quantum dot spin manipulation, spin-photon entanglement and the generation of single-photon and entangled photon pair states with nearly ideal properties. The role of semiconductor microcavities, nanophotonic interfaces as well as quantum photonic integrated circuits is emphasized. The latest theoretical and experimental studies of phonon-dressed light matter interaction, single-dot lasing and resonance fluorescence in QD cavity systems are also provided. The book is written by the leading experts in the field.
Logarithm Versus Square Root:Comparing Quantum Fisher Information
Institute of Scientific and Technical Information of China (English)
LUO Shun-Long
2007-01-01
In classical statistics,the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities.In quantum theory,this uniqueness breaks down,and there are many natural quantum analogues of the Fisher information,among which two particular versions distinguish themselves by their intuitive and informational significance:The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement,and is defined via the square root of the density operator.The second arises from Helstrom's study of quantum detection in 1967,and is defined via the symmetric logarithmic derivative.The aim of this paper is to compare these two versions of quantum Fisher information,and to establish two informational inequalities relating them.
How much a quantum measurement is informative?
Energy Technology Data Exchange (ETDEWEB)
Dall' Arno, Michele [Graduate School of Information Science, Nagoya University, Nagoya, 464-8601 (Japan); ICFO-Institut de Ciencies Fotoniques, E-08860 Castelldefels, Barcelona (Spain); Quit Group, Dipartimento di Fisica, via Bassi 6, I-27100 Pavia (Italy); D' Ariano, Giacomo Mauro [Quit Group, Dipartimento di Fisica, via Bassi 6, I-27100 Pavia, Italy and Istituto Nazionale di Fisica Nucleare, Gruppo IV, via Bassi 6, I-27100 Pavia (Italy); Sacchi, Massimiliano F. [Quit Group, Dipartimento di Fisica, via Bassi 6, I-27100 Pavia, Italy and Istituto di Fotonica e Nanotecnologie (INF-CNR), P.zza L. da Vinci 32, I-20133, Milano (Italy)
2014-12-04
The informational power of a quantum measurement is the maximum amount of classical information that the measurement can extract from any ensemble of quantum states. We discuss its main properties. Informational power is an additive quantity, being equivalent to the classical capacity of a quantum-classical channel. The informational power of a quantum measurement is the maximum of the accessible information of a quantum ensemble that depends on the measurement. We present some examples where the symmetry of the measurement allows to analytically derive its informational power.
The quantum theory of nonlinear optics
Drummond, Peter D
2014-01-01
Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamic...
Local, nonlocal quantumness and information theoretic measures
Agrawal, Pankaj; Sazim, Sk; Chakrabarty, Indranil; Pati, Arun K.
2016-08-01
It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by information theoretic quantities such as quantum discord, but not by the conventional measures of entanglement. We argue that a state displays quantumness, that can be of local and nonlocal origin. Information theoretic measures not only characterize the nonlocal quantumness, but also the local quantumness, such as the “local superposition”. This can be a reason, why such measures are nonzero, when there is no entanglement. We consider a generalized version of the Werner state to demonstrate the interplay of local quantumness, nonlocal quantumness and classical mixedness of a state.
Resource Theory of Quantum States Out of Thermal Equilibrium
Brandão, Fernando G. S. L.; Horodecki, Michał; Oppenheim, Jonathan; Renes, Joseph M.; Spekkens, Robert W.
2013-01-01
The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here, we return to the basic questions of thermodynamics using the formalism of resource t...
The Resource Theory of Quantum States Out of Thermal Equilibrium
Brandão, Fernando G. S. L.; Horodecki, Michał; Oppenheim, Jonathan; Renes, Joseph M.; Spekkens, Robert W.
2011-01-01
The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here we return to the basic questions of thermodynamics using the formalism of resource th...
Quantum field theory II introductions to quantum gravity, supersymmetry and string theory
Manoukian, Edouard B
2016-01-01
This book takes a pedagogical approach to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics. The first part of the book introduces quantum gravity, without requiring previous knowledge of general relativity (GR). The necessary geometrical aspects are derived afresh leading to explicit general Lagrangians for gravity, including that of general relativity. The quantum aspect of gravitation, as described by the graviton, is introduced and perturbative quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute the one-loop contribution to the theory and renormalizability aspects of the perturbative theory are also discussed. This follows by introducing only the very basics of a non-perturbative, background-independent, formulation of quantum gravity, referred to as “loop quantum gravity”, which gives rise to a quantization of space. In the second part the author in...
Quantum gravity from descriptive set theory
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S
2004-03-01
We start from Hilbert's criticism of the axioms of classical geometry and the possibility of abandoning the Archimedean axiom. Subsequently we proceed to the physical possibility of a fundamental limitation on the smallest length connected to certain singular points in spacetime and below which measurements become meaningless, Finally we arrive at the conclusion that maximising the Hawking-Bekenstein informational content of spacetime makes the existence of a transfinite geometry for physical 'spacetime' not only plausible but probably inevitable. The main part of the paper is then concerned with a proposal for a mathematical description of a transfinite, non-Archimedean geometry using descriptive set theory. Nevertheless, and despite all abstract mathematics, we remain quite close to similar lines of investigation initiated by physicists like A. Wheeler, D. Finkelstein and G. 'tHooft. In particular we introduce a logarithmic gauge transformation linking classical gravity with the electro weak via a version of informational entropy. That way we may claim to have accomplished an important step towards a general theory of quantum gravity using {epsilon}{sup ({infinity}}{sup )} and complexity theory and finding that {alpha}{sub G}=(2){sup {alpha}}{sup -bar{sub ew-1}} congruent with (1.7)(10){sup 38} where {alpha}{sub G} is the dimensionless Newton gravity constant, and {alpha}{sub ew}{approx_equal}128 is the fine structure constant at the electro weak scale.
Emergence Of A Classical World From Within Quantum Theory
Poulin, D
2005-01-01
The starting point of this dissertation is that a quantum state represents the observer's knowledge about the system of interest. As it has been pointed out several times by the opponents of this epistemic interpretation, it is difficult to reconcile this point of view with our common notion of “physical reality”, which exists independently of our monitoring, and can be discovered without disturbance. Indeed, if quantum theory is correct, it should apply to classical systems—including measurement devices—as well as to any other system. In this dissertation, we will study the quantum mechanisms responsible for our perception of the world and demonstrate how they lead to the emergence of an operational objective reality from within quantum theory: several observers gathering information through these mechanisms will arrive at a common consensus about the properties of the world. The two mechanisms we study in great detail are the redundant proliferation of information in ...
Pragmatic Information in Quantum Mechanics
Roederer, Juan G
2015-01-01
An objective definition of pragmatic information and the consideration of recent results about information processing in the human brain can help overcome some traditional difficulties with the interpretation of quantum mechanics. Rather than attempting to define information ab initio, I introduce the concept of interaction between material bodies as a primary concept. Two distinct categories can be identified: 1) Interactions which can always be reduced to a superposition of physical interactions (forces) between elementary constituents; 2) Interactions between complex bodies which cannot be reduced to a superposition of interactions between parts, and in which patterns and forms (in space and/or time) play the determining role. Pragmatic information is then defined as the correspondence between a given pattern and the ensuing pattern-specific change. I will show that pragmatic information is a biological concept that plays no active role in the purely physical domain; it only does so when a living organism ...
Cosmological perturbation theory and quantum gravity
Brunetti, Romeo; Hack, Thomas-Paul; Pinamonti, Nicola; Rejzner, Katarzyna
2016-01-01
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Cosmological perturbation theory and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)
2016-08-04
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Quantum coding theory with realistic physical constraints
Yoshida, Beni
2010-01-01
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum error-correcting codes with geometrically local generators, (b) the feasibility of a self-correcting quantum memory. To investigate these problems, we study stabilizer codes supported by local interaction terms with translation and scale symmetries on a $D$-dimensional lattice. Our analysis uses the notion of topology emerging in geometric shapes of logical operators, which sheds a surprising new light on theory of quantum codes with physical constraints.
Quantum theory of electroabsorption in semiconductor nanocrystals.
Tepliakov, Nikita V; Leonov, Mikhail Yu; Baranov, Alexander V; Fedorov, Anatoly V; Rukhlenko, Ivan D
2016-01-25
We develop a simple quantum-mechanical theory of interband absorption by semiconductor nanocrystals exposed to a dc electric field. The theory is based on the model of noninteracting electrons and holes in an infinitely deep quantum well and describes all the major features of electroabsorption, including the Stark effect, the Franz-Keldysh effect, and the field-induced spectral broadening. It is applicable to nanocrystals of different shapes and dimensions (quantum dots, nanorods, and nanoplatelets), and will prove useful in modeling and design of electrooptical devices based on ensembles of semiconductor nanocrystals.
Toward a physical theory of quantum cognition.
Takahashi, Taiki
2014-01-01
Recently, mathematical models based on quantum formalism have been developed in cognitive science. The target articles in this special issue of Topics in Cognitive Science clearly illustrate how quantum theoretical formalism can account for various aspects of human judgment and decision making in a quantitatively and mathematically rigorous manner. In this commentary, we show how future studies in quantum cognition and decision making should be developed to establish theoretical foundations based on physical theory, by introducing Taketani's three-stage theory of the development of science. Also, implications for neuroeconomics (another rapidly evolving approach to human judgment and decision making) are discussed.
Quantum Stability of Chameleon Field Theories
Upadhye, Amol; Khoury, Justin
2012-01-01
Chameleon scalar fields are dark energy candidates which suppress fifth forces in high density regions of the universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound $m 0.0042$\\,eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well-controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential.
Generalizing Prototype Theory: A Formal Quantum Framework
Directory of Open Access Journals (Sweden)
Diederik eAerts
2016-03-01
Full Text Available Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Mathematical aspects of quantum field theories
Strobl, Thomas
2015-01-01
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...
Generalizing Prototype Theory: A Formal Quantum Framework.
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Generalizing Prototype Theory: A Formal Quantum Framework
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
Cui, Ping
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO
Quantum gravity, effective fields and string theory
Bjerrum-Bohr, N E J
2004-01-01
We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy leading quantum corrections to both the Schwarzschild and Kerr metrics. The leading quantum corrections to the pure gravitational potential between two sources are also calculated, both in the mixed theory of scalar QED and quantum gravity and in the pure gravitational theory. The (Kawai-Lewellen-Tye) string theory gauge/gravity relations is next dealt with. We investigate if the KLT-operator mapping extends to the case of higher derivative effective operators. The KLT-relations are generalized, taking the effective field theory viewpoint, and remarkable tree-level amplitude relations between the field theory operators are derived. Quantum gravity is finally looked at from the the perspective of taking the limit of infinitely many spatial dimensions. It is verified that only a c...
Principles and methods of quantum information technologies
Semba, Kouichi
2016-01-01
This book presents the research and development-related results of the “FIRST” Quantum Information Processing Project, which was conducted from 2010 to 2014 with the support of the Council for Science, Technology and Innovation of the Cabinet Office of the Government of Japan. The project supported 33 research groups and explored five areas: quantum communication, quantum metrology and sensing, coherent computing, quantum simulation, and quantum computing. The book is divided into seven main sections. Parts I through V, which consist of twenty chapters, focus on the system and architectural aspects of quantum information technologies, while Parts VI and VII, which consist of eight chapters, discuss the superconducting quantum circuit, semiconductor spin and molecular spin technologies. Readers will be introduced to new quantum computing schemes such as quantum annealing machines and coherent Ising machines, which have now arisen as alternatives to standard quantum computers and are designed to successf...
Quantum field theory from classical statistics
Wetterich, C
2011-01-01
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...
Super-relativity in the quantum theory
Leifer, P
2007-01-01
The relativity to the measuring device in quantum theory, i.e. the covariance of local dynamical variables relative transformations to moving quantum reference frame in Hilbert space, may be achieved only by the rejection of super-selection rule. In order to avoid the subjective nuance, I emphasis that the notion of "measurement" here, is nothing but the covariant differentiation procedure in the functional quantum phase space $CP(N-1)$, having pure objective sense of evolution. Transition to the local moving quantum reference frame leads to some particle-like solutions of quasi-linear field PDE in the dynamical space-time. Thereby, the functionally covariant quantum dynamics gives the perspective to unify the Einstein relativity and quantum principles which are obviously contradictable under the standard approaches.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael; Siopsis, George; Weedbrook, Christian
2015-12-01
The year 1982 is often credited as the year that theoretical quantum computing was started with a keynote speech by Richard Feynman, who proposed a universal quantum simulator, the idea being that if you had such a machine you could in principle "imitate any quantum system, including the physical world." With that in mind, we present an algorithm for a continuous-variable quantum computing architecture which gives an exponential speedup over the best-known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on continuous-variable states that is feasible with today's technology.
Quantum theory of laser-stimulated desorption
Slutsky, M. S.; George, T. F.
1978-01-01
A quantum theory of laser-stimulated desorption (LSDE) is presented and critically analyzed. It is shown how LSDE depends on laser-pulse characteristics and surface-lattice dynamics. Predictions of the theory for a Debye model of the lattice dynamics are compared to recent experimental results.
Book Review Bohmian Mechanics and Quantum Theory
Jäger, G
1999-01-01
A review of "Bohmian Mechanics and Quantum Theory: An Appraisal" (James Cushing, Arthur Fine and Sheldon Goldstein, Eds.), an extensive collection of articles on Bohmian mechanics. In addition to broad, critical overviews of Bohmian mechanics, the reviewed collection contains extensions and hybrid versions of the theory, as are several detailed applications to practical situtations.
Quantum Field Theory in de Sitter spacetime
So, Ashaq Hussain; Sibuea, Marlina Rosalinda; Akhoon, Shabir Ahmad; Khanday, Bilal Nisar; Majeed, Sajad Ul; Rather, Asloob Ahmad; Nahvi, Ishaq
2013-01-01
In this paper we will analyse quantum ?eld theory on de Sitter space- time. We will ?rst analyse a general scalar and vector ?eld theory on de Sitter spacetime. This is done by ?rst calculating these propagators on four-Sphere and then analytically continuing it to de Sitter spacetime.
Computer animations of quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Cohen, E. (Centre d' Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique)
1992-07-01
A visualization mehtod for quantum field theories based on the transfer matrix formalism is presented. It generates computer animations simulating the time evolution of complex physical systems subject to local Hamiltonians. The method may be used as a means of gaining insight to theories such as QCD, and as an educational tool in explaining high-energy physics. (orig.).
Quantum field theory in a semiotic perspective
Energy Technology Data Exchange (ETDEWEB)
Dosch, H.G. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Mueller, V.F. [Technische Univ. Kaiserslautern (Germany). Fachbereich Physik; Sieroka, N. [Zurich Univ. (Switzerland)
2005-07-01
Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincare, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)
Theory and application of quantum molecular dynamics
Zeng Hui Zhang, John
1999-01-01
This book provides a detailed presentation of modern quantum theories for treating the reaction dynamics of small molecular systems. Its main focus is on the recent development of successful quantum dynamics theories and computational methods for studying the molecular reactive scattering process, with specific applications given in detail for a number of benchmark chemical reaction systems in the gas phase and the gas surface. In contrast to traditional books on collision in physics focusing on abstract theory for nonreactive scattering, this book deals with both the development and the appli
PREFACE: Quantum Information, Communication, Computation and Cryptography
Benatti, F.; Fannes, M.; Floreanini, R.; Petritis, D.
2007-07-01
The application of quantum mechanics to information related fields such as communication, computation and cryptography is a fast growing line of research that has been witnessing an outburst of theoretical and experimental results, with possible practical applications. On the one hand, quantum cryptography with its impact on secrecy of transmission is having its first important actual implementations; on the other hand, the recent advances in quantum optics, ion trapping, BEC manipulation, spin and quantum dot technologies allow us to put to direct test a great deal of theoretical ideas and results. These achievements have stimulated a reborn interest in various aspects of quantum mechanics, creating a unique interplay between physics, both theoretical and experimental, mathematics, information theory and computer science. In view of all these developments, it appeared timely to organize a meeting where graduate students and young researchers could be exposed to the fundamentals of the theory, while senior experts could exchange their latest results. The activity was structured as a school followed by a workshop, and took place at The Abdus Salam International Center for Theoretical Physics (ICTP) and The International School for Advanced Studies (SISSA) in Trieste, Italy, from 12-23 June 2006. The meeting was part of the activity of the Joint European Master Curriculum Development Programme in Quantum Information, Communication, Cryptography and Computation, involving the Universities of Cergy-Pontoise (France), Chania (Greece), Leuven (Belgium), Rennes1 (France) and Trieste (Italy). This special issue of Journal of Physics A: Mathematical and Theoretical collects 22 contributions from well known experts who took part in the workshop. They summarize the present day status of the research in the manifold aspects of quantum information. The issue is opened by two review articles, the first by G Adesso and F Illuminati discussing entanglement in continuous variable
Relativity, symmetry and the structure of quantum theory I Galilean quantum theory
Klink, William H
2015-01-01
Quantum theory is one of the most successful of all physical theories. Our everyday world is dominated by devices that function because of knowledge of the quantum world. Yet many, physicists and non-physicists alike, find the theory which explains the behavior of the quantum world baffling and strange. This book is the first in a series of three that argues that relativity and symmetry determine the structure of quantum theory. That is to say, the structure of quantum theory is what it is because of relativity and symmetry. There are different types of relativity, each leading to a particular type of quantum theory. This book deals specifically with what we call Newton relativity, the form of relativity built into Newtonian mechanics, and the quantum theory to which it gives rise, which we call Galilean (often misleadingly called non-relativistic) quantum theory. Key Features: • Meaning and significance of the term of relativity; discussion of the principle of relativity. • Relation of symmetry to relati...
Quantum field theory in a nutshell
Zee, A
2010-01-01
Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading
Ehrenfest's adiabatic hypothesis in Bohr's quantum theory
Pérez, Enric
2015-01-01
It is widely known that Paul Ehrenfest formulated and applied his adiabatic hypothesis in the early 1910s. Niels Bohr, in his first attempt to construct a quantum theory in 1916, used it for fundamental purposes in a paper which eventually did not reach the press. He decided not to publish it after having received the new results by Sommerfeld in Munich. Two years later, Bohr published "On the quantum theory of line-spectra." There, the adiabatic hypothesis played an important role, although it appeared with another name: the principle of mechanical transformability. In the subsequent variations of his theory, Bohr never suppressed this principle completely. We discuss the role of Ehrenfest's principle in the works of Bohr, paying special attention to its relation to the correspondence principle. We will also consider how Ehrenfest faced Bohr's uses of his more celebrated contribution to quantum theory, as well as his own participation in the spreading of Bohr's ideas.
Information theory of molecular systems
Nalewajski, Roman F
2006-01-01
As well as providing a unified outlook on physics, Information Theory (IT) has numerous applications in chemistry and biology owing to its ability to provide a measure of the entropy/information contained within probability distributions and criteria of their information ""distance"" (similarity) and independence. Information Theory of Molecular Systems applies standard IT to classical problems in the theory of electronic structure and chemical reactivity. The book starts by introducing the basic concepts of modern electronic structure/reactivity theory based upon the Density Functional Theory
Phase Information in Quantum Oracle Computing
Machta, J.
1998-01-01
Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantum computer but not a classical computer. One consequence of this observation is that there is an oracle which is of no assistance to a classical computer but which allows a quantum computer to solve undecidable problems. Thus useful relativized separations between quantum and classical complexity classes must exclude the transmissio...
Entanglement in non-Hermitian quantum theory
Indian Academy of Sciences (India)
Arun K Pati
2009-09-01
Entanglement is one of the key features of quantum world that has no classical counterpart. This arises due to the linear superposition principle and the tensor product structure of the Hilbert space when we deal with multiparticle systems. In this paper, we will introduce the notion of entanglement for quantum systems that are governed by non-Hermitian yet $\\mathcal{PT}$ -symmetric Hamiltonians. We will show that maximally entangled states in usual quantum theory behave like non-maximally entangled states in $\\mathcal{PT}$ -symmetric quantum theory. Furthermore, we will show how to create entanglement between two $\\mathcal{PT}$ qubits using non-Hermitian Hamiltonians and discuss the entangling capability of such interaction Hamiltonians that are non-Hermitian in nature.
Quantum Field Theory on Noncommutative Spaces
Szabó, R J
2003-01-01
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
Numerical approach of the quantum circuit theory
Silva, J. J. B.; Duarte-Filho, G. C.; Almeida, F. A. G.
2017-03-01
In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.
Numerical approach of the quantum circuit theory
Energy Technology Data Exchange (ETDEWEB)
Silva, J.J.B., E-mail: jaedsonfisica@hotmail.com; Duarte-Filho, G.C.; Almeida, F.A.G.
2017-03-15
In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.
Quantum reality theory and philosophy
Allday, Jonathan
2009-01-01
PrefaceIntroductionAuthorPart I Our First Quantum Object: Light Some Opening Thoughts A Little Light Reading Lasers and Video Cameras Photons An Interference Experiment with Photons Interference as a Wave Effect Mach-Zehnder with Photons Delayed Choice Summary Endnotes Interlude 1: Another Interference Experiment Particles Electrons The Electron Gun The Stern-Gerlach Experiment Turning Things Round Things Get More Puzzling So, Where Did It Go? What Does It All Mean? Some Indications with Other Particles The Long and the Short of It Summary Endnotes Quantum States Where Are We Now? Describing C
Quantum Field Theory from First Principles
Esposito, Giampiero
2000-01-01
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential operators of Laplace type. There are however deep reasons to modify such a scheme and allow for pseudo-differential boundary-value problems. When the boundary operator is allowed to be pseudo-differential while remaining a projector, the conditions on its kernel...
Mossbauer neutrinos in quantum mechanics and quantum field theory
Kopp, Joachim
2009-01-01
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detecti...
Dwivedi, Yogesh K; Schneberger, Scott L
2011-01-01
The overall mission of this book is to provide a comprehensive understanding and coverage of the various theories and models used in IS research. Specifically, it aims to focus on the following key objectives: To describe the various theories and models applicable to studying IS/IT management issues. To outline and describe, for each of the various theories and models, independent and dependent constructs, reference discipline/originating area, originating author(s), seminal articles, level of analysis (i.e. firm, individual, industry) and links with other theories. To provide a critical revie
Fisher Information of Wavefunctions: Classical and Quantum
Institute of Scientific and Technical Information of China (English)
LUO Shun-Long
2006-01-01
A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first,deiined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second,defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions.It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.
Casimir Effects in Renormalizable Quantum Field Theories
Graham, N; Weigel, H; Graham, Noah; Jaffe, Robert L.; Weigel, Herbert
2002-01-01
We review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.
Casimir Effects in Renormalizable Quantum Field Theories
Graham, Noah; Jaffe, Robert L.; Weigel, Herbert
We present a framework for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.
Loop quantum gravity as an effective theory
Bojowald, Martin
2012-01-01
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable ambiguities at the dynamical level, allows for a meaningful phenomenology to be developed, by which it becomes falsifiable. The tradiational problems plaguing canonical quantum-gravity theories, such as the anomaly issue or the problem of time, can be overcome or are irrelevant at the effective level, resulting in consistent means of physical evaluations. This contribution presents aspects of canonical equations and related notions of (deformed) space-time structures and discusses implications in loop quantum gravity, such as signature change at high density from holonomy corrections, and falsifiability thanks to inverse-triad corrections.
String Theory, Unification and Quantum Gravity
Stelle, K S
2012-01-01
An overview is given of the way in which the unification program of particle physics has evolved into the proposal of superstring theory as a prime candidate for unifying quantum gravity with the other forces and particles of nature. A key concern with quantum gravity has been the problem of ultraviolet divergences, which is naturally solved in string theory by replacing particles with spatially extended states as the fundamental excitations. String theory turns out, however, to contain many more extended-object states than just strings. Combining all this into an integrated picture, called M-theory, requires recognition of the r\\^ole played by a web of nonperturbative duality symmetries suggested by the nonlinear structures of the field-theoretic supergravity limits of string theory.
Basic Concepts of a Quantum Event Theory
Bostroem, K J
2004-01-01
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. Time and space are treated on exactly the same footing, namely as quantum mechanical observables on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics and cannot be formulated within the framework of unitary dynamics. As a most important aspect, the theory breaks with the concept of a continuously flowing time in favour of a discrete jump process in spacetime. All physical statements are formulated in terms of detector events rather than particle states. The physical object under consideration is a spinless particle in empty space. Yet the theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the strict sense. The Maxwell equations are derived as a straightforward consequence of some fundamental commutation relations. In the non-relativistic limit, and in the limit of infinitely small time uncertain...
Modern Quantum Technologies of Information Security
Korchenko, Oleksandr; Gnatyuk, Sergiy
2010-01-01
In the paper systematization and classification of modern quantum technologies of the information security against cyber-terrorist attack are carried out. The characteristic of the basic directions of quantum cryptography from the viewpoint of used quantum technologies is given. The qualitative analysis of advantages and disadvantages of concrete quantum protocols is made. The current status of a problem of practical quantum cryptography using in telecommunication networks is considered. In particular, the short review of existing commercial systems of quantum key distribution is given.
Undergraduate Lecture Notes in Topological Quantum Field Theory
2008-01-01
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
Quantum Holonomy Theory and Hilbert Space Representations
Aastrup, Johannes
2016-01-01
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state exist is left for later publications.
Quantum mechanics of 4-derivative theories
Energy Technology Data Exchange (ETDEWEB)
Salvio, Alberto [Universidad Autonoma de Madrid and Instituto de Fisica Teorica IFT-UAM/CSIC, Departamento de Fisica Teorica, Madrid (Spain); Strumia, Alessandro [Dipartimento di Fisica, Universita di Pisa (Italy); CERN, Theory Division, Geneva (Switzerland); INFN, Pisa (Italy)
2016-04-15
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm. (orig.)
The physical principles of the quantum theory
Heisenberg, Werner
1949-01-01
The contributions of few contemporary scientists have been as far reaching in their effects as those of Nobel Laureate Werner Heisenberg. His matrix theory is one of the bases of modern quantum mechanics, while his ""uncertainty principle"" has altered our whole philosophy of science.In this classic, based on lectures delivered at the University of Chicago, Heisenberg presents a complete physical picture of quantum theory. He covers not only his own contributions, but also those of Bohr, Dirac, Bose, de Broglie, Fermi, Einstein, Pauli, Schrodinger, Somerfield, Rupp, ·Wilson, Germer, and others
On deformation theory of quantum vertex algebras
Grosse, H; Grosse, Harald; Schlesinger, Karl-Georg
2005-01-01
We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual Hochschild complex of an assocative algebra. We show that this system of equations results from an action principle. This might be the starting point for a perturbative treatment of the deformation problem of quantum vertex algebras. Our action generalizes the action of the Kodaira-Spencer theory of gravity and might therefore also be of relevance for applications in string theory.
Quantum mechanics of 4-derivative theories.
Salvio, Alberto; Strumia, Alessandro
2016-01-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
Lütkenhaus, N.; Shields, A. J.
2009-04-01
descriptions and are based on observable tests during the run of QKD sessions. It is now 25 years since the first proposal for QKD was published and 20 since the first experimental realization. The intervening years have brought several technological and theoretical advances, which have driven new insights into the application of quantum theory to the wider field of information technology. We are looking forward to the new twists and turns this field will take in the next 25 years! Focus on Quantum Cryptography: Theory and Practice Contents Security of continuous-variable quantum key distribution: towards a de Finetti theorem for rotation symmetry in phase space A Leverrier, E Karpov, P Grangier and N J Cerf Optical networking for quantum key distribution and quantum communications T E Chapuran, P Toliver, N A Peters, J Jackel, M S Goodman, R J Runser, S R McNown, N Dallmann, R J Hughes, K P McCabe, J E Nordholt, C G Peterson, K T Tyagi, L Mercer and H Dardy Proof-of-concept of real-world quantum key distribution with quantum frames I Lucio-Martinez, P Chan, X Mo, S Hosier and W Tittel Composability in quantum cryptography Jörn Müller-Quade and Renato Renner Distributed authentication for randomly compromised networks Travis R Beals, Kevin P Hynes and Barry C Sanders Feasibility of 300 km quantum key distribution with entangled states Thomas Scheidl, Rupert Ursin, Alessandro Fedrizzi, Sven Ramelow, Xiao-Song Ma, Thomas Herbst, Robert Prevedel, Lothar Ratschbacher, Johannes Kofler, Thomas Jennewein and Anton Zeilinger Decoy-state quantum key distribution with both source errors and statistical fluctuations Xiang-Bin Wang, Lin Yang, Cheng-Zhi Peng and Jian-Wei Pan High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres D Stucki, N Walenta, F Vannel, R T Thew, N Gisin, H Zbinden, S Gray, C R Towery and S Ten Topological optimization of quantum key distribution networks R Alléaume, F Roueff, E Diamanti and N Lütkenhaus The SECOQC quantum key
The physics of forgetting: Landauer's erasure principle and information theory
Plenio, MB; Vitelli, V
2001-01-01
This article discusses the concept of information and its intimate relationship with physics. After an introduction of all the necessary quantum mechanical and information theoretical concepts we analyze Landauer's principle that states that the erasure of information is inevitably accompanied by the generation of heat. We employ this principle to rederive a number of results in classical and quantum information theory whose rigorous mathematical derivations are difficult. This demonstrates t...
Holism, physical theories and quantum mechanics
Seevinck, M. P.
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.
Wilson lines in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Cherednikov, Igor Olegovich [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.; Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Mertens, Tom; Veken, Frederik F. van der [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.
2014-07-01
Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.
Quantum information processing and relativistic quantum fields
Benincasa, Dionigi M. T.; Borsten, Leron; Buck, Michel; Dowker, Fay
2014-04-01
It is shown that an ideal measurement of a one-particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light-crossing time of the packet in that frame. Moreover, these results are shown to apply not only to ideal measurements but also to unitary transformations that rotate two orthogonal one-particle states into each other. In light of these observations, possible restrictions on the allowed types of intervention are considered. A more physical approach to such questions is to construct explicit models of the interventions as interactions between the field and other quantum systems such as detectors. The prototypical Unruh-DeWitt detector couples to the field operator itself and so most likely respects relativistic causality. On the other hand, detector models which couple to a finite set of frequencies of field modes are shown to lead to superluminal signalling. Such detectors do, however, provide successful phenomenological models of atom-qubits interacting with quantum fields in a cavity but are valid only on time scales many orders of magnitude larger than the light-crossing time of the cavity.
Quantum bouncer: theory and experiment
Vankov, Anatoli Andrei
2009-01-01
The quantum bouncer (QB) concept is a known QM textbook example of confined particle, namely, a solution to the 1D Schroedinger equation for a linear potential (the so-called Airy equation). It would be a great methodological challenge to create such a QM object in laboratory. An attempt of observation of the QB ``running'' in the horizontal direction was recently made by the international team at the Laue-Langevin Institute, Grenoble. The experiment was performed with ultra-cold neutrons. In this paper, the experiment is analyzed in view of the authors' claim that ``neutron quantum states in Earth gravitational field'' are observed. The experimental apparatus is designed for measurements of horizontal flux of neutrons passing through an absorbing wave guide with a variable height of absorber. From our analysis, it follows, however, that in such a layout measured data are not sensitive to quantum probability density in the vertical direction. The overall conclusion is made that the experimental data do not co...
Wavelet-Based Quantum Field Theory
Directory of Open Access Journals (Sweden)
Mikhail V. Altaisky
2007-11-01
Full Text Available The Euclidean quantum field theory for the fields $phi_{Delta x}(x$, which depend on both the position $x$ and the resolution $Delta x$, constructed in SIGMA 2 (2006, 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.
Scattering theory the quantum theory of nonrelativistic collisions
Taylor, John R
2006-01-01
This graduate-level text is intended for any student of physics who requires a thorough grounding in the quantum theory of nonrelativistic scattering. It is designed for readers who are already familiar with the general principles of quantum mechanics and who have some small acquaintance with scattering theory. Study of this text will allow students of atomic or nuclear physics to begin reading the literature and tackling real problems, with a complete grasp of the underlying principles. For students of high-energy physics, it provides the necessary background for later study of relativistic p
Quantum Holonomy Theory, Lattice-Independent Formulation
Aastrup, Johannes
2016-01-01
Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD-algebra, which essentially encodes how local degrees of freedom are moved on a three-dimensional manifold. In this paper we continue the development of the theory by providing a lattice-independent formulation. We first define a Dirac type operator over a configuration space of Ashtekar connections and use it to formulate a graded version of the QHD-algebra. Next we formulate necessary conditions for a state to exist on this algebra and use the GNS construction to build a kinematical Hilbert space. Finally we find that operators, that correspond to the Dirac and gravitational Hamiltonians in a semi-classical limit, are background independent.
Towards the mathematics of quantum field theory
Paugam, Frédéric
2014-01-01
The aim of this book is to introduce mathematicians (and, in particular, graduate students) to the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in play. This should in turn promote interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, even if the mathematical one is the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second...
Memory-based quantum repeater in quantum information communication
Institute of Scientific and Technical Information of China (English)
Wu Xiang-Sheng
2004-01-01
This paper studies the quantum repeater in quantum information communication. We propose to introduce the photon buffer mechanism for storing photons, which uses fibre delay loops as photon memories and a programmable 1 × N switcher for distributing photon delay time. Meanwhile, we also consider entanglement purification and entanglement swapping restoration at an entanglement purification or entanglement swapping failure and introduce a protection link mechanism that allows the photonic quantum repeater of a broken connection to initiate a connection restoration process.
Boolean approach to dichotomic quantum measurement theories
Nagata, K.; Nakamura, T.; Batle, J.; Abdalla, S.; Farouk, A.
2017-02-01
Recently, a new measurement theory based on truth values was proposed by Nagata and Nakamura [Int. J. Theor. Phys. 55, 3616 (2016)], that is, a theory where the results of measurements are either 0 or 1. The standard measurement theory accepts a hidden variable model for a single Pauli observable. Hence, we can introduce a classical probability space for the measurement theory in this particular case. Additionally, we discuss in the present contribution the fact that projective measurement theories (the results of which are either +1 or -1) imply the Bell, Kochen, and Specker (BKS) paradox for a single Pauli observable. To justify our assertion, we present the BKS theorem in almost all the two-dimensional states by using a projective measurement theory. As an example, we present the BKS theorem in two-dimensions with white noise. Our discussion provides new insight into the quantum measurement problem by using this measurement theory based on the truth values.
Hierarchical theory of quantum adiabatic evolution
Zhang, Qi; Gong, Jiangbin; Wu, Biao
2014-12-01
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau-Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.
Dual Field Theories of Quantum Computation
Vanchurin, Vitaly
2016-01-01
Given two quantum states of $N$ q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large $N$ limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an $N+1$ dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an $N$ dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli $Z$ matrices. Since such situation is not generic we call it the $Z$-problem. On the dual field the...
Tempel, David G; Aspuru-Guzik, Alán
2012-01-01
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.
Quantum game theory and open access publishing
Hanauske, Matthias; Bernius, Steffen; Dugall, Berndt
2007-08-01
The digital revolution of the information age and in particular the sweeping changes of scientific communication brought about by computing and novel communication technology, potentiate global, high grade scientific information for free. The arXiv, for example, is the leading scientific communication platform, mainly for mathematics and physics, where everyone in the world has free access on. While in some scientific disciplines the open access way is successfully realized, other disciplines (e.g. humanities and social sciences) dwell on the traditional path, even though many scientists belonging to these communities approve the open access principle. In this paper we try to explain these different publication patterns by using a game theoretical approach. Based on the assumption, that the main goal of scientists is the maximization of their reputation, we model different possible game settings, namely a zero sum game, the prisoners’ dilemma case and a version of the stag hunt game, that show the dilemma of scientists belonging to “non-open access communities”. From an individual perspective, they have no incentive to deviate from the Nash equilibrium of traditional publishing. By extending the model using the quantum game theory approach it can be shown, that if the strength of entanglement exceeds a certain value, the scientists will overcome the dilemma and terminate to publish only traditionally in all three settings.
Quantum Lie theory a multilinear approach
Kharchenko, Vladislav
2015-01-01
This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
PREFACE Quantum Groups, Quantum Foundations and Quantum Information: a Festschrift for Tony Sudbery
Weigert, Stefan
2010-11-01
On 29 July 2008, Professor Anthony Thomas Sudbery - known as Tony to his friends and colleagues - celebrated his 65th birthday. To mark this occasion and to honour Tony's scientific achievements, a 2-day Symposion was held at the University of York on 29-30 September 2008 under the sponsorship of the Institute of Physics and the London Mathematical Society. The breadth of Tony's research interests was reflected in the twelve invited lectures by A Beige, I Bengtsson, K Brown, N Cerf, E Corrigan, J Ladyman, A J Macfarlane, S Majid, C Manogue, S Popescu, J Ryan and R W Tucker. This Festschrift, also made possible by the generosity of the IOP and the LMS, reproduces the majority of these contributions together with other invited papers. Tony obtained his PhD from the University of Cambridge in 1970. His thesis, written under the guidance of Alan Macfarlane, is entitled Some aspects of chiral su(3) × su(3) symmetry in hadron dynamics. He arrived in York in 1971 with his wife Rodie, two young daughters, a lively mind and a very contemporary shock of hair. He was at that stage interested in mathematical physics and so was classed as an applied mathematician in the departmental division in place at that time. But luckily Tony did not fit into this category. His curiosity is combined with a good nose for problems and his capacity for knocking off conjectures impressed us all. Within a short time of his arrival he was writing papers on group theory, complex analysis and combinatorics, while continuing to work on quantum mechanics. His important paper on quaternionic analysis is an example of the imagination and elegance of his ideas. By developing a derivative, he replaced the relatively obscure analytical theory of quaternions by one informed by modern complex analysis. Other interests emerged, centred round the quantum: quantum mechanics and its foundations, quantum groups and quantum information. He didn't just dabble in these areas but mastered them, gaining a national
Quantum Field Theory and Decoherence in the Early Universe
Koksma, J. F.
2011-06-01
by realising that higher order, non-Gaussian correlators are usually perturbatively suppressed. A quantum system with a large entropy corresponds to an effectively classical, stochastic system. To allow for a quantitative comparison between our correlator approach and the conventional approach to decoherence, we apply both formalisms to two simple quantum mechanical models. We find that the entropy in the conventional approach to decoherence quite generically reveals secular growth, indicating physically unacceptable behaviour. The conventional approach furthermore suffers from the fact that no well-established treatment to take perturbative corrections into account exists, nor has the framework of renormalisation ever been implemented. Our correlator approach to decoherence is taylored to applications in quantum field theory. We perform the first realistic study of decoherence in a renormalised quantum field theoretical setting. Using out-of-equilibrium field theory techniques, we extract two quantitative measures of decoherence in our model: the total amount of decoherence and the decoherence rate. The main finding in this part of the thesis is that, although a pure state remains pure under unitary evolution, an observer perceives this state over time as a mixed state with positive entropy as non-Gaussianities are dynamically generated. Alternatively, one could say that a realistic observer cannot probe all information about the system and thus discerns a loss of coherence of the pure state
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory.
Quantum Transport Theory for Photonic Networks
Lei, Chan U
2010-01-01
In this paper, we develop a quantum transport theory to describe photonic transport in photonic networks. The photonic networks concerned in the paper consist of all-optical circuits incorporating photonic bandgap waveguides and driven resonators. The photoncurrents flowing through waveguides are entirely determined from the exact master equation of the driven resonators. The master equation of the driven resonators is obtained by explicitly eliminating all the waveguide degrees of freedom while the back-reactions between resonators and waveguides are fully taken into account. The relations between the driven photonic dynamics and photoncurrents are obtained. The quantum dissipation and quantum noise effects in photonic transport are also fully addressed. As an illustration, the theory is applied to the transport phenomena of a driven nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic transport through the driven resonator is demonstrated.
Quantum theory of elementary processes
Galiautdinov, Andrei
2002-01-01
In modern physics, one of the greatest divides is that between space-time and quantum fields, as the fiber bundle of the Standard Model indicates. However on the operational grounds the fields and spacetime are not very different. To describe a field in an experimental region we have to assign coordinates to the points of that region in order to speak of the "when" and "where" of the field itself. But to operationally study the topology and to coordinatize the region of spacetime, the use of ...
Theory of controlled quantum dynamics
Energy Technology Data Exchange (ETDEWEB)
De Martino, Salvatore; De Siena, Silvio; Illuminati, Fabrizio [Dipartimento di Fisica, Universita di Salerno, and INFN, Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy)
1997-06-07
We introduce a general formalism to obtain localized quantum wavepackets as dynamically controlled systems, in the framework of Nelson stochastic quantization. We show that in general the control is linear, and it amounts to introducing additional time-dependent terms in the potential. In this way one can construct for general systems either coherent packets following classical motion with constant dispersion, or coherent packets following classical motion whose time-dependent dispersion remains bounded for all times. We show that in the operatorial language our scheme amounts to introducing a suitable generalization to arbitrary potentials of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator. (author)
Theory of controlled quantum dynamics
De Martino, S; Illuminati, F; Martino, Salvatore De; Siena, Silvio De; Illuminati, Fabrizio
1997-01-01
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general linear, and it amounts to introduce additional quadratic and linear time-dependent terms to the given potential. In this way one can construct for general systems either coherent packets moving with constant dispersion, or dynamically squeezed packets whose spreading remains bounded for all times. In the standard operatorial framework our scheme corresponds to a suitable generalization of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator.
Quantum theory, deformation and integrability
Carroll, R
2000-01-01
About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between qua
The Quantum Theory of Magnetism
Majlis, Norberto
2000-01-01
This book is intended as a basic text for a two-term graduate course for physicists, engineers and chemists with a background in quantum and statistical mechanics. What sets it apart from other publications on the subject is its extensive use of Greenâ€™s function techniques and its detailed discussion of the application of the mean-field approximation and dipoleâ€"dipole interactions in one, two and three dimensions. A chapter each has been devoted to low-dimensional systems, surface magnetism and layered systems. A total of 60 exercises have also been included.
The Quantum Information of Cosmological Correlations
Lim, Eugene A
2014-01-01
It has been shown that the primordial perturbations sourced by inflation are driven to classicality by unitary evolution alone. However, their coupling with the environment such as photons and subsequent decoherence renders the cosmological correlations quantum, losing primordial information in the process. We argue that the quantumness of the resulting cosmological correlations is given by quantum discord, which captures non-classical behavior beyond quantum entanglement. By considering the environment as a quantum channel in which primordial information contained in the perturbations is transmitted to us, we can then ask how much of this information is inaccessible. We show that this amount of information is given by the discord of the joint primordial perturbations-environment system. To illustrate these points, we model the joint system as a mixed bi-modal Gaussian state, and show that quantum discord is dependent on the basis which decoherence occurs.
Genre theory in information studies
Andersen, Jack
2015-01-01
This book highlights the important role genre theory plays within information studies. It illustrates how modern genre studies inform and enrich the study of information, and conversely how the study of information makes its own independent contributions to the study of genre.
A Structurally Relativistic Quantum Theory. Part 1: Foundations
Grgin, Emile
2012-01-01
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A new number system with the properties needed to support an inherently relativistic quantum theory is brought to light and investigated to a point sufficient for applications.
Wilson lines in quantum field theory
Cherednikov, Igor O; Veken, Frederik F van der
2014-01-01
The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum field theory. It teaches how to perform independently with some elementary calculations on Wilson lines, and shows the recent development of the subject in different important areas of research.
Connecting and unmasking relativity and quantum theory
Koning, de W.L.; Willigenburg, van L.G.
2015-01-01
The answer lies right in front of us, but we refuse to see it. Both relativity and quantum theory, the two pillars of fundamental physics, are modified in this paper to make them also explain the physical phenomena they describe. With this explanation, all current inconsistencies between the two van
Formalism and Interpretation in Quantum Theory
Wilce, Alexander
2010-04-01
Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation.
CDT: an entropic theory of quantum gravity
Ambjorn, J.; Goerlich, A.; Jurkiewicz, J.; Loll, R.
2010-01-01
In these lectures we describe how a theory of quantum gravity may be constructed in terms of a lattice formulation based on so-called causal dynamical triangulations (CDT). We discuss how the continuum limit can be obtained and how to define and measure diffeomorphism-invariant correlators. In four
Resource theory of quantum states out of thermal equilibrium.
Brandão, Fernando G S L; Horodecki, Michał; Oppenheim, Jonathan; Renes, Joseph M; Spekkens, Robert W
2013-12-20
The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here, we return to the basic questions of thermodynamics using the formalism of resource theories developed in quantum information theory and show that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically many copies of a quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution.
Resource Theory of Quantum States Out of Thermal Equilibrium
Brandão, Fernando G. S. L.; Horodecki, Michał; Oppenheim, Jonathan; Renes, Joseph M.; Spekkens, Robert W.
2013-12-01
The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here, we return to the basic questions of thermodynamics using the formalism of resource theories developed in quantum information theory and show that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically many copies of a quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution.
Quantum Information Processing and Relativistic Quantum Fields
Benincasa, Dionigi M T; Buck, Michel; Dowker, Fay
2014-01-01
It is shown that an ideal measurement of a one-particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light-crossing time of the packet in that frame. Moreover, these results are shown to apply not only to ideal measurements but also to unitary transformations that rotate two orthogonal one-particle states into each other. In light of these observations, possible restrictions on the allowed types of intervention are considered. A more physical approach to such questions is to construct explicit models of the interventions as interactions between the field and other quantum systems such as detectors. The prototypical Unruh-DeWitt detector couples to the field operator itself and so most likely respects relativistic causality. On the other hand, detector models which couple to a finite set of frequencies of ...
Thornberg, Robert
2012-01-01
There is a widespread idea that in grounded theory (GT) research, the researcher has to delay the literature review until the end of the analysis to avoid contamination--a dictum that might turn educational researchers away from GT. Nevertheless, in this article the author (a) problematizes the dictum of delaying a literature review in classic…
Phase space view of quantum mechanical systems and Fisher information
Energy Technology Data Exchange (ETDEWEB)
Nagy, Á., E-mail: anagy@madget.atomki.hu
2016-06-17
Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
3rd UK-QFT Meeting: Non-Perturbative Quantum Field Theory and Quantum Gravity
2014-01-01
The meeting aims to bringing together Students, Postdoctoral Researchers and Senior Scientists to discuss recent trends in advanced Quantum Field Theory and Quantum Gravity. The format of the meeting is a series of informal talks to allow for discussion and the exchange of ideas amongst participants. We plan for up to 8 slots for short presentations depending on demand and one final longer seminar given by Frank Saueressig (Mainz). This is the third meeting of its kind and details on the previous two can be found on the following: 1st UK-QFT Meeting: Non-perturbative aspects in field theory (KCL) 2nd UK-QFT Meeting: Advances in quantum field theory and gravity (Sussex)
Photonic quantum information: science and technology.
Takeuchi, Shigeki
2016-01-01
Recent technological progress in the generation, manipulation and detection of individual single photons has opened a new scientific field of photonic quantum information. This progress includes the realization of single photon switches, photonic quantum circuits with specific functions, and the application of novel photonic states to novel optical metrology beyond the limits of standard optics. In this review article, the recent developments and current status of photonic quantum information technology are overviewed based on the author's past and recent works.
Geometric theory of information
2014-01-01
This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.
Black Holes and Quantum Theory: The Fine Structure Constant Connection
Directory of Open Access Journals (Sweden)
Cahill R. T.
2006-10-01
Full Text Available The new dynamical theory of space is further confirmed by showing that the effective “black hole” masses M BH in 19 spherical star systems, from globular clusters to galaxies, with masses M , satisfy the prediction that M BH = α 2 M , where α is the fine structure constant. As well the necessary and unique generalisations of the Schr ̈ odinger and Dirac equations permit the first derivation of gravity from a deeper theory, showing that gravity is a quantum effect of quantum matter interacting with the dynamical space. As well the necessary generalisation of Maxwell’s equations displays the observed light bending effects. Finally it is shown from the generalised Dirac equation where the spacetime mathematical formalism, and the accompanying geodesic prescription for matter trajectories, comes from. The new theory of space is non-local and we see many parallels between this and quantum theory, in addition to the fine structure constant manifesting in both, so supporting the argument that space is a quantum foam system, as implied by the deeper information-theoretic theory known as Process Physics. The spatial dynamics also provides an explanation for the “dark matter” effect and as well the non-locality of the dynamics provides a mechanism for generating the uniformity of the universe, so explaining the cosmological horizon problem.
Quantum communication and other quantum information technologies
CSIR Research Space (South Africa)
Roux, FS
2014-02-01
Full Text Available phase screen calculations: 0 1 2 3 w 0/r0 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 T a n g l e l = 1 l = 2 l = 3 l = 4 l = 5 l = 6 l = 7 – p. 40/41 Conclusions ⊲ Quantum communication, which enables fundamentally secure communication, is a new technology...) = ∫∫ E∗m(r1)En(r2)ψ(r1)ψ∗(r2) × exp [ −12Dθ (|r1 − r2|) ] d2r1 d2r2 Function of only w 0/r0 (contains all parameters including z) Evaluated at z = 0 aC. Paterson, Phys. Rev. Lett., 94, 153901 (2005) – p. 22/41 Entanglement decay Decay of qubit OAM...
Coherent control of quantum systems as a resource theory
Matera, J. M.; Egloff, D.; Killoran, N.; Plenio, M. B.
2016-08-01
Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a technological point of view. In this work, we establish a resource theory describing this setting and explore relations to the theory of coherence, entanglement and information processing. Specifically, for the coherent control of quantum systems, the relevant resources of entanglement and coherence are found to be equivalent and closely related to a measure of discord. The results are then applied to the DQC1 protocol and the precision of the final measurement is expressed in terms of the available resources.
Quantum Theory without Planck's Constant
Ralston, John P
2012-01-01
Planck's constant was introduced as a fundamental scale in the early history of quantum mechanics. We find a modern approach where Planck's constant is absent: it is unobservable except as a constant of human convention. Despite long reference to experiment, review shows that Planck's constant cannot be obtained from the data of Ryberg, Davisson and Germer, Compton, or that used by Planck himself. In the new approach Planck's constant is tied to macroscopic conventions of Newtonian origin, which are dispensable. The precision of other fundamental constants is substantially improved by eliminating Planck's constant. The electron mass is determined about 67 times more precisely, and the unit of electric charge determined 139 times more precisely. Improvement in the experimental value of the fine structure constant allows new types of experiment to be compared towards finding "new physics." The long-standing goal of eliminating reliance on the artifact known as the International Prototype Kilogram can be accompl...
Discrete Scalar Quantum Field Theory
Gudder, Stan
2016-01-01
We begin with a description of spacetime by a 4-dimensional cubic lattice $\\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\\sscripthat$ corresponds to a cubic lattice of energy-momentum. This description implies that there is a discrete set of possible particle masses. We then define discrete scalar quantum fields on $\\sscript$. These fields are employed to define interaction Hamiltonians and scattering operators. Although the scattering operator $S$ cannot be computed exactly, approximations are possible. Whether $S$ is unitary is an unsolved problem. Besides the definitions of these operators, our main assumption is conservation of energy-momentum for a scattering process. This article concludes with various examples of perturbation approximations. These include simplified versions of electron-electron and electron-proton scattering as well as simple decay processes. We also define scattering cross-sections, decay ...
Theory of quantum Loschmidt echoes
Prosen, T; Znidaric, M; Prosen, Tomaz; Seligman, Thomas H.; Znidaric, Marko
2003-01-01
In this paper we review our recent work on the theoretical approach to quantum Loschmidt echoes, i.e. various properties of the so called echo dynamics -- the composition of forward and backward time evolutions generated by two slightly different Hamiltonians, such as the state autocorrelation function (fidelity) and the purity of a reduced density matrix traced over a subsystem (purity fidelity). Our main theoretical result is a linear response formalism, expressing the fidelity and purity fidelity in terms of integrated time autocorrelation function of the generator of the perturbation. Surprisingly, this relation predicts that the decay of fidelity is the slower the faster the decay of correlations. In particular for a static (time-independent) perturbation, and for non-ergodic and non-mixing dynamics where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a time scale 1/delta as opposed to mixing dynamics where the fidelity is found to decay...
Spinning Particles in Quantum Mechanics and Quantum Field Theory
Corradini, Olindo
2015-01-01
The first part of the lectures, given by O. Corradini, covers introductory material on quantum-mechanical Feynman path integrals, which are here derived and applied to several particle models. We start considering the nonrelativistic bosonic particle, for which we compute the exact path integrals for the case of the free particle and for the harmonic oscillator, and then describe perturbation theory for an arbitrary potential. We then move to relativistic particles, both bosonic and fermionic (spinning) particles. We first investigate them from the classical view-point, studying the symmetries of their actions, then consider their canonical quantization and path integrals, and underline the role these models have in the study of space-time quantum field theories (QFT), by introducing the "worldline" path integral representation of propagators and effective actions. We also describe a special class of spinning particles that constitute a first-quantized approach to higher-spin fields. Since the fifties the qua...
Problem Book in Quantum Field Theory
Radovanovič, Voja
2008-01-01
The Problem Book in Quantum Field Theory contains about 200 problems with solutions or hints that help students to improve their understanding and develop skills necessary for pursuing the subject. It deals with the Klein-Gordon and Dirac equations, classical field theory, canonical quantization of scalar, Dirac and electromagnetic fields, the processes in the lowest order of perturbation theory, renormalization and regularization. The solutions are presented in a systematic and complete manner. The material covered and the level of exposition make the book appropriate for graduate and undergraduate students in physics, as well as for teachers and researchers. The new edition is a corrected paperback edition for students.
Noncommutative Time in Quantum Field Theory
Salminen, Tapio
2011-01-01
We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-K\\"all\\'{e}n equation) and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of light-like noncommutativity.
Completely local interpretation of quantum field theory
Sverdlov, Roman
2010-01-01
The purpose of this paper is to come up with a framework that "converts" existing concepts from configuration space to ordinary one. This is done by modeling our universe as a big "computer" that simulates configuration space. If that "computer" exists in ordinary space and is ran by "classical" laws, our theory becomes "classical" by default. We have first applied this concept to a version of quantum field theory in which elementary particles have size (that is, a theory that does not yet exists). After that, we have also done the same with Pilot Wave model of discrete jumps, due to D\\"urr et el.
Quantum Finite Elements for Lattice Field Theory
Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan
2016-01-01
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
Solvay 1927: Quantum Theory at the Crossroads
Valentini, Antony
2011-04-01
We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. The proceedings of the conference contain much unexpected material, and are remarkable for their clear identification of key issues that remain controversial to this day. After providing a general overview, we focus on the extensive discussions of de Broglie's pilot-wave theory, which de Broglie presented for a many-body system, including the much misunderstood critique by Pauli.
Information theory and statistics
Kullback, Solomon
1997-01-01
Highly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.
Student friendly quantum field theory basic principles & quantum electrodynamics
Klauber, Robert D
2013-01-01
By incorporating extensive student input and innovative teaching methodologies, this book aims to make the process of learning quantum field theory easier, and thus more rapid, profound, and efficient, for both students and instructors. Comprehensive explanations are favored over conciseness, every step in derivations is included, and ‘big picture’ overviews are provided throughout. Typical student responses indicate how well the text achieves its aim.
Locality and entanglement in bandlimited quantum field theory
Pye, Jason; Kempf, Achim
2015-01-01
We consider a model for a Planck scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1+1 dimension and we find a transition between logarithmic and linear scaling of the entropy, which is the expected 1+1 dimensional analog of the transition from an area to a volume law. We also use entanglement entropy and mutual information as measures to probe in detail the localizability of the field degre...
Colloquium: Protecting quantum information against environmental noise
Suter, Dieter; Álvarez, Gonzalo A.
2016-10-01
Quantum technologies represent a rapidly evolving field in which the specific properties of quantum mechanical systems are exploited to enhance the performance of various applications such as sensing, transmission, and processing of information. Such devices can be useful only if the quantum systems also interact with their environment. However, the interactions with the environment can degrade the specific quantum properties of these systems, such as coherence and entanglement. It is therefore essential that the interaction between a quantum system and the environment is controlled in such a way that the unwanted effects of the environment are suppressed while the necessary interactions are retained. This Colloquium gives an overview, aimed at newcomers to this field, of some of the challenges that need to be overcome to achieve this goal. A number of techniques have been developed for this purpose in different areas of physics including magnetic resonance, optics, and quantum information. They include the application of static or time-dependent fields to the quantum system, which are designed to average the effect of the environmental interactions to zero. Quantum error correction schemes were developed to detect and eliminate certain errors that occur during the storage and processing of quantum information. In many physical systems, it is useful to use specific quantum states that are intrinsically less susceptible to environmental noise for encoding the quantum information. The dominant contribution to the loss of information is pure dephasing, i.e., through the loss of coherence in quantum mechanical superposition states. Accordingly, most schemes for reducing loss of information focus on dephasing processes. This is also the focus of this Colloquium.
Quantum cellular automaton theory of light
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-01
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space-time and mechanics (D'Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
Quantum cellular automaton theory of light
Energy Technology Data Exchange (ETDEWEB)
Bisio, Alessandro, E-mail: alessandro.bisio@unipv.it; D’Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-15
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space–time and mechanics (D’Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
Information: theory, brain, and behavior.
Jensen, Greg; Ward, Ryan D; Balsam, Peter D
2013-11-01
In the 65 years since its formal specification, information theory has become an established statistical paradigm, providing powerful tools for quantifying probabilistic relationships. Behavior analysis has begun to adopt these tools as a novel means of measuring the interrelations between behavior, stimuli, and contingent outcomes. This approach holds great promise for making more precise determinations about the causes of behavior and the forms in which conditioning may be encoded by organisms. In addition to providing an introduction to the basics of information theory, we review some of the ways that information theory has informed the studies of Pavlovian conditioning, operant conditioning, and behavioral neuroscience. In addition to enriching each of these empirical domains, information theory has the potential to act as a common statistical framework by which results from different domains may be integrated, compared, and ultimately unified.
Information Theory in Scientific Visualization
Directory of Open Access Journals (Sweden)
Chaoli Wang
2011-01-01
Full Text Available In recent years, there is an emerging direction that leverages information theory to solve many challenging problems in scientific data analysis and visualization. In this article, we review the key concepts in information theory, discuss how the principles of information theory can be useful for visualization, and provide specific examples to draw connections between data communication and data visualization in terms of how information can be measured quantitatively. As the amount of digital data available to us increases at an astounding speed, the goal of this article is to introduce the interested readers to this new direction of data analysis research, and to inspire them to identify new applications and seek solutions using information theory.
INFORMATION: THEORY, BRAIN, AND BEHAVIOR
Jensen, Greg; Ward, Ryan D.; Balsam, Peter D.
2016-01-01
In the 65 years since its formal specification, information theory has become an established statistical paradigm, providing powerful tools for quantifying probabilistic relationships. Behavior analysis has begun to adopt these tools as a novel means of measuring the interrelations between behavior, stimuli, and contingent outcomes. This approach holds great promise for making more precise determinations about the causes of behavior and the forms in which conditioning may be encoded by organisms. In addition to providing an introduction to the basics of information theory, we review some of the ways that information theory has informed the studies of Pavlovian conditioning, operant conditioning, and behavioral neuroscience. In addition to enriching each of these empirical domains, information theory has the potential to act as a common statistical framework by which results from different domains may be integrated, compared, and ultimately unified. PMID:24122456
Complex numbers in quantum theory
Maynard, Glenn
In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: "What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function." This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. (Abstract shortened by ProQuest.).
Conformal invariance in quantum field theory
Todorov, Ivan T; Petkova, Valentina B
1978-01-01
The present volume is an extended and up-to-date version of two sets of lectures by the first author and it reviews more recent work. The notes aim to present a self-contained exposition of a constructive approach to conformal invariant quantum field theory. Other parts in application of the conformal group to quantum physics are only briefly mentioned. The relevant mathematical material (harmonic analysis on Euclidean conformal groups) is briefly summarized. A new exposition of physical applications is given, which includes an explicit construction of the vacuum operator product expansion for the free zero mass fields.
From Bell's inequalities to quantum information: a new quantum revolution
CERN. Geneva
2015-01-01
In 1964, John Stuart Bell discovered that it is possible to settle the debate experimentally, by testing the famous "Bell's inequalities", and to show directly that the revolutionary concept of entanglement is indeed a reality. A long series of experiments closer and closer to the ideal scheme presented by Bell has confirmed that entanglement is indeed "a great quantum mystery", to use the words of Feynman. Based on that concept, a new field of research has emerged, quantum information, where one uses quantum bits, the so-called “qubits”, to encode the information and process it. Entanglement ...
Information Theory of Networks
Directory of Open Access Journals (Sweden)
Matthias Dehmer
2011-11-01
Full Text Available The paper puts the emphasis on surveying information-theoretic network measures for analyzing the structure of networks. In order to apply the quantities interdisciplinarily, we also discuss some of their properties such as their structural interpretation and uniqueness.
Quantum mechanics, common sense and the black hole information paradox
Danielsson, U H; Danielsson, Ulf H.; Schiffer, Marcelo
1993-01-01
The purpose of this paper is to analyse, in the light of information theory and with the arsenal of (elementary) quantum mechanics (EPR correlations, copying machines, teleportation, mixing produced in sub-systems owing to a trace operation, etc.) the scenarios available on the market to resolve the so-called black-hole information paradox. We shall conclude that the only plausible ones are those where either the unitary evolution of quantum mechanics is given up, in which information leaks continuously in the course of black-hole evaporation through non-local processes, or those in which the world is polluted by an infinite number of meta-stable remnants.
Quantum mechanics, common sense, and the black hole information paradox
Danielsson, Ulf H.; Schiffer, Marcelo
1993-11-01
The purpose of this paper is to analyze, in the light of information theory and with the arsenal of (elementary) quantum mechanics (EPR, correlations, copying machines, teleportation, mixing produced in subsystems owing to a trace operation, etc.) the scenarios available on the market to resolve the so-called black hole information paradox. We shall conclude that the only plausible ones are those where either the unitary evolution of quantum mechanics is given up, in which information leaks continuously in the course of black hole evaporation through nonlocal processes, or those in which the world is polluted by an infinite number of metastable remnants.
Deriving quantum theory from its local structure and reversibility.
de la Torre, Gonzalo; Masanes, Lluís; Short, Anthony J; Müller, Markus P
2012-08-31
We investigate the class of physical theories with the same local structure as quantum theory but potentially different global structure. It has previously been shown that any bipartite correlations generated by such a theory can be simulated in quantum theory but that this does not hold for tripartite correlations. Here we explore whether imposing an additional constraint on this space of theories-that of dynamical reversibility-will allow us to recover the global quantum structure. In the particular case in which the local systems are identical qubits, we show that any theory admitting at least one continuous reversible interaction must be identical to quantum theory.
The universality question for noncommutative quantum field theory
Schlesinger, K G
2006-01-01
Present day physics rests on two main pillars: General relativity and quantum field theory. We discuss the deep and at the same time problematic interplay between these two theories. Based on an argument by Doplicher, Fredenhagen, and Roberts, we propose a possible universality property for noncommutative quantum field theory in the sense that any theory of quantum gravity should involve quantum field theories on noncommutative space-times as a special limit. We propose a mathematical framework to investigate such a universality property and start the discussion of its mathematical properties. The question of its connection to string theory could be a starting point for a new perspective on string theory.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-07
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
Quantum information processing through nuclear magnetic resonance
Energy Technology Data Exchange (ETDEWEB)
Bulnes, J.D.; Sarthour, R.S.; Oliveira, I.S. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Bonk, F.A.; Azevedo, E.R. de; Bonagamba, T.J. [Sao Paulo Univ., Sao Carlos, SP (Brazil). Inst. de Fisica; Freitas, J.C.C. [Espirito Santo Univ., Vitoria, ES (Brazil). Dept. de Fisica
2005-09-15
We discuss the applications of Nuclear Magnetic Resonance (NMR) to quantum information processing, focusing on the use of quadrupole nuclei for quantum computing. Various examples of experimental implementation of logic gates are given and compared to calculated NMR spectra and their respective density matrices. The technique of Quantum State Tomography for quadrupole nuclei is briefly described, and examples of measured density matrices in a two-qubit I = 3/2 spin system are shown. Experimental results of density matrices representing pseudo-Bell states are given, and an analysis of the entropy of theses states is made. Considering an NMR experiment as a depolarization quantum channel we calculate the entanglement fidelity and discuss the criteria for entanglement in liquid state NMR quantum information. A brief discussion on the perspectives for NMR quantum computing is presented at the end. (author)
Information theory and superefficiency
Barron, Andrew; Hengartner, Nicolas
1998-01-01
The asymptotic risk of efficient estimators with Kullback–Leibler loss in smoothly parametrized statistical models is $k/2_n$, where $k$ is the parameter dimension and $n$ is the sample size. Under fairly general conditions, we given a simple information-theoretic proof that the set of parameter values where any arbitrary estimator is superefficient is negligible. The proof is based on a result of Rissanen that codes have asymptotic redundancy not smaller than $(k/2)\\log n$,...
Hydrodynamic transport functions from quantum kinetic theory
Calzetta, E A; Ramsey, S
2000-01-01
Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu, Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. For a real scalar field with $\\lambda \\Phi ^{4}$ self-interaction we need to include 4 loop graphs in the equation of motion. This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. Yaffe, Phys. Rev. D53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear response theory and the imaginary-time formalism of thermal field theory. Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success...