Quantum Secure Group Communication.

Science.gov (United States)

Li, Zheng-Hong; Zubairy, M Suhail; Al-Amri, M

2018-03-01

We propose a quantum secure group communication protocol for the purpose of sharing the same message among multiple authorized users. Our protocol can remove the need for key management that is needed for the quantum network built on quantum key distribution. Comparing with the secure quantum network based on BB84, we show our protocol is more efficient and securer. Particularly, in the security analysis, we introduce a new way of attack, i.e., the counterfactual quantum attack, which can steal information by "invisible" photons. This invisible photon can reveal a single-photon detector in the photon path without triggering the detector. Moreover, the photon can identify phase operations applied to itself, thereby stealing information. To defeat this counterfactual quantum attack, we propose a quantum multi-user authorization system. It allows us to precisely control the communication time so that the attack can not be completed in time.

A Quantum Groups Primer

Science.gov (United States)

Majid, Shahn

2002-05-01

Here is a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes for the Part III pure mathematics course at Cambridge University, the book is suitable as a primary text for graduate courses in quantum groups or supplementary reading for modern courses in advanced algebra. The material assumes knowledge of basic and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The volume is a primer for mathematicians but it will also be useful for mathematical physicists.

From field theory to quantum groups

CERN Document Server

Jancewicz, B

1996-01-01

Professor Jerzy Lukierski, an outstanding specialist in the domain of quantum groups, will reach on May 21, 1995 the age of sixty. This is a birthday volume dedicated to him. It assumes the form of a collection of papers on a wide range of topics in modern research area from theoretical high energy physics to mathematical physics. Various topics of quantum groups will be treated with a special emphasis. Quantum groups is nowadays a very fashionable subject both in mathematics and high energy physics.

Generalized quantum groups

International Nuclear Information System (INIS)

Leivo, H.P.

1992-01-01

The algebraic approach to quantum groups is generalized to include what may be called an anyonic symmetry, reflecting the appearance of phases more general than ±1 under transposition. (author). 6 refs

Invariant subsets under compact quantum group actions

OpenAIRE

Huang, Huichi

2012-01-01

We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.

Quantum group of isometries in classical and noncommutative geometry

International Nuclear Information System (INIS)

Goswami, D.

2007-04-01

We formulate a quantum generalization of the notion of the group of Riemannian isometries for a compact Riemannian manifold, by introducing a natural notion of smooth and isometric action by a compact quantum group on a classical or noncommutative manifold described by spectral triples, and then proving the existence of a universal object (called the quantum isometry group) in the category of compact quantum groups acting smoothly and isometrically on a given (possibly noncommutative) manifold. Our formulation accommodates spectral triples which are not of type II. We give an explicit description of quantum isometry groups of commutative and noncommutative tori, and in this context, obtain the quantum double torus defined in [7] as the universal quantum group of holomorphic isometries of the noncommutative torus. (author)

Quantum group and Manin plane related to a coloured braid group representation

International Nuclear Information System (INIS)

Basu Mallick, B.

1993-07-01

By considering 'coloured' braid group representation we have obtained a quantum group, which reduces to the standards GL q (2) and GL pq (2) cases at some particular limits of the 'colour' parameters. In spite of quite complicated nature, all of these new quantum group relations can be expressed neatly in the Heisenberg-Weyl form, for a nontrivial choice of the basis elements. Furthermore, it is possible to associate invariant Manin planes, parametrized by the 'colour' variables, with such quantum group structure. (author). 26 refs

Quantum Groups, Property (T), and Weak Mixing

Science.gov (United States)

Brannan, Michael; Kerr, David

2018-06-01

For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having almost invariant vectors. This is a generalization of a theorem of Bekka and Valette from the group setting and was previously established in the case of low dual by Daws, Skalski, and Viselter. Our approach uses spectral techniques and is completely different from those of Bekka-Valette and Daws-Skalski-Viselter. By a separate argument we furthermore extend the result to second countable nonunimodular locally compact quantum groups, which are shown in particular not to have property (T), generalizing a theorem of Fima from the discrete setting. We also obtain quantum group versions of characterizations of property (T) of Kerr and Pichot in terms of the Baire category theory of weak mixing representations and of Connes and Weiss in terms of the prevalence of strongly ergodic actions.

Modular groups in quantum field theory

International Nuclear Information System (INIS)

Borchers, H.-J.

2000-01-01

The author discusses the connection of Lagrangean quantum field theory, perturbation theory, the Lehmann-Symanzik-Zimmermann theory, Wightman's quantum field theory, the Euclidean quantum field theory, and the Araki-Haag-Kastler theory of local observables with modular groups. In this connection he considers the PCT-theorem, and the tensor product decomposition. (HSI)

Bicovariant differential calculus on quantum groups and wave mechanics

International Nuclear Information System (INIS)

Carow-Watamura, U.; Watamura, S.; Hebecker, A.; Schlieker, M.; Weich, W.

1992-01-01

The bicovariant differential calculus on quantum groups defined by Woronowicz and later worked out explicitly by Carow-Watamura et al. and Jurco for the real quantum groups SU q (N) and SO q (N) through a systematic construction of the bicovariant bimodules of these quantum groups, is reviewed for SU q (2) and SO q (N). The resulting vector fields build representations of the quantized universal enveloping algebras acting as covariant differential operators on the quantum groups and their associated quantum spaces. As an application, a free particle stationary wave equation on quantum space is formulated and solved in terms of a complete set of energy eigenfunctions. (author) 15 refs

Three lectures on quantum groups: Representations, duality, real forms

International Nuclear Information System (INIS)

Dobrev, V.K.

1992-07-01

Quantum groups appeared first as quantum algebra, i.e. as one parameter deformations of the numerical enveloping algebras of complex Lie algebras, in the study of the algebraic aspects of quantum integrable systems. Then quantum algebras related to triparametric solutions of the quantum Yang-Baxter equation were axiomatically introduced as (pseudo) quasi-triangular Hopf algebras. Later, a theory of formal deformations has been developed and the notion of quasi-Hopf algebra has been introduced. In other approaches to quantum groups the objects are called quantum matrix groups and are Hopf algebras in chirality to the quantum algebras. The representations of U q (G), the chirality and the real forms associated to these approaches are discussed here. Refs

Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces

International Nuclear Information System (INIS)

Chu, Chong-Sun; Zumino, B.

1995-01-01

The vector fields of the quantum Lie algebra are described for the quantum groups GL q (n), SL q (N) and SO q (N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU q (N) and SO q (N,R) are discussed in detail

Quantum groups, non-commutative differential geometry and applications

International Nuclear Information System (INIS)

Schupp, P.; California Univ., Berkeley, CA

1993-01-01

The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related sciences. A generalization of unitary time evolution is proposed and studied for a simple 2-level system, leading to non-conservation of microscopic entropy, a phenomenon new to quantum mechanics. A Cartan calculus that combines functions, forms, Lie derivatives and inner derivations along general vector fields into one big algebra is constructed for quantum groups and then extended to quantum planes. The construction of a tangent bundle on a quantum group manifold and an BRST type approach to quantum group gauge theory are given as further examples of applications. The material is organized in two parts: Part I studies vector fields on quantum groups, emphasizing Hopf algebraic structures, but also introducing a ''quantum geometric'' construction. Using a generalized semi-direct product construction we combine the dual Hopf algebras A of functions and U of left-invariant vector fields into one fully bicovariant algebra of differential operators. The pure braid group is introduced as the commutant of Δ(U). It provides invariant maps A → U and thereby bicovariant vector fields, casimirs and metrics. This construction allows the translation of undeformed matrix expressions into their less obvious quantum algebraic counter parts. We study this in detail for quasitriangular Hopf algebras, giving the determinant and orthogonality relation for the ''reflection'' matrix. Part II considers the additional structures of differential forms and finitely generated quantum Lie algebras -- it is devoted to the construction of the Cartan calculus, based on an undeformed Cartan identity

Coherent states for quantum compact groups

CERN Document Server

Jurco, B

1996-01-01

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the q--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}

Integrable lattice models and quantum groups

International Nuclear Information System (INIS)

Saleur, H.; Zuber, J.B.

1990-01-01

These lectures aim at introducing some basic algebraic concepts on lattice integrable models, in particular quantum groups, and to discuss some connections with knot theory and conformal field theories. The list of contents is: Vertex models and Yang-Baxter equation; Quantum sl(2) algebra and the Yang-Baxter equation; U q sl(2) as a symmetry of statistical mechanical models; Face models; Face models attached to graphs; Yang-Baxter equation, braid group and link polynomials

Coherent states for quantum compact groups

International Nuclear Information System (INIS)

Jurco, B.; Stovicek, P.; CTU, Prague

1996-01-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A l , B l , C l and D l . The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)

Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2) and SO(3) groups

International Nuclear Information System (INIS)

Podles, P.

1995-01-01

We prove that each action of a compact matrix quantum group on a compact quantum space can be decomposed into irreducible representations of the group. We give the formula for the corresponding multiplicities in the case of the quotient quantum spaces. We describe the subgroups and the quotient spaces of quantum SU(2) and SO(3) groups. (orig.)

Duality and quantum groups

International Nuclear Information System (INIS)

Alvarez-Gaume, L.; Gomez, C.; Sierra, G.

1990-01-01

We show that the duality properties of Rational Conformal Field Theories follow from the defining relations and the representation theory of quantum groups. The fusion and braiding matrices are q-analogues of the 6j-symbols and the modular transformation matrices are obtained from the properties of the co-multiplication. We study in detail the Wess-Zumino-Witten models and the rational gaussian models as examples, but carry out the arguments in general. We point out the connections with the Chern-Simons approach. We give general arguments of why the general solution to the polynomial equations of Moore and Seiberg describing the duality properties of Rational Conformal Field Theories defines a Quantum Group acting on the space of conformal blocks. A direct connection between Rational Theories and knot invariants is also presented along the lines of Jones' original work. (orig.)

Coherent states for quantum compact groups

Energy Technology Data Exchange (ETDEWEB)

Jurco, B. [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Stovicek, P. [Ceske Vysoke Uceni Technicke, Prague (Czech Republic). Dept. of Mathematics]|[CTU, Prague (Czech Republic). Doppler Inst.

1996-12-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A{sub l}, B{sub l}, C{sub l} and D{sub l}. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)

Notes on quantum groups

International Nuclear Information System (INIS)

Pressley, A.; Chari, V.; Tata Inst. of Fundamental Research, Bombay

1990-01-01

The authors presents an introduction to quantum groups defined as a deformation of the universal enveloping algebra of a Lie algebra. After the description of Hopf algebras with some examples the approach of Drinfel'd and Jimbo is described, where the quantization of a Lie algebra represents a Hopf algebra, defined over the algebra of formal power series in an indetermined h. The authors show that this approach arises from a r-matrix, which satisfies the classical Yang-Baxter equation. As example quantum sl 2 is considered. Furthermore the approaches of Manin and Woroniwicz and the R-matrix approach are described. (HSI)

Complex quantum group, dual algebra and bicovariant differential calculus

International Nuclear Information System (INIS)

Carow-Watamura, U.; Watamura, Satoshi

1993-01-01

The method used to construct the bicovariant bimodule in ref. [CSWW] is applied to examine the structure of the dual algebra and the bicovariant differential calculus of the complex quantum group. The complex quantum group Fun q (SL(N, C)) is defined by requiring that it contains Fun q (SU(N)) as a subalgebra analogously to the quantum Lorentz group. Analyzing the properties of the fundamental bimodule, we show that the dual algebra has the structure of the twisted product Fun q (SU(N))x tilde Fun q (SU(N)) reg *. Then the bicovariant differential calculi on the complex quantum group are constructed. (orig.)

Quantum Fourier transform, Heisenberg groups and quasi-probability distributions

International Nuclear Information System (INIS)

Patra, Manas K; Braunstein, Samuel L

2011-01-01

This paper aims to explore the inherent connection between Heisenberg groups, quantum Fourier transform (QFT) and (quasi-probability) distribution functions. Distribution functions for continuous and finite quantum systems are examined from three perspectives and all of them lead to Weyl-Gabor-Heisenberg groups. The QFT appears as the intertwining operator of two equivalent representations arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of the Wigner function from the marginal distributions via inverse Radon transform giving explicit formulae. We consider some applications of our approach to quantum information processing and quantum process tomography.

Winter School on Operator Spaces, Noncommutative Probability and Quantum Groups

CERN Document Server

2017-01-01

Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems.  A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions.  The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The l...

Category O for quantum groups

DEFF Research Database (Denmark)

Andersen, Henning Haahr; Mazorchuk, Volodymyr

2015-01-01

We study the BGG-categories O_q associated to quantum groups. We prove that many properties of the ordinary BGG-category O for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition...... for simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan–Lusztig conjectures for O and for finite-dimensional U_q-modules we are able to determine all irreducible characters as well as the characters of all indecomposable tilting modules in O_q . As a consequence......, we also recover the known result that the generic quantum case behaves like the classical category O....

Introduction to quantum groups

International Nuclear Information System (INIS)

Monteiro, Marco A.R.

1994-01-01

An elementary introduction to quantum groups is presented. The example of Universal Enveloping Algebra of deformed SU(2) is analysed in detail. It is also discussed systems made up of bosonic q-oscillators at finite temperature within the formalism of Thermo-Field Dynamics. (author). 39 refs

Quantum gravity with matter and group field theory

International Nuclear Information System (INIS)

Krasnov, Kirill

2007-01-01

A generalization of the matrix model idea to quantum gravity in three and higher dimensions is known as group field theory (GFT). In this paper we study generalized GFT models that can be used to describe 3D quantum gravity coupled to point particles. The generalization considered is that of replacing the group leading to pure quantum gravity by the twisted product of the group with its dual-the so-called Drinfeld double of the group. The Drinfeld double is a quantum group in that it is an algebra that is both non-commutative and non-cocommutative, and special care is needed to define group field theory for it. We show how this is done, and study the resulting GFT models. Of special interest is a new topological model that is the 'Ponzano-Regge' model for the Drinfeld double. However, as we show, this model does not describe point particles. Motivated by the GFT considerations, we consider a more general class of models that are defined not using GFT, but the so-called chain mail techniques. A general model of this class does not produce 3-manifold invariants, but has an interpretation in terms of point particle Feynman diagrams

Group field theory and simplicial quantum gravity

International Nuclear Information System (INIS)

Oriti, D

2010-01-01

We present a new group field theory for 4D quantum gravity. It incorporates the constraints that give gravity from BF theory and has quantum amplitudes with the explicit form of simplicial path integrals for first-order gravity. The geometric interpretation of the variables and of the contributions to the quantum amplitudes is manifest. This allows a direct link with other simplicial gravity approaches, like quantum Regge calculus, in the form of the amplitudes of the model, and dynamical triangulations, which we show to correspond to a simple restriction of the same.

Quantum renormalization group approach to quantum coherence and multipartite entanglement in an XXZ spin chain

Energy Technology Data Exchange (ETDEWEB)

Wu, Wei [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Beijing Computational Science Research Center, Beijing 100193 (China); Xu, Jing-Bo, E-mail: xujb@zju.edu.cn [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)

2017-01-30

We investigate the performances of quantum coherence and multipartite entanglement close to the quantum critical point of a one-dimensional anisotropic spin-1/2 XXZ spin chain by employing the real-space quantum renormalization group approach. It is shown that the quantum criticality of XXZ spin chain can be revealed by the singular behaviors of the first derivatives of renormalized quantum coherence and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized quantum coherence and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical point of XXZ spin chain. - Highlights: • The QPT of XXZ chain is studied by renormalization group. • The renormalized coherence and multiparticle entanglement is investigated. • Scaling laws of renormalized coherence and multiparticle entanglement are revealed.

Braid group representation on quantum computation

Energy Technology Data Exchange (ETDEWEB)

Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com [Department of Computational Sciences, Bandung Institute of Technology (Indonesia); Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id [Algebra Research Group, Bandung Institute of Technology (Indonesia)

2015-09-30

There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.

25 Years of Quantum Groups: from Definition to Classification

Directory of Open Access Journals (Sweden)

A. Stolin

2008-01-01

Full Text Available In mathematics and theoretical physics, quantum groups are certain non-commutative, non-cocommutative Hopf algebras, which first appeared in the theory of quantum integrable models and later they were formalized by Drinfeld and Jimbo. In this paper we present a classification scheme for quantum groups, whose classical limit is a polynomial Lie algebra. As a consequence we obtain deformed XXX and XXZ Hamiltonians. 

Quantum gravity and the renormalisation group

International Nuclear Information System (INIS)

Litim, D.

2011-01-01

The Standard Model of particle physics is remarkably successful in describing three out of the four known fundamental forces of Nature. But what is up with gravity? Attempts to understand quantum gravity on the same footing as the other forces still face problems. Some time ago, it has been pointed out that gravity may very well exist as a fundamental quantum field theory provided its high-energy behaviour is governed by a fixed point under the renormalisation group. In recent years, this 'asymptotic safety' scenario has found significant support thanks to numerous renormalisation group studies, lattice simulations, and new ideas within perturbation theory. The lectures will give an introduction into the renormalisation group approach for quantum gravity, aimed at those who haven't met the topic before. After an introduction and overview, the key ideas and concepts of asymptotic safety for gravity are fleshed out. Results for gravitational high-energy fixed points and scaling exponents are discussed as well as key features of the gravitational phase diagram. The survey concludes with some phenomenological implications of fixed point gravity including the physics of black holes and particle physics beyond the Standard Model. (author)

A secure quantum group signature scheme based on Bell states

International Nuclear Information System (INIS)

Zhang Kejia; Song Tingting; Zuo Huijuan; Zhang Weiwei

2013-01-01

In this paper, we propose a new secure quantum group signature with Bell states, which may have applications in e-payment system, e-government, e-business, etc. Compared with the recent quantum group signature protocols, our scheme is focused on the most general situation in practice, i.e. only the arbitrator is trusted and no intermediate information needs to be stored in the signing phase to ensure the security. Furthermore, our scheme has achieved all the characteristics of group signature—anonymity, verifiability, traceability, unforgetability and undeniability, by using some current developed quantum and classical technologies. Finally, a feasible security analysis model for quantum group signature is presented. (paper)

Factorizable sheaves and quantum groups

CERN Document Server

Bezrukavnikov, Roman; Schechtman, Vadim

1998-01-01

The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity. These representations are realized as some spaces of vanishing cycles of perverse sheaves over configuration spaces. As an application, the bundles of conformal blocks over the moduli spaces of curves are studied. The book is intended for specialists in group representations and algebraic geometry.

Positive Nonlinear Dynamical Group Uniting Quantum Mechanics and Thermodynamics

OpenAIRE

Beretta, Gian Paolo

2006-01-01

We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy stat...

Algebras of functions on compact quantum groups, Schubert cells and quantum tori

International Nuclear Information System (INIS)

Levendorskij, S.; Soibelman, Ya.

1991-01-01

The structure of Poisson Lie groups on a simple compact group are parametrized by pairs (a, u), where aelement ofR, uelement ofΛ 2 f R , and f R is a real Cartan subalgebra of complexification of Lie algebra of the group in question. In the present article the description of the symplectic leaves for all pairs (a, u) is given. Also, the corresponding quantized algebras of functions are constructed and their irreducible representations are described. In the course of investigation Schubert cells and quantum tori appear. At the end of the article the quantum analog of the Weyl group is constructed and some of its applications, among them the formula for the universal R-matrix, are given. (orig.)

q-trace for quantum groups and q-deformed Yang-Mills theory

International Nuclear Information System (INIS)

Isaev, A.P.; Popowicz, Z.

1992-01-01

The definitions of orbits and q-trace for the quantum groups are introduced. Then the q-trace is used to construct the invariants for the quantum group orbits and to formulate the q-deformed Yang-Mills theory. The amusing formal relation of the Weinberg type mixing angle with the quantum group deformation parameter is discussed. (orig.)

About the differential calculus on the quantum groups

International Nuclear Information System (INIS)

Bernard, D.

1992-01-01

Given a solution R of the Yang-Baxter equation admitting a quasi-triangular decomposition we define a quasi-triangular quantum Lie algebra. We describe how to any quasi-triangular quantum Lie algebra U(G R ) is associated a Hopf algebra F(G R ) with a differential calculus on it such that the algebra of the quantum Lie derivatives is the algebra U(G R ). This allows us to make the connection between the differential calculus on quantum groups and the exchange algebras of the algebraic Bethe ansatz. (orig.)

Group field theories for all loop quantum gravity

Science.gov (United States)

Oriti, Daniele; Ryan, James P.; Thürigen, Johannes

2015-02-01

Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

Fusion Rings for Quantum Groups

DEFF Research Database (Denmark)

Andersen, Henning Haahr; Stroppel, Catharina

2014-01-01

We study the fusion rings of tilting modules for a quantum group at a root of unity modulo the tensor ideal of negligible tilting modules. We identify them in type A with the combinatorial rings from Korff, C., Stroppel, C.: The sl(ˆn)k-WZNW fusion ring: a combinato-rial construction...... and a realisation as quotient of quantum cohomology. Adv. Math. 225(1), 200–268, (2010) and give a similar description of the sp2n-fusion ring in terms of non-commutative symmetric functions. Moreover we give a presentation of all fusion rings in classical types as quotients of polynomial rings. Finally we also...... compute the fusion rings for type G2....

Quantum algebras as quantizations of dual Poisson–Lie groups

International Nuclear Information System (INIS)

Ballesteros, Ángel; Musso, Fabio

2013-01-01

A systematic computational approach for the explicit construction of any quantum Hopf algebra (U z (g), Δ z ) starting from the Lie bialgebra (g, δ) that gives the first-order deformation of the coproduct map Δ z is presented. The procedure is based on the well-known ‘quantum duality principle’, namely the fact that any quantum algebra can be viewed as the quantization of the unique Poisson–Lie structure (G*, Λ g ) on the dual group G*, which is obtained by exponentiating the Lie algebra g* defined by the dual map δ*. From this perspective, the coproduct for U z (g) is just the pull-back of the group law for G*, and the Poisson analogues of the quantum commutation rules for U z (g) are given by the unique Poisson–Lie structure Λ g on G* whose linearization is the Poisson analogue of the initial Lie algebra g. This approach is shown to be a very useful technical tool in order to solve the Lie bialgebra quantization problem explicitly since, once a Lie bialgebra (g, δ) is given, the full dual Poisson–Lie group (G*, Λ) can be obtained either by applying standard Poisson–Lie group techniques or by implementing the algorithm presented here with the aid of symbolic manipulation programs. As a consequence, the quantization of (G*, Λ) will give rise to the full U z (g) quantum algebra, provided that ordering problems are appropriately fixed through the choice of certain local coordinates on G* whose coproduct fulfils a precise ‘quantum symmetry’ property. The applicability of this approach is explicitly demonstrated by reviewing the construction of several instances of quantum deformations of physically relevant Lie algebras such as sl(2,R), the (2+1) anti-de Sitter algebra so(2, 2) and the Poincaré algebra in (3+1) dimensions. (paper)

Inhomogeneous Quantum Invariance Group of Multi-Dimensional Multi-parameter Deformed Boson Algebra

International Nuclear Information System (INIS)

Altintas Azmi Ali; Arik Metin; Arikan Ali Serdar; Dil Emre

2012-01-01

We investigate the inhomogeneous invariance quantum group of the d-dimensional d-parameter deformed boson algebra. It is found that the homogeneous part of this quantum group is given by the d-parameter deformed general linear group. We construct the R-matrix which collects all information about the non-commuting structure of the quantum group for the two-dimensional case. (general)

Non-commutative representation for quantum systems on Lie groups

Energy Technology Data Exchange (ETDEWEB)

Raasakka, Matti Tapio

2014-01-27

The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a {sup *}-algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R{sup d}, U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase

Non-commutative representation for quantum systems on Lie groups

International Nuclear Information System (INIS)

Raasakka, Matti Tapio

2014-01-01

The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a * -algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R d , U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase space path

Quantum group symmetry of classical and noncommutative geometry

Indian Academy of Sciences (India)

Debashish Goswami

2016-07-01

Jul 1, 2016 ... universal enveloping algebra U(L) of a Lie algebra L, (iv) ... Kustermans defined locally compact quantum groups too. .... There are other versions of quantum isometries formulated by me ..... classical connected spaces when either the space is ..... Etingof-Walton's paper, we have : (i) M0 is open and dense,.

Fusion Rings for Quantum Groups

DEFF Research Database (Denmark)

Andersen, Henning Haahr; Stroppel, Catharina

2012-01-01

We study the fusion rings of tilting modules for a quantum group at a root of unity modulo the tensor ideal of negligible tilting modules. We identify them in type A with the combinatorial rings from [12] and give a similar description of the sp2n-fusion ring in terms of noncommutative symmetric...

Introduction to compact (matrix) quantum groups and Banica ...

Indian Academy of Sciences (India)

Moritz Weber

2017-11-27

Nov 27, 2017 ... Building on this, we define Banica–Speicher quantum .... four vertices) are ... A compact Hausdorff space X gives rise to a commutative unitalC .... (a) Recall the construction of the group C ..... Having formulated the features of the Haar integration in 'quantum terms', ...... paper: When is the map in [30, Prop.

Quantum E(2) group and and its Pontryagin dual

International Nuclear Information System (INIS)

Woronowicz, S.L.

1991-01-01

The quantum deformation of the group of motions of the plane and its Pontryagin dual are described in detail. It is shown that the Pontryagin dual is a quantum deformation of the group of transformations of the plane generated by translations and dilations. An explicit expression for the unitary bicharacter describing the Pontryagin duality is found. The Heisenberg commutation relations are written down. (orig.)

Diffeomorphism Group Representations in Relativistic Quantum Field Theory

Energy Technology Data Exchange (ETDEWEB)

Goldin, Gerald A. [Rutgers Univ., Piscataway, NJ (United States); Sharp, David H. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-12-20

We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.

Tailoring surface groups of carbon quantum dots to improve photoluminescence behaviors

International Nuclear Information System (INIS)

Tian, Ruixue; Hu, Shengliang; Wu, Lingling; Chang, Qing; Yang, Jinlong; Liu, Jun

2014-01-01

Highlights: • We develop a facile and green method to tailor surface groups. • Photoluminescence behaviors of carbon quantum dots are improved by tailoring their surface groups. • Highly luminescent efficiency is produced by amino-hydrothermal treatment of reduced carbon quantum dots. - Abstract: A facile and green method to tailor surface groups of carbon quantum dots (CQDs) is developed by hydrothermal treatment in an autoclave. The photoluminescence (PL) behaviors of CQDs depend on the types of surface groups. Highly efficient photoluminescence is obtained through amino-hydrothermal treatment of the CQDs reduced by NaBH 4 . The effects of surface groups on PL behavior are attributed to the degrees of energy band bending induced by surface groups

Quantum theory, groups and representations an introduction

CERN Document Server

Woit, Peter

2017-01-01

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific ...

PREFACE Quantum Groups, Quantum Foundations and Quantum Information: a Festschrift for Tony Sudbery

Science.gov (United States)

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

Renormalization group in quantum mechanics

International Nuclear Information System (INIS)

Polony, J.

1996-01-01

The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright copyright 1996 Academic Press, Inc

Infinite dimensional groups and algebras in quantum physics

International Nuclear Information System (INIS)

Ottesen, J.T.

1995-01-01

This book is an introduction to the application of infite-dimensional groups and algebras in quantum physics. Especially considered are the spin representation of the infinite-dimensional orthogonal group, the metaplectic representation of the infinite-dimensional symplectic groups, and Loop and Virasoro algebras. (HSI)

Reducibility of quantum representations of mapping class groups

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Fjelstad, Jens

2010-01-01

that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture...... this decomposition is a complete decomposition into irreducible representations for high enough levels....

On the geometry of inhomogeneous quantum groups

Energy Technology Data Exchange (ETDEWEB)

Aschieri, Paolo [Scuola Normale Superiore, Pisa (Italy)

1998-01-01

The author gives a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case. He further analyzes the relation between differential calculus and quantum Lie algebra of left (right) invariant vectorfields. Equivalent definitions of bicovariant differential calculus are studied and their geometrical interpretation is explained. From these data he constructs and analyzes the space of vectorfields, and naturally introduces a contraction operator and a Lie derivative. Their properties are discussed.

Cosmology from group field theory formalism for quantum gravity.

Science.gov (United States)

Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo

2013-07-19

We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.

Group-III vacancy induced InxGa1-xAs quantum dot interdiffusion

International Nuclear Information System (INIS)

Djie, H. S.; Wang, D.-N.; Ooi, B. S.; Hwang, J. C. M.; Gunawan, O.

2006-01-01

The impact of group-III vacancy diffusion, generated during dielectric cap induced intermixing, on the energy state transition and the inhomogeneity reduction in the InGaAs/GaAs quantum-dot structure is investigated. We use a three-dimensional quantum-dot diffusion model and photoluminescence data to determine the thermal and the interdiffusion properties of the quantum dot. The band gap energy variation related to the dot uniformity is found to be dominantly affected by the height fluctuation. A group-III vacancies migration energy H m for InGaAs quantum dots of 1.7 eV was deduced. This result is similar to the value obtained from the bulk and GaAs/AlGaAs quantum-well materials confirming the role of SiO 2 capping enhanced group-III vacancy induced interdiffusion in the InGaAs quantum dots

A remark on the motivic Galois group and the quantum coadjoint action

International Nuclear Information System (INIS)

Grosse, H.; Schlesinger, K.-G.

2006-01-01

It has been suggested that the Grothendieck-Teichmueller group GT should act on the Duflo isomorphism of su(2), but the corresponding realization of GT turned out to be trivial. We show that a solvable quotient of the motivic Galois group - which is supposed to agree with GT - is closely related to the quantum coadjoint action on U q (sl 2 ) for q a root of unity, i.e. in the quantum group case one has a nontrivial realization of a quotient of the motivic Galois group. From a discussion of the algebraic properties of this realization we conclude that in more general cases than U q (sl 2 ) it should be related to a quantum version of the motivic Galois group. Finally, we discuss the relation of our construction to quantum field and string theory and explain what we believe to be the 'physical reason' behind this relation between the motivic Galois group and the quantum coadjoint action. This might be a starting point for the generalization of our construction to more involved examples. (orig.)

Paragrassmann analysis and quantum groups

International Nuclear Information System (INIS)

Filippov, A.T.; Isaev, A.P.; Kurdikov, A.B.

1992-01-01

Paragrassmann algebras with one and many paragrassmann variables are considered from the algebraic point of view without using the Green anzatz. A differential operator with respect to paragrassmann variable and a covariant para-super-derivative are introduced giving a natural generalization of the Grassmann calculus to a paragrassmann one. Deep relations between paragrassmann and quantum groups with deformation parameters being root of unity are established. 20 refs

Endomorphism Algebras of Tensor Powers of Modules for Quantum Groups

DEFF Research Database (Denmark)

Andersen, Therese Søby

We determine the ring structure of the endomorphism algebra of certain tensor powers of modules for the quantum group of sl2 in the case where the quantum parameter is allowed to be a root of unity. In this case there exists -- under a suitable localization of our ground ring -- a surjection from...... the group algebra of the braid group to the endomorphism algebra of any tensor power of the Weyl module with highest weight 2. We take a first step towards determining the kernel of this map by reformulating well-known results on the semisimplicity of the Birman-Murakami-Wenzl algebra in terms of the order...... of the quantum parameter. Before we arrive at these main results, we investigate the structure of the endomorphism algebra of the tensor square of any Weyl module....

Multi-group dynamic quantum secret sharing with single photons

Energy Technology Data Exchange (ETDEWEB)

Liu, Hongwei [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Ma, Haiqiang, E-mail: hqma@bupt.edu.cn [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Wei, Kejin [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Yang, Xiuqing [School of Science, Beijing Jiaotong University, Beijing 100044 (China); Qu, Wenxiu; Dou, Tianqi; Chen, Yitian; Li, Ruixue; Zhu, Wu [School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China)

2016-07-15

In this letter, we propose a novel scheme for the realization of single-photon dynamic quantum secret sharing between a boss and three dynamic agent groups. In our system, the boss can not only choose one of these three groups to share the secret with, but also can share two sets of independent keys with two groups without redistribution. Furthermore, the security of communication is enhanced by using a control mode. Compared with previous schemes, our scheme is more flexible and will contribute to a practical application. - Highlights: • A multi-group dynamic quantum secret sharing with single photons scheme is proposed. • Any one of the groups can be chosen to share secret through controlling the polarization of photons. • Two sets of keys can be shared simultaneously without redistribution.

New construction of quantum error-avoiding codes via group representation of quantum stabilizer codes

Energy Technology Data Exchange (ETDEWEB)

Xiao, Hailin [Wenzhou University, College of Physics and Electronic Information Engineering, Wenzhou (China); Southeast University, National Mobile Communications Research Laboratory, Nanjing (China); Guilin University of Electronic Technology, Ministry of Education, Key Laboratory of Cognitive Radio and Information Processing, Guilin (China); Zhang, Zhongshan [University of Science and Technology Beijing, Beijing Engineering and Technology Research Center for Convergence Networks and Ubiquitous Services, Beijing (China); Chronopoulos, Anthony Theodore [University of Texas at San Antonio, Department of Computer Science, San Antonio, TX (United States)

2017-10-15

In quantum computing, nice error bases as generalization of the Pauli basis were introduced by Knill. These bases are known to be projective representations of finite groups. In this paper, we propose a group representation approach to the study of quantum stabilizer codes. We utilize this approach to define decoherence-free subspaces (DFSs). Unlike previous studies of DFSs, this type of DFSs does not involve any spatial symmetry assumptions on the system-environment interaction. Thus, it can be used to construct quantum error-avoiding codes (QEACs) that are fault tolerant automatically. We also propose a new simple construction of QEACs and subsequently develop several classes of QEACs. Finally, we present numerical simulation results encoding the logical error rate over physical error rate on the fidelity performance of these QEACs. Our study demonstrates that DFSs-based QEACs are capable of providing a generalized and unified framework for error-avoiding methods. (orig.)

The real symplectic groups quantum mechanics and optics

International Nuclear Information System (INIS)

Arvind; Mukunda, N.

1995-01-01

We present a utilitarian review of the family of matrix groups Sp(2n,R), in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of Sp(2n,R). Global decomposition theorems, interesting subgroups and their generators are described. Turning to n-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and developed a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under Sp(2n,R) action are delineated. (author). 22 refs

Group contractions in quantum field theory

International Nuclear Information System (INIS)

Concini, C. De; Vitiello, G.

1979-01-01

General theorems are given for SU(n) and SO(n). A projective geometry argument is also presented with disclosure of the occurrence a group contraction mechanism as a geometric consequence of spontaneous breakdown of symmetry. It is also shown that a contraction of the conformal group gives account of the number of degrees of freedom of an n-pseudoparticle system in an Euclidean SU(2) gauge invariant Yang-Mills theory, in agreement with the result obtained by algebraic geometry methods. Low-energy theorems and ordered states symmetry patterns are observable manifestations of group contractions. These results seem to support the conjecture that the transition from quantum to classical physics involves a group contraction mechanism. (author)

Wigner functions for noncommutative quantum mechanics: A group representation based construction

Energy Technology Data Exchange (ETDEWEB)

Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com [Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada)

2015-12-15

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.

An introduction to quantum groups and non-commutative differential calculus

International Nuclear Information System (INIS)

Azcarraga, J.A. de; Rodenas, F.

1995-01-01

An introduction to quantum groups and quantum spaces is presented, and the non-commutative calculus on them is discussed. The case of q-Minkowski space is presented as an illustrative example. A set of useful expressions and formulae are collected in an appendix. 45 refs

Quantum spaces, central extensions of Lie groups and related quantum field theories

Science.gov (United States)

Poulain, Timothé; Wallet, Jean-Christophe

2018-02-01

Quantum spaces with su(2) noncommutativity can be modelled by using a family of SO(3)-equivariant differential *-representations. The quantization maps are determined from the combination of the Wigner theorem for SU(2) with the polar decomposition of the quantized plane waves. A tracial star-product, equivalent to the Kontsevich product for the Poisson manifold dual to su(2) is obtained from a subfamily of differential *-representations. Noncommutative (scalar) field theories free from UV/IR mixing and whose commutative limit coincides with the usual ϕ 4 theory on ℛ3 are presented. A generalization of the construction to semi-simple possibly non simply connected Lie groups based on their central extensions by suitable abelian Lie groups is discussed. Based on a talk presented by Poulain T at the XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25), Prague, June 6-10 2017.

Quasi quantum group covariant q-oscillators

International Nuclear Information System (INIS)

Schomerus, V.

1992-05-01

If q is a p-th root of unity there exists a quasi-co-associative truncated quantum group algebra U T q (sl 2 ) whose indecomposable representations are the physical representations of U q (sl 2 ), whose co-product yields the truneated tensor product of physical representations of U q (sl 2 ), and whose R-matrix satisfies quasi Yang Baxter equations. For primitive p-th roots q, we consider a 2-dimensional q-oscillator which admits U T q (sl 2 ) as a symmetry algebra. Its wave functions lie in a space F T q of 'functions on the truncated quantum plane', i.e. of polynomials in noncommuting complex coordinate functions z a , on which multiplication operators Z a and the elements of U T q (sl 2 ) can act. This illustrates the concept of quasi quantum planes. Due to the truncation, the Hilbert space of states is finite dimensional. The subspaces F T(n) of monomials in x a of n-th degree vanish for n ≥ p-1, and F T(n) carries the 2J+1 dimensional irreducible representation of U T q (sl 2 ) if n=2J, J=0, 1/2, ... 1/2(p-2). Partial derivatives δ a are introduced. We find a *-operation on the algebra of multiplication operators Z i and derivatives δ b such that the adjoints Z * a act as differentiation on the truncated quantum plane. Multiplication operators Z a ('creation operators') and their adjoints ('annihilation operators') obey q -1/2 -commutation relations. The *-operation is used to determine a positive definite scalar product on the truncated quantum plane F T q . Some natural candidates of Hamiltonians for the q-oscillators are determined. (orig./HSI)

L^2-Betti numbers of rigid C*-tensor categories and discrete quantum groups

DEFF Research Database (Denmark)

Kyed, David; Raum, Sven; Vaes, Stefaan

2017-01-01

of the representation category $Rep(G)$ and thus, in particular, invariant under monoidal equivalence. As an application, we obtain several new computations of $L^2$-Betti numbers for discrete quantum groups, including the quantum permutation groups and the free wreath product groups. Finally, we obtain upper bounds...

A Third-Party E-Payment Protocol Based on Quantum Group Blind Signature

Science.gov (United States)

Zhang, Jian-Zhong; Yang, Yuan-Yuan; Xie, Shu-Cui

2017-09-01

A third-party E-payment protocol based on quantum group blind signature is proposed in this paper. Our E-payment protocol could protect user's anonymity as the traditional E-payment systems do, and also have unconditional security which the classical E-payment systems can not provide. To achieve that, quantum key distribution, one-time pad and quantum group blind signature are adopted in our scheme. Furthermore, if there were a dispute, the manager Trent can identify who tells a lie.

Group covariant protocols for quantum string commitment

International Nuclear Information System (INIS)

Tsurumaru, Toyohiro

2006-01-01

We study the security of quantum string commitment (QSC) protocols with group covariant encoding scheme. First we consider a class of QSC protocol, which is general enough to incorporate all the QSC protocols given in the preceding literatures. Then among those protocols, we consider group covariant protocols and show that the exact upperbound on the binding condition can be calculated. Next using this result, we prove that for every irreducible representation of a finite group, there always exists a corresponding nontrivial QSC protocol which reaches a level of security impossible to achieve classically

Topological quantum field theories in terms of coloured graphs associated to quantum groups

International Nuclear Information System (INIS)

Karowski, M.

1993-01-01

Apart from obvious mathematical applications the investigation is motivated by the problem of braid group statistics in physics. Statistics is one of the central concepts in many body quantum systems. Consider a system of two identical particles located at x 1 and x 2 in R d with Schroedinger wave function ψ(x 1 , x 2 ). Under the exchange of particles with these coordinates one usually has Bose or Fermi statistics in case ψ(x 2 , x 1 )=±ψ(x-1,x T 2). For a quick access to the problem consider the following classical geometric space-time description of the exchange of position for two identical particles, reflecting itself in two quantum mechanical transformation laws. We briefly review the set-up of topological quantum field theory and present our new formulation in terms of coloured graphs. (orig.)

Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group

International Nuclear Information System (INIS)

Majid, S.

1993-01-01

Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided group versions of the standard quantum groups U q (g). They have the same FRT generators l ± but a matrix braided-coproduct ΔL=LxL, where L=l + Sl - , and are self-dual. As an application, the degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices BM 1 (2); it is a braided-commutative bialgebra in a braided category. As a second application, we show that the quantum double D(U q (sl 2 )) (also known as the 'quantum Lorentz group') is the semidirect product as an algebra of two copies of U q (sl 2 ), and also a semidirect product as a coalgebra if we use braid statistics. We find various results of this type for the doubles of general quantum groups and their semi-limits as doubles of the Lie algebras of Poisson Lie groups. (orig.)

Representations of braid group obtained from quantum sl(3) enveloping algebra

International Nuclear Information System (INIS)

Ma Zhongqi.

1989-07-01

The quantum Clebsch-Gordan coefficients for the coproduct 6x6 of the quantum sl(3) enveloping algebra are computed. Based on the representation 6, the representation of the braid group and the corresponding link polynomial are obtained. The link polynomials based on the representations of the quantum sl(3) enveloping algebra with one row Young tableau are discussed. (author). 11 refs, 3 tabs

Differential geometry on Hopf algebras and quantum groups

International Nuclear Information System (INIS)

Watts, P.

1994-01-01

The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined

The unitary-group formulation of quantum chemistry

International Nuclear Information System (INIS)

Campbell, L.L.

1990-01-01

The major part of this dissertation establishes group theoretical techniques that are applicable to the quantum-mechanical many-body atomic and molecular problems. Several matrix element evaluation methods for many-body states are developed. The generator commutation method using generator states is presented for the first time as a complete algorithm, and a computer implementation of the method is developed. A major result of this work is the development of a new method of calculation called the freeon tensor product (FTP) method. This method is much simpler and for many purposes superior to the GUGA procedure (graphical unitary group approach), widely used in configuration interaction calculations. This dissertation is also concerned with the prediction of atomic spectra. In principle spectra can be computed by the methods of ab initio quantum chemistry. In practice these computations are difficult, expensive, time consuming, and not uniformly successful. In this dissertation, the author employs a semi-empirical group theoretical analysis of discrete spectra is the exact analog of the Fourier analysis of continuous functions. In particular, he focuses on the spectra of atoms with incomplete p, d, and f shells. The formulas and techniques are derived in a fashion that apply equally well for more complex systems, as well as the isofreeon model of spherical nuclei

Schr\\"odinger group and quantum finance

OpenAIRE

Romero, Juan M.; Lavana, Ulises; Martínez, Elio

2013-01-01

Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schr\\"odinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equation symmetries, the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schr\\"odinger algebra representation is co...

Quantum groups, orthogonal polynomials and applications to some dynamical systems; Groupes quantiques, polynomes orthogonaux et applications a quelques systemes dynamiques

Energy Technology Data Exchange (ETDEWEB)

Campigotto, C

1993-12-01

The first part is concerned with the introduction of quantum groups as an extension of Lie groups. In particular, we study the case of unitary enveloping algebras in dimension 2. We then connect the quantum group formalism to the construction of g CGC recurrent relations. In addition, we construct g-deformed Krawtchouck and Meixner orthogonal polynomials and list their respective main characteristics. The second part deals with some dynamical systems from a classical, a quantum and a gp-analogue point of view. We investigate the Coulomb Kepler system by using the canonical namical systems which contain as special cases some interesting systems for nuclear of atomic physics and for quantum chemistry, such as the Hartmann system, the ring-shaped oscillator, the Smarodinsky-Winternitz system, the Aharonov-Bohen system and the dyania of Dirac and Schroedinger. (author). 291 refs.

Evolution of quantum and classical strategies on networks by group interactions

International Nuclear Information System (INIS)

Li Qiang; Chen Minyou; Iqbal, Azhar; Abbott, Derek

2012-01-01

In this paper, quantum strategies are introduced within evolutionary games in order to investigate the evolution of quantum and classical strategies on networks in the public goods game. Comparing the results of evolution on a scale-free network and a square lattice, we find that a quantum strategy outperforms the classical strategies, regardless of the network. Moreover, a quantum strategy dominates the population earlier in group interactions than it does in pairwise interactions. In particular, if the hub node in a scale-free network is occupied by a cooperator initially, the strategy of cooperation will prevail in the population. However, in other situations, a quantum strategy can defeat the classical ones and finally becomes the dominant strategy in the population. (paper)

Exceptional gauge groups and quantum theory

International Nuclear Information System (INIS)

Horwitz, L.P.; Biedenharn, L.C.

1979-01-01

It is shown that a Hilbert space over the real Clifford algebra C 7 provides a mathematical framework, consistent with the structure of the usual quantum mechanical formalism, for models for the unification of weak, electromagnetic and strong interactions utilizing the exceptional Lie groups. In particular, in case no further structure is assumed beyond that of C 7 , the group of automorphisms leaving invariant a minimal subspace acts, in the ideal generated by that subspace, as G 2 , and the subgroup of this group leaving one generating element (e 7 ) fixed acts, in this ideal, as the color gauge group SU(3). A generalized phase algebra AcontainsC 7 is defined by the requirement that quantum mechanical states can be consistently constructed for a theory in which the smallest linear manifolds are closed over the subalgebra C(1,e 7 ) (isomorphic to the complex field) of C 7 . Eight solutions are found for the generalized phase algebra, corresponding (up to an overall sign), in effect, to the use of +- e 7 as imaginary unit in each of four superselection sectors. Operators linear over these alternative forms of imanary unit provide distinct types of ''lepton--quark'' and ''quark--quark'' transitions. The subgroup in A which leaves expectation values of operators linear over A invariant is its unitary subgroup U(4), and is a realization (explicitly constructed) of the U(4) invariance of the complex scalar product. An embedding of the algebraic Hilbert space into the complex space defined over C(1,e 7 ) is shown to lead to a decomposition into ''lepton and ''quark'' superselection subspaces. The color SU(3) subgroup of G 2 coincides with the SU(3) subgroup of the generalized phase U(4) which leaves the ''lepton'' space invariant. The problem of constructing tensor products is studied, and some remarks are made on observability and the role of nonassociativity

A quantum group structure in integrable conformal field theories

International Nuclear Information System (INIS)

Smit, D.J.

1990-01-01

We discuss a quantization prescription of the conformal algebras of a class of d=2 conformal field theories which are integrable. We first give a geometrical construction of certain extensions of the classical Virasoro algebra, known as classical W algebras, in which these algebras arise as the Lie algebra of the second Hamiltonian structure of a generalized Korteweg-de Vries hierarchy. This fact implies that the W algebras, obtained as a reduction with respect to the nilpotent subalgebras of the Kac-Moody algebra, describe the intergrability of a Toda field theory. Subsequently we determine the coadjoint operators of the W algebras, and relate these to classical Yang-Baxter matrices. The quantization of these algebras can be carried out using the concept of a so-called quantum group. We derive the condition under which the representations of these quantum groups admit a Hilbert space completion by exploring the relation with the braid group. Then we consider a modification of the Miura transformation which we use to define a quantum W algebra. This leads to an alternative interpretation of the coset construction for Kac-Moody algebras in terms of nonlinear integrable hierarchies. Subsequently we use the connection between the induced braid group representations and the representations of the mapping class group of Riemann surfaces to identify an action of the W algebras on the moduli space of stable curves, and we give the invariants of this action. This provides a generalization of the situation for the Virasoro algebra, where such an invariant is given by the so-called Mumford form which describes the partition function of the bosonic string. (orig.)

Special relativity and quantum theory: a collection of papers on the Poincari Group

International Nuclear Information System (INIS)

Noz, M.E.; Kim, Y.S.

1988-01-01

When the present form of quantum mechanics was formulated in 1927, the most pressing problem was how to make it consistent with special relativity. This still remains a most important and urgent theoretical problem in physics. The underlying language for both disciplines is group theory, and E.P. Wigner's 1939 paper on the Poincari group laid the foundation for unifying the concepts and algorithms of quantum mechanics and special relativity. This volume comprises forty-five papers, including those by P.A.M. Dirac, R.P. Feynman, S. Weinberg, E.P. Wigner and H. Yukawa, covering representations of the Poincari group, time-energy uncertainty relation, covariant pictures of quantum bound states, Lorentz-Dirac deformation in high-enery physics, gauge degrees of freedom for massless particles, group contractions applied to the large-momentum/zero-mass limit, localization problems, and physical applications of the Lorentz group

On the renormalization group equations of quantum electrodynamics

International Nuclear Information System (INIS)

Hirayama, Minoru

1980-01-01

The renormalization group equations of quantum electrodynamics are discussed. The solution of the Gell-Mann-Low equation is presented in a convenient form. The interrelation between the Nishijima-Tomozawa equation and the Gell-Mann-Low equation is clarified. The reciprocal effective charge, so to speak, turns out to play an important role to discuss renormalization group equations. Arguments are given that the reciprocal effective charge vanishes as the renormalization momentum tends to infinity. (author)

Quantum gravity and the functional renormalization group the road towards asymptotic safety

CERN Document Server

Reuter, Martin

2018-01-01

During the past two decades the gravitational asymptotic safety scenario has undergone a major transition from an exotic possibility to a serious contender for a realistic theory of quantum gravity. It aims at a mathematically consistent quantum description of the gravitational interaction and the geometry of spacetime within the realm of quantum field theory, which keeps its predictive power at the highest energies. This volume provides a self-contained pedagogical introduction to asymptotic safety, and introduces the functional renormalization group techniques used in its investigation, along with the requisite computational techniques. The foundational chapters are followed by an accessible summary of the results obtained so far. It is the first detailed exposition of asymptotic safety, providing a unique introduction to quantum gravity and it assumes no previous familiarity with the renormalization group. It serves as an important resource for both practising researchers and graduate students entering thi...

Renormalization group and fixed points in quantum field theory

International Nuclear Information System (INIS)

Hollowood, Timothy J.

2013-01-01

This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.

Independence of automorphism group, center, and state space of quantum logics

International Nuclear Information System (INIS)

Navara, M.

1992-01-01

We prove that quantum logics (-orthomodular posets) admit full independence of the attributes important within the foundations of quantum mechanics. Namely, we present the construction of quantum logics with given sublogics (=physical subsystems), automorphism groups, centers (=open-quotes classical partsclose quotes of the systems), and state spaces. Thus, all these open-quotes parametersclose quotes are independent. Our result is rooted in the line of investigation carried out by Greechie; Kallus and Trnkova; Kalmbach; and Navara and Ptak; and considerably enriches the known algebraic methods in orthomodular posets. 19 refs., 1 fig

Quantum mechanics, group theory, and C60

International Nuclear Information System (INIS)

Rioux, F.

1994-01-01

The recent discovery of a new allotropic form of carbon and its production in macroscopic amounts has generated a tremendous amount of research activity in chemistry, physics, and material science. It has also provided educators with an exciting new vehicle for breathing fresh life into some old, well-established methods and principles. Recently, for example, Boo demonstrated the power of group theory in classifying existing and hypothetical fullerenes by their symmetries. In a similar spirit this note describes a model for the electronic structure of C 60 based on the most elementary principles of quantum mechanics and group theory

Scaling algebras and renormalization group in algebraic quantum field theory

International Nuclear Information System (INIS)

Buchholz, D.; Verch, R.

1995-01-01

For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined. (orig.)

Symmetry groups of state vectors in canonical quantum gravity

International Nuclear Information System (INIS)

Witt, D.M.

1986-01-01

In canonical quantum gravity, the diffeomorphisms of an asymptotically flat hypersurface S, not connected to the identity, but trivial at infinity, can act nontrivially on the quantum state space. Because state vectors are invariant under diffeomorphisms that are connected to the identity, the group of inequivalent diffeomorphisms is a symmetry group of states associated with S. This group is the zeroth homotopy group of the group of diffeomorphisms fixing a frame of infinity on S. It is calculated for all hypersurfaces of the form S = S 3 /G-point, where the removed point is thought of as infinity on S and the symmetry group S is the zeroth homotopy group of the group of diffeomorphisms of S 3 /G fixing a point and frame, denoted π 0 Diff/sub F/(S 3 /G). Before calculating π 0 Diff/sub F/ (S 3 /G), it is necessary to find π 0 of the group of diffeomorphisms. Once π 0 Diff(S 3 /G) is known, π 0 Diff/sub x/ 0 (S 3 /G) is calculated using a fiber bundle involving Diff(S 3 /G), Diff/sub x/ 0 (S 3 /G), and S 3 /G. Finally, a fiber bundle involving Diff/sub F/(S 3 /G), Diff(S 3 /G), and the bundle of frames over S 3 /G is used along with π 0 Diff/sub x/ 0 (S 3 /G) to calculate π 0 Diff/sub F/(S 3 /G)

Proceedings of quantum field theory, quantum mechanics, and quantum optics

International Nuclear Information System (INIS)

Dodonov, V.V.; Man; ko, V.I.

1991-01-01

This book contains papers presented at the XVIII International Colloquium on Group Theoretical Methods in Physics held in Moscow on June 4-9, 1990. Topics covered include; applications of algebraic methods in quantum field theory, quantum mechanics, quantum optics, spectrum generating groups, quantum algebras, symmetries of equations, quantum physics, coherent states, group representations and space groups

A new class of group field theories for 1st order discrete quantum gravity

NARCIS (Netherlands)

Oriti, D.; Tlas, T.

2008-01-01

Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman

On coherent states for the simplest quantum groups

International Nuclear Information System (INIS)

Jurco, B.

1991-01-01

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU q (2) and the discrete series of representations of SU q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on C, a sphere, and the Lobatchevsky plane are discussed. (orig.)

Thermodynamics of two-parameter quantum group Bose and Fermi gases

International Nuclear Information System (INIS)

Algin, A.

2005-01-01

The high and low temperature thermodynamic properties of the two-parameter deformed quantum group Bose and Fermi gases with SU p/q (2) symmetry are studied. Starting with a SU p/q (2)-invariant bosonic as well as fermionic Hamiltonian, several thermodynamic functions of the system such as the average number of particles, internal energy and equation of state are derived. The effects of two real independent deformation parameters p and q on the properties of the systems are discussed. Particular emphasis is given to a discussion of the Bose-Einstein condensation phenomenon for the two-parameter deformed quantum group Bose gas. The results are also compared with earlier undeformed and one-parameter deformed versions of Bose and Fermi gas models. (author)

On coherent states for the simplest quantum groups

Energy Technology Data Exchange (ETDEWEB)

Jurco, B. (Palackeho Univ., Olomouc (Czechoslovakia). Dept. of Optics)

1991-01-01

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU{sub q}(2) and the discrete series of representations of SU{sub q}(1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on C, a sphere, and the Lobatchevsky plane are discussed. (orig.).

Quantum groups in hadron phenomenology

International Nuclear Information System (INIS)

Gavrilik, A.M.

1997-01-01

We show that application of quantum unitary groups, in place of ordinary flavor SU(n f ), to such static aspects of hadron phenomenology as hadron masses and mass formulas is indeed fruitful. So-called q-deformed mass formulas are given for octet baryons 1/2 + and decuplet baryons 3/2 + , as well as for the case of vector mesons 1 - involving heavy flavors. For deformation parameter q, rigid fixation of values is used. New mass sum rules of remarkable accuracy are presented. As shown in decuplet case, the approach accounts for effects highly nonlinear in SU(3)-breaking. Topological implication (possible connection with knots) for singlet vector mesons and the relation q ↔ Θ c (Cabibbo angle) in case of baryons are considered

Quantum field theory and phase transitions: universality and renormalization group

International Nuclear Information System (INIS)

Zinn-Justin, J.

2003-08-01

In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)

Open problems and results in the group theoretic approach to quantum gravity via the BMS group and its generalizations

International Nuclear Information System (INIS)

Melas, Evangelos

2011-01-01

The Bondi-Metzner-Sachs group B is the common asymptotic group of all asymptotically flat (lorentzian) space-times, and is the best candidate for the universal symmetry group of General Relativity. However, in quantum gravity, complexified or euclidean versions of General Relativity are frequently considered. McCarthy has shown that there are forty-two generalizations of B for these versions of the theory and a variety of further ones, either real in any signature, or complex. A firm foundation for quantum gravity can be laid by following through the analogue of Wigner's programme for special relativity with B replacing the Poincare group P. Here the main results which have been obtained so far in this research programme are reported and the more important open problems are stated.

Group representations, error bases and quantum codes

Energy Technology Data Exchange (ETDEWEB)

Knill, E

1996-01-01

This report continues the discussion of unitary error bases and quantum codes. Nice error bases are characterized in terms of the existence of certain characters in a group. A general construction for error bases which are non-abelian over the center is given. The method for obtaining codes due to Calderbank et al. is generalized and expressed purely in representation theoretic terms. The significance of the inertia subgroup both for constructing codes and obtaining the set of transversally implementable operations is demonstrated.

Quantum group based theory for antiferromagnetism and superconductivity: proof and further evidence

Energy Technology Data Exchange (ETDEWEB)

Alam, Sher; Mamun, S.M.; Yanagisawa, T.; Khan, Hayatullah; Rahman, M.O.; Termizi, J.A.S

2003-10-15

Previously one of us presented a conjecture to model antiferromagnetism and high temperature superconductivity and their 'unification' by quantum group symmetry rather than the corresponding classical symmetry in view of the critique by Baskaran and Anderson of Zhang's classical SO(5) model. This conjecture was further sharpened, experimental evidence and the important role of 1-d systems (stripes) was emphasized and moreover the relationship between quantum groups and strings via WZWN models were given in an earlier paper. In this brief note we give and discuss mathematical proof of this conjecture, which completes an important part of this idea, since previously an explicit simple mathematical proof was lacking. It is important to note that in terms of physics that the arbitrariness (freedom) of the d-wave factor g{sup 2}(k) is tied to quantum group symmetry whereas in order to recover classical SO(5) one must set it to unity in an adhoc manner. We comment on the possible connection between this freedom and the pseudogap behaviour in the cuprates.

Towards the Baum-Connes' analytical assembly map for the actions of discrete quantum groups

International Nuclear Information System (INIS)

Goswami, D.; Kuku, A.O.

2002-07-01

Given an action of a discrete quantum group (in the sense of Van Daele, Kustermans and Effros-Ruan) A on a C*-algebra C, satisfying some regularity assumptions resembling the proper Γ-compact action for a classical discrete group Γ on some space, we are able to construct canonical maps μ r i (μ i respectively) (i=0,1) from the A-equivariant K-homology groups KK i A (C,C) to the K-theory groups K i (A-circumflex r ) (K i (A-circumflex) respectively), where A-circumflex r and A-circumflex stand for the quantum analogues of the reduced and full group C*-algebras. We follow the steps of the construction of the classical Baum-Connes map, although in the context of quantum group the nontrivial modular property of the invariant weights (and the related fact that the square of the antipode is not identity) has to be taken into serious consideration, making it somewhat tricky to guess and prove the correct definitions of relevant Hilbert module structures. (author)

Loop space representation of quantum general relativity and the group of loops

International Nuclear Information System (INIS)

Gambini, R.

1991-01-01

The action of the constraints of quantum general relativity on a general state in the loop representation is coded in terms of loop derivatives. These differential operators are related to the infinitesimal generators of the group of loops and generalize the area derivative first considered by Mandelstam. A new sector of solutions of the physical states space of nonperturbative quantum general relativity is found. (orig.)

The K-Z Equation and the Quantum-Group Difference Equation in Quantum Self-dual Yang-Mills Theory

OpenAIRE

Chau, Ling-Lie; Yamanaka, Itaru

1995-01-01

From the time-independent current $\\tcj(\\bar y,\\bar k)$ in the quantum self-dual Yang-Mills (SDYM) theory, we construct new group-valued quantum fields $\\tilde U(\\bar y,\\bar k)$ and $\\bar U^{-1}(\\bar y,\\bar k)$ which satisfy a set of exchange algebras such that fields of $\\tcj(\\bar y,\\bar k)\\sim\\tilde U(\\bar y,\\bar k)~\\partial\\bar y~\\tilde U^{-1}(\\bar y,\\bar k)$ satisfy the original time-independent current algebras. For the correlation functions of the products of the $\\tilde U(\\bar y,\\bar k...

Dynamical renormalization group approach to relaxation in quantum field theory

International Nuclear Information System (INIS)

Boyanovsky, D.; Vega, H.J. de

2003-01-01

The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths

Matter coupled to quantum gravity in group field theory

International Nuclear Information System (INIS)

Ryan, James

2006-01-01

We present an account of a new model incorporating 3d Riemannian quantum gravity and matter at the group field theory level. We outline how the Feynman diagram amplitudes of this model are spin foam amplitudes for gravity coupled to matter fields and discuss some features of the model. To conclude, we describe some related future work

Quantum symmetry in quantum theory

International Nuclear Information System (INIS)

Schomerus, V.

1993-02-01

Symmetry concepts have always been of great importance for physical problems like explicit calculations, classification or model building. More recently, new 'quantum symmetries' ((quasi) quantum groups) attracted much interest in quantum theory. It is shown that all these quantum symmetries permit a conventional formulation as symmetry in quantum mechanics. Symmetry transformations can act on the Hilbert space H of physical states such that the ground state is invariant and field operators transform covariantly. Models show that one must allow for 'truncation' in the tensor product of representations of a quantum symmetry. This means that the dimension of the tensor product of two representations of dimension σ 1 and σ 2 may be strictly smaller than σ 1 σ 2 . Consistency of the transformation law of field operators local braid relations leads us to expect, that (weak) quasi quantum groups are the most general symmetries in local quantum theory. The elements of the R-matrix which appears in these local braid relations turn out to be operators on H in general. It will be explained in detail how examples of field algebras with weak quasi quantum group symmetry can be obtained. Given a set of observable field with a finite number of superselection sectors, a quantum symmetry together with a complete set of covariant field operators which obey local braid relations are constructed. A covariant transformation law for adjoint fields is not automatic but will follow when the existence of an appropriate antipode is assumed. At the example of the chiral critical Ising model, non-uniqueness of the quantum symmetry will be demonstrated. Generalized quantum symmetries yield examples of gauge symmetries in non-commutative geometry. Quasi-quantum planes are introduced as the simplest examples of quasi-associative differential geometry. (Weak) quasi quantum groups can act on them by generalized derivations much as quantum groups do in non-commutative (differential-) geometry

Fundamental group of dual graphs and applications to quantum space time

International Nuclear Information System (INIS)

Nada, S.I.; Hamouda, E.H.

2009-01-01

Let G be a connected planar graph with n vertices and m edges. It is known that the fundamental group of G has 1 -(n - m) generators. In this paper, we show that if G is a self-dual graph, then its fundamental group has (n - 1) generators. We indicate that these results are relevant to quantum space time.

Covariant differential complexes of quantum linear groups

International Nuclear Information System (INIS)

Isaev, A.P.; Pyatov, P.N.

1993-01-01

We consider the possible covariant external algebra structures for Cartan's 1-forms (Ω) on G L q (N) and S L q (N). Our starting point is that Ω s realize an adjoint representation of quantum group and all monomials of Ω s possess the unique ordering. For the obtained external algebras we define the differential mapping d possessing the usual nilpotence condition, and the generally deformed version of Leibnitz rules. The status of the known examples of G L q (N)-differential calculi in the proposed classification scheme and the problems of S L q (N)-reduction are discussed. (author.). 26 refs

Higgs inflation and quantum gravity: an exact renormalisation group approach

International Nuclear Information System (INIS)

Saltas, Ippocratis D.

2016-01-01

We use the Wilsonian functional Renormalisation Group (RG) to study quantum corrections for the Higgs inflationary action including the effect of gravitons, and analyse the leading-order quantum gravitational corrections to the Higgs' quartic coupling, as well as its non-minimal coupling to gravity and Newton's constant, at the inflationary regime and beyond. We explain how within this framework the effect of Higgs and graviton loops can be sufficiently suppressed during inflation, and we also place a bound on the corresponding value of the infrared RG cut-off scale during inflation. Finally, we briefly discuss the potential embedding of the model within the scenario of Asymptotic Safety, while all main equations are explicitly presented

Introduction to the renormalization group study in relativistic quantum field theory

International Nuclear Information System (INIS)

Mignaco, J.A.; Roditi, I.

1985-01-01

An introduction to the renormalization group approach in relativistic quantum field theories is presented, beginning with a little historical about the subject. Further, this problem is discussed from the point of view of the perturbation theory. (L.C.) [pt

Global dimensions for Lie groups at level k and their conformally exceptional quantum subgroups

CERN Document Server

Coquereaux, Robert

2010-01-01

We obtain formulae giving global dimensions for fusion categories defined by Lie groups G at level k and for the associated module-categories obtained via conformal embeddings. The results can be expressed in terms of Lie quantum superfactorials of type G. The later are related, for the type Ar, to the quantum Barnes function.

The quantum group structure of 2D gravity and minimal models. Pt. 1

International Nuclear Information System (INIS)

Gervais, J.L.

1990-01-01

On the unit circle, an infinite family of chiral operators is constructed, whose exchange algebra is given by the universal R-matrix of the quantum group SL(2) q . This establishes the precise connection between the chiral algebra of two dimensional gravity or minimal models and this quantum group. The method is to relate the monodromy properties of the operator differential equations satisfied by the generalized vertex operators with the exchange algebra of SL(2) q . The formulae so derived, which generalize an earlier particular case worked out by Babelon, are remarkably compact and may be entirely written in terms of 'q-deformed' factorials and binomial coefficients. (orig.)

Field on Poincare group and quantum description of orientable objects

Energy Technology Data Exchange (ETDEWEB)

Gitman, D.M. [Universidade de Sao Paulo, Instituto de Fisica, Caixa Postal 66318-CEP, Sao Paulo, S.P. (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engineering, Electronics and Automation, Moscow (Russian Federation)

2009-05-15

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincare group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group {pi}=G x G. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points x element of G/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix Z element of Spin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties. (orig.)

Group field theory formulation of 3D quantum gravity coupled to matter fields

International Nuclear Information System (INIS)

Oriti, Daniele; Ryan, James

2006-01-01

We present a new group field theory describing 3D Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs coloured with SU(2) algebraic data, from which one can reconstruct at once a three-dimensional simplicial complex representing spacetime and its geometry, like in the Ponzano-Regge formulation of pure 3D quantum gravity, and the Feynman graphs for the matter fields. The model then assigns quantum amplitudes to these fat graphs given by spin foam models for gravity coupled to interacting massive spinning point particles, whose properties we discuss

Point group invariants in the Uqp(u(2)) quantum algebra picture

International Nuclear Information System (INIS)

Kibler, M.

1993-07-01

Some consequences of a qp-quantization of a point group invariant developed in the enveloping algebra of SU(2) are examined. A set of open problems concerning such invariants in the U qp (u(2)) quantum algebra picture is briefly discussed. (author) 18 refs

Hidden Uq (sl(2)) Uq (sl(2)) Quantum Group Symmetry in Two Dimensional Gravity

Science.gov (United States)

Cremmer, Eugène; Gervais, Jean-Loup; Schnittger, Jens

1997-02-01

In a previous paper, the quantum-group-covariant chiral vertex operators in the spin 1/2 representation were shown to act, by braiding with the other covariant primaries, as generators of the well known Uq(sl(2)) quantum group symmetry (for a single screening charge). Here, this structure is transformed to the Bloch wave/Coulomb gas operator basis, thereby establishing for the first time its quantum group symmetry properties. A Uq(sl(2)) otimes Uq(sl(2)) symmetry of a novel type emerges: The two Cartan-generator eigenvalues are specified by the choice of matrix element (Vermamodules); the two Casimir eigenvalues are equal and specified by the Virasoro weight of the vertex operator considered; the co-product is defined with a matching condition dictated by the Hilbert space structure of the operator product. This hidden symmetry possesses a novel Hopf-like structure compatible with these conditions. At roots of unity it gives the right truncation. Its (non-linear) connection with the Uq(sl(2)) previously discussed is disentangled.

sl (6,r) as the group of symmetries for non relativistic quantum systems

African Journals Online (AJOL)

It is shown that the 13 one parameter generators of the Lie group SL(6, R) are the maximal group of symmetries for nonrelativistic quantum systems. The group action on the set of states S Ĥ (H complex Hilbert space) preserves transition probabilities as well as the dynamics of the system. By considering a prolongation of ...

Group-velocity dispersion effects on quantum noise of a fiber optical soliton in phase space

International Nuclear Information System (INIS)

Ju, Heongkyu; Lee, Euncheol

2010-01-01

Group-velocity dispersion (GVD) effects on quantum noise of ultrashort pulsed light are theoretically investigated at the soliton energy level, using Gaussian-weighted pseudo-random distribution of phasors in phase space for the modeling of quantum noise properties including phase noise, photon number noise, and quantum noise shape in phase space. We present the effects of GVD that mixes the different spectral components in time, on the self-phase modulation(SPM)-induced quantum noise properties in phase space such as quadrature squeezing, photon-number noise, and tilting/distortion of quantum noise shape in phase space, for the soliton that propagates a distance of the nonlinear length η NL = 1/( γP 0 ) (P 0 is the pulse peak power and γ is the SPM parameter). The propagation dependence of phase space quantum noise properties for an optical soliton is also provided.

On left Hopf algebras within the framework of inhomogeneous quantum groups for particle algebras

Energy Technology Data Exchange (ETDEWEB)

Rodriguez-Romo, Suemi [Facultad de Estudios Superiores Cuautitlan, Universidad Nacional Autonoma de Mexico (Mexico)

2012-10-15

We deal with some matters needed to construct concrete left Hopf algebras for inhomogeneous quantum groups produced as noncommutative symmetries of fermionic and bosonic creation/annihilation operators. We find a map for the bidimensional fermionic case, produced as in Manin's [Quantum Groups and Non-commutative Hopf Geometry (CRM Univ. de Montreal, 1988)] seminal work, named preantipode that fulfills all the necessary requirements to be left but not right on the generators of the algebra. Due to the complexity and importance of the full task, we consider our result as an important step that will be extended in the near future.

Remark on Hopf images in quantum permutation groups $S_n^+$

OpenAIRE

Józiak, Paweł

2016-01-01

Motivated by a question of A.~Skalski and P.M.~So{\\l}tan about inner faithfulness of the S.~Curran's map, we revisit the results and techniques of T.~Banica and J.~Bichon's Crelle paper and study some group-theoretic properties of the quantum permutation group on $4$ points. This enables us not only to answer the aforementioned question in positive in case $n=4, k=2$, but also to classify the automorphisms of $S_4^+$, describe all the embeddings $O_{-1}(2)\\subset S_4^+$ and show that all the ...

Symmetry Groups for the Decomposition of Reversible Computers, Quantum Computers, and Computers in between

Directory of Open Access Journals (Sweden)

Alexis De Vos

2011-06-01

Full Text Available Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e., the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with w bits and the decomposition of an arbitrary quantum circuit with w qubits. Both decompositions use the control gate as building block, i.e., a circuit transforming only one (qubit, the transformation being controlled by the other w−1 (qubits. We explain why the former circuit can be decomposed into 2w − 1 control gates, whereas the latter circuit needs 2w − 1 control gates. We investigate whether computer circuits, not based on the full unitary group but instead on a subgroup of the unitary group, may be decomposable either into 2w − 1 or into 2w − 1 control gates.

A novel quantum group signature scheme without using entangled states

Science.gov (United States)

Xu, Guang-Bao; Zhang, Ke-Jia

2015-07-01

In this paper, we propose a novel quantum group signature scheme. It can make the signer sign a message on behalf of the group without the help of group manager (the arbitrator), which is different from the previous schemes. In addition, a signature can be verified again when its signer disavows she has ever generated it. We analyze the validity and the security of the proposed signature scheme. Moreover, we discuss the advantages and the disadvantages of the new scheme and the existing ones. The results show that our scheme satisfies all the characteristics of a group signature and has more advantages than the previous ones. Like its classic counterpart, our scheme can be used in many application scenarios, such as e-government and e-business.

Isometric coactions of compact quantum groups on compact ...

Indian Academy of Sciences (India)

a compact quantum metric space in the framework of Rieffel, where the ... This problem can be formulated and studied in various settings. ... The spaces we are interested in this paper are metric spaces, both classical and quantum. ... He has given a definition for a quantum symmetry of a classical ...... by the construction of I.

Quantum reference frames and quantum transformations

International Nuclear Information System (INIS)

Toller, M.

1997-01-01

A quantum frame is defined by a material object following the laws of quantum mechanics. The present paper studies the relations between quantum frames, which are described by some generalization of the Poincare' group. The possibility of using a suitable quantum group is examined, but some arguments are given which show that a different mathematical structure is necessary. Some simple examples in lower-dimensional space-times are treated. They indicate the necessity of taking into account some ''internal'' degrees of freedom of the quantum frames, that can be disregarded in a classical treatment

A complete formulation of Baum-Connes' conjecture for the action of discrete quantum groups

International Nuclear Information System (INIS)

Goswami, D.; Kuku, A.O.

2003-01-01

We formulate a version of Baum-Connes' conjecture for a discrete quantum group, building on our earlier work. Given such a quantum group A, we construct a directed family {ε F } of C*-algebras (F varying over some suitable index set), borrowing previous ideas, such that there is a natural action of A on each ε F satisfying the assumptions of [8], which makes it possible to define the 'analytical assembly map', say μ i r,F , i=0,1, from the A- equivariant K-homology groups of ε F to the K-theory groups of the 'reduced' dual A-circumflex r . As a result, we can define the Baum-Connes' maps μ i r : lim→ KK i A (ε F ,C) → K i (A-circumflex r ), and in the classical case, i.e. when A is C 0 (G) for a discrete group, the isomorphism of the above maps for i=0,1 is equivalent to the Baum-Connes' conjecture. (author)

Quantum group structure and local fields in the algebraic approach to 2D gravity

CERN Document Server

Schnittger, Jens

1994-01-01

This review contains a summary of work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself - and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.

The quantum double in integrable quantum field theory

International Nuclear Information System (INIS)

Bernard, D.; LeClair, A.

1993-01-01

Various aspects of recent works on affine quantum group symmetry of integrable 2D quantum field theory are reviewed and further clarified. A geometrical meaning is given to the quantum double, and other properties of quantum groups. The S-matrix is identified with the universal R-matrix. Multiplicative presentations of the yangian double are analyzed. (orig.)

Quantum group structure and local fields in the algebraic approach to 2D gravity

Science.gov (United States)

Schnittger, J.

1995-07-01

This review contains a summary of the work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables — the Liouville exponentials and the Liouville field itself — and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.

Quantum phase transition by employing trace distance along with the density matrix renormalization group

International Nuclear Information System (INIS)

Luo, Da-Wei; Xu, Jing-Bo

2015-01-01

We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs

Quantum Codes From Negacyclic Codes over Group Ring ( Fq + υFq) G

International Nuclear Information System (INIS)

Koroglu, Mehmet E.; Siap, Irfan

2016-01-01

In this paper, we determine self dual and self orthogonal codes arising from negacyclic codes over the group ring ( F q + υF q ) G . By taking a suitable Gray image of these codes we obtain many good parameter quantum error-correcting codes over F q . (paper)

The quantum group, Harper equation and structure of Bloch eigenstates on a honeycomb lattice

International Nuclear Information System (INIS)

Eliashvili, M; Tsitsishvili, G; Japaridze, G I

2012-01-01

The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of a homogeneous magnetic field. Provided the magnetic flux per unit hexagon is a rational of the elementary flux, the one-particle Hamiltonian is expressed in terms of the generators of the quantum group U q (sl 2 ). Employing the functional representation of the quantum group U q (sl 2 ), the Harper equation is rewritten as a system of two coupled functional equations in the complex plane. For the special values of quasi-momentum, the entangled system admits solutions in terms of polynomials. The system is shown to exhibit a certain symmetry allowing us to resolve the entanglement, and a basic single equation determining the eigenvalues and eigenstates (polynomials) is obtained. Equations specifying the locations of the roots of polynomials in the complex plane are found. Employing numerical analysis, the roots of polynomials corresponding to different eigenstates are solved and diagrams exhibiting the ordered structure of one-particle eigenstates are depicted. (paper)

Irreducible quantum group modules with finite dimensional weight spaces

DEFF Research Database (Denmark)

Pedersen, Dennis Hasselstrøm

a finitely generated U q -module which has finite dimensional weight spaces and is a sum of those. Our approach follows the procedures used by S. Fernando and O. Mathieu to solve the corresponding problem for semisimple complex Lie algebra modules. To achieve this we have to overcome a number of obstacles...... not present in the classical case. In the process we also construct twisting functors rigerously for quantum group modules, study twisted Verma modules and show that these admit a Jantzen filtration with corresponding Jantzen sum formula....

Manin's quantum spaces and standard quantum mechanics

International Nuclear Information System (INIS)

Floratos, E.G.

1990-01-01

Manin's non-commutative coordinate algebra of quantum groups is shown to be identical, for unitary coordinates, with the conventional operator algebras of quantum mechanics. The deformation parameter q is a pure phase for unitary coordinates. When q is a root of unity. Manin's algebra becomes the matrix algebra of quantum mechanics for a discretized and finite phase space. Implications for quantum groups and the associated non-commutative differential calculus of Wess and Zumino are discussed. (orig.)

Group Theoretical Approach for Controlled Quantum Mechanical Systems

National Research Council Canada - National Science Library

Tarn, Tzyh-Jong

2007-01-01

The aim of this research is the study of controllability of quantum mechanical systems and feedback control of de-coherence in order to gain an insight on the structure of control of quantum systems...

Surveying the quantum group symmetries of integrable open spin chains

Science.gov (United States)

Nepomechie, Rafael I.; Retore, Ana L.

2018-05-01

Using anisotropic R-matrices associated with affine Lie algebras g ˆ (specifically, A2n(2), A2n-1 (2) , Bn(1), Cn(1), Dn(1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of g ˆ . We show that these transfer matrices also have a duality symmetry (for the cases Cn(1) and Dn(1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n-1 (2) , Bn(1) and Dn(1)). A key simplification is achieved by working in a certain "unitary" gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.

The Jordan-Schwinger realization of two-parametric quantum group Slq,s(2)

International Nuclear Information System (INIS)

Jing Sicong.

1991-10-01

In order to construct the Jordan-Schwinger realization for two-parametric quantum group Sl q,s (2), two independent q, s-deformed harmonic oscillators are defined in this paper and the Heisenberg commutation relations of the q, s-deformed oscillator are also derived by Schwinger's contraction procedure. (author). 11 refs

Fourier transform and the Verlinde formula for the quantum double of a finite group

NARCIS (Netherlands)

Koornwinder, T.H.; Schroers, B.J.; Slingerland, J.K.; Bais, F.A.

1999-01-01

We define a Fourier transform $S$ for the quantum double $D(G)$ of a finite group $G$. Acting on characters of $D(G)$, $S$ and the central ribbon element of $D(G)$ generate a unitary matrix representation of the group $SL(2,Z)$. The characters form a ring over the integers under both the algebra

Quantum renormalization group approach to geometric phases in spin chains

International Nuclear Information System (INIS)

Jafari, R.

2013-01-01

A relation between geometric phases and criticality of spin chains are studied using the quantum renormalization-group approach. I have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative, and its position, scales with the exponent of the system size

Laughlin states on the Poincare half-plane and its quantum group symmetry

OpenAIRE

Alimohammadi, M.; Sadjadi, H. Mohseni

1996-01-01

We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.

Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1

CERN Document Server

Cremmer, E; Schnittger, J; Cremmer, E; Gervais, J L; Schnittger, J

1996-01-01

A simple connection between the universal R matrix of U_q(sl(2)) (for spins \\demi and J) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an explicit operator realization of the co-product action on the covariant operators. It allows us to derive the quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of U_q(sl(2)) realized by (what we call) fixed point commutation relations. This is explained by showing that the link between the algebra of field transformations and that of the co-product generators is much weaker than previously thought. The central charges of our extended U_q(sl(2)) algebra, which includes the Liouville zero-mode momentum in a nontrivial way are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quant...

Quantum groups, roots of unity and particles on quantized Anti-de Sitter space

International Nuclear Information System (INIS)

Steinacker, H.

1997-01-01

Quantum groups in general and the quantum Anti-de Sitter group U q (so(2,3)) in particular are studied from the point of view of quantum field theory. The author shows that if q is a suitable root of unity, there exist finite-dimensional, unitary representations corresponding to essentially all the classical one-particle representations with (half) integer spin, with the same structure at low energies as in the classical case. In the massless case for spin ≥ 1, open-quotes naiveclose quotes representations are unitarizable only after factoring out a subspace of open-quotes pure gaugesclose quotes, as classically. Unitary many-particle representations are defined, with the correct classical limit. Furthermore, the author identifies a remarkable element Q in the center of U q (g), which plays the role of a BRST operator in the case of U q (so(2,3)) at roots of unity, for any spin ≥ 1. The associated ghosts are an intrinsic part of the indecomposable representations. The author shows how to define an involution on algebras of creation and anihilation operators at roots of unity, in an example corresponding to non-identical particles. It is shown how nonabelian gauge fields appear naturally in this framework, without having to define connections on fiber bundles. Integration on Quantum Euclidean space and sphere and on Anti-de Sitter space is studied as well. The author gives a conjecture how Q can be used in general to analyze the structure of indecomposable representations, and to define a new, completely reducible associative (tensor) product of representations at roots of unity, which generalizes the standard open-quotes truncatedclose quotes tensor product as well as many-particle representations

Quantum groups, roots of unity and particles on quantized Anti-de Sitter space

Energy Technology Data Exchange (ETDEWEB)

Steinacker, Harold [Univ. of California, Berkeley, CA (United States). Dept. of Physics

1997-05-23

Quantum groups in general and the quantum Anti-de Sitter group U_q(so(2,3)) in particular are studied from the point of view of quantum field theory. The author shows that if q is a suitable root of unity, there exist finite-dimensional, unitary representations corresponding to essentially all the classical one-particle representations with (half) integer spin, with the same structure at low energies as in the classical case. In the massless case for spin ≥ 1, "naive" representations are unitarizable only after factoring out a subspace of "pure gauges", as classically. Unitary many-particle representations are defined, with the correct classical limit. Furthermore, the author identifies a remarkable element Q in the center of U_q(g), which plays the role of a BRST operator in the case of U_q(so(2,3)) at roots of unity, for any spin ≥ 1. The associated ghosts are an intrinsic part of the indecomposable representations. The author shows how to define an involution on algebras of creation and anihilation operators at roots of unity, in an example corresponding to non-identical particles. It is shown how nonabelian gauge fields appear naturally in this framework, without having to define connections on fiber bundles. Integration on Quantum Euclidean space and sphere and on Anti-de Sitter space is studied as well. The author gives a conjecture how Q can be used in general to analyze the structure of indecomposable representations, and to define a new, completely reducible associative (tensor) product of representations at roots of unity, which generalizes the standard "truncated" tensor product as well as many-particle representations.

Compact quantum group C*-algebras as Hopf algebras with approximate unit

International Nuclear Information System (INIS)

Do Ngoc Diep; Phung Ho Hai; Kuku, A.O.

1999-04-01

In this paper, we construct and study the representation theory of a Hopf C*-algebra with approximate unit, which constitutes quantum analogue of a compact group C*-algebra. The construction is done by first introducing a convolution-product on an arbitrary Hopf algebra H with integral, and then constructing the L 2 and C*-envelopes of H (with the new convolution-product) when H is a compact Hopf *-algebra. (author)

Quantum group random walks in strongly correlated 2+1 D spin systems

International Nuclear Information System (INIS)

Protogenov, A.P.; Rostovtsev, Yu.V.; Verbus, V.A.

1994-06-01

We consider the temporal evolution of strong correlated degrees of freedom in 2+1 D spin systems using the Wilson operator eigenvalues as variables. It is shown that the quantum-group diffusion equation at deformation parameter q being the k-th root of unity has the polynomial solution of degree k. (author). 20 refs, 1 tab

On the algebraic structure of differential calculus on quantum groups

International Nuclear Information System (INIS)

Rad'ko, O.V.; Vladimirov, A.A.

1997-01-01

Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups - coordinate functions, differential forms, Lie derivatives, and inner derivatives - as the cross-product algebra of two mutually dual graded Hopf algebras. This construction, properly taking into account Hopf-algebraic properties of Woronowicz's bicovariant calculus, provides a direct proof of the Cartan identity and of many other useful relations. A detailed comparison with other approaches is also given

A generalized Wigner function for quantum systems with the SU(2) dynamical symmetry group

International Nuclear Information System (INIS)

Klimov, A B; Romero, J L

2008-01-01

We introduce a Wigner-like quasidistribution function to describe quantum systems with the SU(2) dynamic symmetry group. This function is defined in a three-dimensional group manifold and can be used to represent the states defined in several SU(2) invariant subspaces. The explicit differential Moyal-like form of the star product is found and analyzed in the semiclassical limit

Quantum mechanical alternative to Arrhenius equation in the interpretation of proton spin-lattice relaxation data for the methyl groups in solids

KAUST Repository

Bernatowicz, Piotr

2015-10-01

Theory of nuclear spin-lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups has recently been given a consistently quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate, i.e., coherence-damping processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin-lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius equation is made. The present observations provide further indications that incoherent motions of molecular moieties in condensed phase can retain quantum character over much broad temperature range than is commonly thought.

Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators

Science.gov (United States)

Siudzińska, Katarzyna; Chruściński, Dariusz

2018-03-01

In matrix algebras, we introduce a class of linear maps that are irreducibly covariant with respect to the finite group generated by the Weyl operators. In particular, we analyze the irreducibly covariant quantum channels, that is, the completely positive and trace-preserving linear maps. Interestingly, imposing additional symmetries leads to the so-called generalized Pauli channels, which were recently considered in the context of the non-Markovian quantum evolution. Finally, we provide examples of irreducibly covariant positive but not necessarily completely positive maps.

Hidden U$_{q}$(sl(2)) x U$_{q}$(sl(2)) quantum group symmetry in two dimensional gravity

CERN Document Server

Cremmer, E; Schnittger, J

1997-01-01

In a previous paper, we proposed a construction of U_q(sl(2)) quantum group symmetry generators for 2d gravity, where we took the chiral vertex operators of the theory to be the quantum group covariant ones established in earlier works. The basic idea was that the covariant fields in the spin 1/2 representation themselves can be viewed as generators, as they act, by braiding, on the other fields exactly in the required way. Here we transform this construction to the more conventional description of 2d gravity in terms of Bloch wave/Coulomb gas vertex operators, thereby establishing for the first time its quantum group symmetry properties. A U_q(sl(2))\\otimes U_q(sl(2)) symmetry of a novel type emerges: The two Cartan-generator eigenvalues are specified by the choice of matrix element (bra/ket Verma-modules); the two Casimir eigenvalues are equal and specified by the Virasoro weight of the vertex operator considered; the co-product is defined with a matching condition dictated by the Hilbert space structure of...

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

Energy Technology Data Exchange (ETDEWEB)

Groh, Kai

2012-10-15

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

International Nuclear Information System (INIS)

Groh, Kai

2012-10-01

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of

Quantum field theory and phase transitions: universality and renormalization group; Theorie quantique des champs et transitions de phase: universalite et groupe de renormalisation

Energy Technology Data Exchange (ETDEWEB)

Zinn-Justin, J

2003-08-01

In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)

Dynamic quantum secret sharing

International Nuclear Information System (INIS)

Jia, Heng-Yue; Wen, Qiao-Yan; Gao, Fei; Qin, Su-Juan; Guo, Fen-Zhuo

2012-01-01

In this Letter we consider quantum secret sharing (QSS) between a sender and a dynamic agent group, called dynamic quantum secret sharing (DQSS). In the DQSS, the change of the agent group is allowable during the procedure of sharing classical and quantum information. Two DQSS schemes are proposed based on a special kind of entangled state, starlike cluster states. Without redistributing all the shares, the changed agent group can reconstruct the sender's secret by their cooperation. Compared with the previous quantum secret sharing scheme, our schemes are more flexible and suitable for practical applications. -- Highlights: ► We consider quantum secret sharing between a sender and a dynamic agent group, called dynamic quantum secret sharing (DQSS). ► In the DQSS, the change of the agent group is allowable during the procedure of sharing classical and quantum information. ► Two DQSS schemes are proposed based on a special kind of entangled state, starlike cluster states. ► Without redistributing all the shares, the changed agent group can reconstruct the sender's secret by their cooperation. ► Compared with the previous quantum secret sharing scheme, our schemes are more flexible and suitable for practical applications.

Growth of group II-VI semiconductor quantum dots with strong quantum confinement and low size dispersion

Science.gov (United States)

Pandey, Praveen K.; Sharma, Kriti; Nagpal, Swati; Bhatnagar, P. K.; Mathur, P. C.

2003-11-01

CdTe quantum dots embedded in glass matrix are grown using two-step annealing method. The results for the optical transmission characterization are analysed and compared with the results obtained from CdTe quantum dots grown using conventional single-step annealing method. A theoretical model for the absorption spectra is used to quantitatively estimate the size dispersion in the two cases. In the present work, it is established that the quantum dots grown using two-step annealing method have stronger quantum confinement, reduced size dispersion and higher volume ratio as compared to the single-step annealed samples. (

Relativistic implications of the quantum phase

International Nuclear Information System (INIS)

Low, Stephen G

2012-01-01

The quantum phase leads to projective representations of symmetry groups in quantum mechanics. The projective representations are equivalent to the unitary representations of the central extension of the group. A celebrated example is Wigner's formulation of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group. However, Wigner's formulation makes no mention of the Weyl-Heisenberg group and the hermitian representation of its algebra that are the Heisenberg commutation relations fundamental to quantum physics. We put aside the relativistic symmetry and show that the maximal quantum symmetry that leaves the Heisenberg commutation relations invariant is the projective representations of the conformally scaled inhomogeneous symplectic group. The Weyl-Heisenberg group and noncommutative structure arises directly because the quantum phase requires projective representations. We then consider the relativistic implications of the quantum phase that lead to the Born line element and the projective representations of an inhomogeneous unitary group that defines a noninertial quantum theory. (Understanding noninertial quantum mechanics is a prelude to understanding quantum gravity.) The remarkable properties of this symmetry and its limits are studied.

Unbounded representations of symmetry groups in gauge quantum field theory. Pt. 1

International Nuclear Information System (INIS)

Voelkel, A.H.

1983-01-01

Symmetry groups and especially the covariance (substitution rules) of the basic fields in a gauge quantum field theory of the Wightman-Garding type are investigated. By means of the continuity properties hidden in the substitution rules it is shown that every unbounded form-isometric representation U of a Lie group has a form-skew-symmetric differential deltaU with dense domain in the unphysical Hilbert space. Necessary and sufficient conditions for the existence of the closures of U and deltaU as well as for the isometry of U are derived. It is proved that a class of representations of the transition group enforces a relativistic confinement mechanism, by which some or all basic fields are confined but certain mixed products of them are not. (orig.)

Quantum photonics

CERN Document Server

Pearsall, Thomas P

2017-01-01

This textbook employs a pedagogical approach that facilitates access to the fundamentals of Quantum Photonics. It contains an introductory description of the quantum properties of photons through the second quantization of the electromagnetic field, introducing stimulated and spontaneous emission of photons at the quantum level. Schrödinger’s equation is used to describe the behavior of electrons in a one-dimensional potential. Tunneling through a barrier is used to introduce the concept of non­locality of an electron at the quantum level, which is closely-related to quantum confinement tunneling, resonant tunneling, and the origin of energy bands in both periodic (crystalline) and aperiodic (non-crystalline) materials. Introducing the concepts of reciprocal space, Brillouin zones, and Bloch’s theorem, the determination of electronic band structure using the pseudopotential method is presented, allowing direct computation of the band structures of most group IV, group III-V, and group II-VI semiconducto...

A quantum mechanical alternative to the Arrhenius equation in the interpretation of proton spin-lattice relaxation data for the methyl groups in solids.

Science.gov (United States)

Bernatowicz, Piotr; Shkurenko, Aleksander; Osior, Agnieszka; Kamieński, Bohdan; Szymański, Sławomir

2015-11-21

The theory of nuclear spin-lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups have recently been given a consistent quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate (i.e., coherence-damping) processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin-lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius equation is made. The present observations provide further indications that incoherent motions of molecular moieties in the condensed phase can retain quantum character over much broader temperature range than is commonly thought.

Generic features of the dynamics of complex open quantum systems: statistical approach based on averages over the unitary group.

Science.gov (United States)

Gessner, Manuel; Breuer, Heinz-Peter

2013-04-01

We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of complex open quantum systems, employing arguments from ensemble theory. We further generalize these results to arbitrary eigenvalue distributions, allowing a detailed comparison of typical regular and chaotic systems with the help of concepts from random matrix theory. To illustrate the physical relevance and the general applicability of our results we present a series of examples related to the fields of open quantum systems and nonequilibrium quantum thermodynamics. These include the effect of initial correlations, the average quantum dynamical maps, the generic dynamics of system-environment pure state entanglement and, finally, the equilibration of generic open and closed quantum systems.

Extreme covariant quantum observables in the case of an Abelian symmetry group and a transitive value space

International Nuclear Information System (INIS)

Haapasalo, Erkka Theodor; Pellonpaeae, Juha-Pekka

2011-01-01

We represent quantum observables as normalized positive operator valued measures and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group G. The value space of such observables is a transitive G-space. We characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables. The results are applied to position, position difference, and time observables.

Quantum measurement in quantum optics

International Nuclear Information System (INIS)

Kimble, H.J.

1993-01-01

Recent progress in the generation and application of manifestly quantum or nonclassical states of the electromagnetic field is reviewed with emphasis on the research of the Quantum Optics Group at Caltech. In particular, the possibilities for spectroscopy with non-classical light are discussed both in terms of improved quantitative measurement capabilities and for the fundamental alteration of atomic radiative processes. Quantum correlations for spatially extended systems are investigated in a variety of experiments which utilize nondegenerate parametric down conversion. Finally, the prospects for measurement of the position of a free mass with precision beyond the standard quantum limit are briefly considered. (author). 38 refs., 1 fig

Learning quantum field theory from elementary quantum mechanics

International Nuclear Information System (INIS)

Gosdzinsky, P.; Tarrach, R.

1991-01-01

The study of the Dirac delta potentials in more than one dimension allows the introduction within the framework of elementary quantum mechanics of many of the basic concepts of modern quantum field theory: regularization, renormalization group, asymptotic freedom, dimensional transmutation, triviality, etc. It is also interesting, by itself, as a nonstandard quantum mechanical problem

Geometrical aspects of quantum spaces

International Nuclear Information System (INIS)

Ho, P.M.

1996-01-01

Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S 1 2 and the quantum complex projective space CP q (N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S q 2 and CP q (N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP q (N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given

Quantum cluster algebra structures on quantum nilpotent algebras

CERN Document Server

Goodearl, K R

2017-01-01

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.

Quantum independent increment processes

CERN Document Server

Franz, Uwe

2006-01-01

This is the second of two volumes containing the revised and completed notes of lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald in March, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present second volume contains the following lectures: "Random Walks on Finite Quantum Groups" by Uwe Franz and Rolf Gohm, "Quantum Markov Processes and Applications in Physics" by Burkhard Kümmerer, Classical and Free Infinite Divisibility and Lévy Processes" by Ole E. Barndorff-Nielsen, Steen Thorbjornsen, and "Lévy Processes on Quantum Groups and Dual Groups" by Uwe Franz.

The quantum Hall effect in quantum dot systems

International Nuclear Information System (INIS)

Beltukov, Y M; Greshnov, A A

2014-01-01

It is proposed to use quantum dots in order to increase the temperatures suitable for observation of the integer quantum Hall effect. A simple estimation using Fock-Darwin spectrum of a quantum dot shows that good part of carriers localized in quantum dots generate the intervals of plateaus robust against elevated temperatures. Numerical calculations employing local trigonometric basis and highly efficient kernel polynomial method adopted for computing the Hall conductivity reveal that quantum dots may enhance peak temperature for the effect by an order of magnitude, possibly above 77 K. Requirements to potentials, quality and arrangement of the quantum dots essential for practical realization of such enhancement are indicated. Comparison of our theoretical results with the quantum Hall measurements in InAs quantum dot systems from two experimental groups is also given

Quantum group symmetries and completeness for \\boldsymbol {A}_{\\boldsymbol {2n}}^{\\boldsymbol{(2)}} open spin chains

Science.gov (United States)

Ahmed, Ibrahim; Nepomechie, Rafael I.; Wang, Chunguang

2017-07-01

We argue that the Hamiltonians for A(2)2n open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries Uq(Bn) and Uq(Cn) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

Quantum symmetries of classical spaces

OpenAIRE

Bhowmick, Jyotishman; Goswami, Debashish; Roy, Subrata Shyam

2009-01-01

We give a general scheme for constructing faithful actions of genuine (noncommutative as $C^*$ algebra) compact quantum groups on classical topological spaces. Using this, we show that: (i) a compact connected classical space can have a faithful action by a genuine compact quantum group, and (ii) there exists a spectral triple on a classical connected compact space for which the quantum group of orientation and volume preserving isometries (in the sense of \\cite{qorient}) is a genuine quantum...

Macdonald polynomials from Sklyanin algebras: A conceptual basis for the p-adics-quantum group connection

International Nuclear Information System (INIS)

Freund, P.G.O.

1992-01-01

We establish a previously conjectured connection between p-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which 'interpolate' between the zonal spherical functions of related real and p-adic symmetric spaces. The elliptic quantum algebras underlie the Z n -Baxter models. We show that in the n→∞ limit, the Jost function for the scattering of first level excitations in the Z n -Baxter model coincides with the Harish-Chandra-like c-function constructed from the Macdonald polynomials associated to the root system A 1 . The partition function of the Z 2 -Baxter model itself is also expressed in terms of this Macdonald-Harish-Chandra c-function albeit in a less simple way. We relate the two parameters q and t of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular the p-acid 'regimes' in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of 'q-deforming' Euler products. (orig.)

Thermodynamic properties of a quantum group boson gas GLp,q(2)

International Nuclear Information System (INIS)

Jellal, Ahmed

2000-10-01

An approach is proposed enabling to effectively describe the behaviour of a bosonic system. The approach uses the quantum group GL p,q (2) formalism. In effect, considering a bosonic Hamiltonian in terms of the GL p,q (2) generators, it is shown that its thermodynamic properties are connected to deformation parameters p and q. For instance, the average number of particles and the pressure have been computed. If p is fixed to be the same value for q, our approach coincides perfectly with some results developed recently in this subject. The ordinary results, of the present system, can be found when we take the limit p = q = 1. (author)

The quantum-field renormalization group in the problem of a growing phase boundary

International Nuclear Information System (INIS)

Antonov, N.V.; Vasil'ev, A.N.

1995-01-01

Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik's assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants (open-quotes chargeclose quotes). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundary and time, δ h and δ t , which satisfy the exact relationship 2 δ h = δ t + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab

The renormalization group of relativistic quantum field theory as a set of generalized, spontaneously broken, symmetry transformations

International Nuclear Information System (INIS)

Maris, Th.A.J.

1976-01-01

The renormalization group theory has a natural place in a general framework of symmetries in quantum field theories. Seen in this way, a 'renormalization group' is a one-parametric subset of the direct product of dilatation and renormalization groups. This subset of spontaneously broken symmetry transformations connects the inequivalent solutions generated by a parameter-dependent regularization procedure, as occurs in renormalized perturbation theory. By considering the global, rather than the infinitesimal, transformations, an expression for general vertices is directly obtained, which is the formal solution of exact renormalization group equations [pt

The functional renormalization group for interacting quantum systems with spin-orbit interaction

International Nuclear Information System (INIS)

Grap, Stephan Michael

2013-01-01

We studied the influence of spin-orbit interaction (SOI) in interacting low dimensional quantum systems at zero temperature within the framework of the functional renormalization group (fRG). Among the several types of spin-orbit interaction the so-called Rashba spin-orbit interaction is especially intriguing for future spintronic applications as it may be tuned via external electric fields. We investigated its effect on the low energy physics of an interacting quantum wire in an applied Zeeman field which is modeled as a generalization of the extended Hubbard model. To this end we performed a renormalization group study of the two particle interaction, including the SOI and the Zeeman field exactly on the single particle level. Considering the resulting two band model, we formulated the RG equations for the two particle vertex keeping the full band structure as well as the non trivial momentum dependence of the low energy two particle scattering processes. In order to solve these equations numerically we defined criteria that allowed us to classify whether a given set of initial conditions flows towards the strongly coupled regime. We found regions in the models parameter space where a weak coupling method as the fRG is applicable and it is possible to calculate additional quantities of interest. Furthermore we analyzed the effect of the Rashba SOI on the properties of an interacting multi level quantum dot coupled to two semi in nite leads. Of special interest was the interplay with a Zeeman field and its orientation with respect to the SOI term. We found a renormalization of the spin-orbit energy which is an experimental quantity used to asses SOI effects in transport measurements, as well as renormalized effective g factors used to describe the Zeeman field dependence. In particular in asymmetrically coupled systems the large parameter space allows for rich physics which we studied by means of the linear conductance obtained via the generalized Landauer

A geometric renormalization group in discrete quantum space-time

International Nuclear Information System (INIS)

Requardt, Manfred

2003-01-01

We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalization group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that this process may generate a fixed limit phase, representing our continuous space-time on a mesoscopic or macroscopic scale, provided that the underlying discrete geometry is critical in a specific sense (geometric long range order). Our point of view is corroborated by a series of analytic and numerical results, which allow us to keep track of the geometric changes, taking place on the various scales of the resolution of space-time. Of particular conceptual importance are the notions of dimension of such random systems on the various scales and the notion of geometric criticality

Quantum cluster algebras and quantum nilpotent algebras

Science.gov (United States)

Goodearl, Kenneth R.; Yakimov, Milen T.

2014-01-01

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry

Directory of Open Access Journals (Sweden)

Chikashi Arita

2012-10-01

Full Text Available We study the entanglement properties of a higher-integer-spin Affleck-Kennedy-Lieb-Tasaki model with quantum group symmetry in the periodic boundary condition. We exactly calculate the finite size correction terms of the entanglement entropies from the double scaling limit. We also evaluate the geometric entanglement, which serves as another measure for entanglement. We find the geometric entanglement reaches its maximum at the isotropic point, and decreases with the increase of the anisotropy. This behavior is similar to that of the entanglement entropies.

Extended quantum mechanics

International Nuclear Information System (INIS)

Pavel Bona

2000-01-01

The work can be considered as an essay on mathematical and conceptual structure of nonrelativistic quantum mechanics which is related here to some other (more general, but also to more special and 'approximative') theories. Quantum mechanics is here primarily reformulated in an equivalent form of a Poisson system on the phase space consisting of density matrices, where the 'observables', as well as 'symmetry generators' are represented by a specific type of real valued (densely defined) functions, namely the usual quantum expectations of corresponding selfjoint operators. It is shown in this paper that inclusion of additional ('nonlinear') symmetry generators (i. e. 'Hamiltonians') into this reformulation of (linear) quantum mechanics leads to a considerable extension of the theory: two kinds of quantum 'mixed states' should be distinguished, and operator - valued functions of density matrices should be used in the role of 'nonlinear observables'. A general framework for physical theories is obtained in this way: By different choices of the sets of 'nonlinear observables' we obtain, as special cases, e.g. classical mechanics on homogeneous spaces of kinematical symmetry groups, standard (linear) quantum mechanics, or nonlinear extensions of quantum mechanics; also various 'quasiclassical approximations' to quantum mechanics are all sub theories of the presented extension of quantum mechanics - a version of the extended quantum mechanics. A general interpretation scheme of extended quantum mechanics extending the usual statistical interpretation of quantum mechanics is also proposed. Eventually, extended quantum mechanics is shown to be (included into) a C * -algebraic (hence linear) quantum theory. Mathematical formulation of these theories is presented. The presentation includes an analysis of problems connected with differentiation on infinite-dimensional manifolds, as well as a solution of some problems connected with the work with only densely defined unbounded

Functional renormalization group methods in quantum chromodynamics

International Nuclear Information System (INIS)

Braun, J.

2006-01-01

We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

Functional renormalization group methods in quantum chromodynamics

Energy Technology Data Exchange (ETDEWEB)

Braun, J.

2006-12-18

We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

Exact synthesis of three-qubit quantum circuits from non-binary quantum gates

Science.gov (United States)

Yang, Guowu; Hung, William N. N.; Song, Xiaoyu; Perkowski, Marek A.

2010-04-01

Because of recent nano-technological advances, nano-structured systems have become highly ordered, making it quantum computing schemas possible. We propose an approach to optimally synthesise quantum circuits from non-permutative quantum gates such as controlled-square-root-of-not (i.e., controlled-V). Our approach reduces the synthesis problem to multiple-valued optimisation and uses group theory. We devise a novel technique that transforms the quantum logic synthesis problem from a multi-valued constrained optimisation problem to a permutable representation. The transformation enables us to use group theory to exploit the symmetric properties of the synthesis problem. Assuming a cost of one for each two-qubit gate, we found all reversible circuits with quantum costs of 4, 5, 6, etc., and give another algorithm to realise these reversible circuits with quantum gates. The approach can be used for both binary permutative deterministic circuits and probabilistic circuits such as controlled random-number generators and hidden Markov models.

Clothed Particles in Quantum Electrodynamics and Quantum Chromodynamics

Directory of Open Access Journals (Sweden)

Shebeko Alexander

2016-01-01

Full Text Available The notion of clothing in quantum field theory (QFT, put forward by Greenberg and Schweber and developed by M. Shirokov, is applied in quantum electrodynamics (QED and quantum chromodynamics (QCD. Along the guideline we have derived a novel analytic expression for the QED Hamiltonian in the clothed particle representation (CPR. In addition, we are trying to realize this notion in QCD (to be definite for the gauge group SU(3 when drawing parallels between QCD and QED.

Applications of the renormalization group approach to problems in quantum field theory

International Nuclear Information System (INIS)

Renken, R.L.

1985-01-01

The presence of fluctuations at many scales of length complicates theories of quantum fields. However, interest is often focused on the low-energy consequences of a theory rather than the short distance fluctuations. In the renormalization-group approach, one takes advantage of this by constructing an effective theory with identical low-energy behavior, but without short distance fluctuations. Three problems of this type are studied here. In chapter 1, an effective lagrangian is used to compute the low-energy consequences of theories of technicolor. Corrections to weak-interaction parameters are found to be small, but conceivably measurable. In chapter 2, the renormalization group approach is applied to second order phase transitions in lattice gauge theories such as the deconfining transition in the U(1) theory. A practical procedure for studying the critical behavior based on Monte Carlo renormalization group methods is described in detail; no numerical results are presented. Chapter 3 addresses the problem of computing the low-energy behavior of atoms directly from Schrodinger's equation. A straightforward approach is described, but is found to be impractical

Unbounded representations of symmetry groups in gauge quantum field theory. II. Integration

International Nuclear Information System (INIS)

Voelkel, A.H.

1986-01-01

Within the gauge quantum field theory of the Wightman--Garding type, the integration of representations of Lie algebras is investigated. By means of the covariance condition (substitution rules) for the basic fields, it is shown that a form skew-symmetric representation of a Lie algebra can be integrated to a form isometric and in general unbounded representation of the universal covering group of a corresponding Lie group provided the conditions (Nelson, Sternheimer, etc.), which are well known for the case of Hilbert or Banach representations, hold. If a form isometric representation leaves the subspace from which the physical Hilbert space is obtained via factorization and completion invariant, then the same is proved to be true for its differential. Conversely, a necessary and sufficient condition is derived for the transmission of the invariance of this subspace under a form skew-symmetric representation of a Lie algebra to its integral

Quantum independent increment processes

CERN Document Server

Franz, Uwe

2005-01-01

This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.

Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2; Point form relativistic quantum mechanics

Science.gov (United States)

Klink, William H.; Schweiger, Wolfgang

2018-03-01

This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantum mechanics to nuclear physics.

Coalitions in the quantum Minority game: Classical cheats and quantum bullies

International Nuclear Information System (INIS)

Flitney, Adrian P.; Greentree, Andrew D.

2007-01-01

In a one-off Minority game, when a group of players agree to collaborate they gain an advantage over the remaining players. We consider the advantage obtained in a quantum Minority game by a coalition sharing an initially entangled state versus that obtained by a coalition that uses classical communication to arrive at an optimal group strategy. In a model of the quantum Minority game where the final measurement basis is randomized, quantum coalitions outperform classical ones when carried out by up to four players, but an unrestricted amount of classical communication is better for larger coalition sizes

3D quantum gravity and effective noncommutative quantum field theory.

Science.gov (United States)

Freidel, Laurent; Livine, Etera R

2006-06-09

We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.

Holographic Quantum States

International Nuclear Information System (INIS)

Osborne, Tobias J.; Eisert, Jens; Verstraete, Frank

2010-01-01

We show how continuous matrix product states of quantum fields can be described in terms of the dissipative nonequilibrium dynamics of a lower-dimensional auxiliary boundary field by demonstrating that the spatial correlation functions of the bulk field correspond to the temporal statistics of the boundary field. This equivalence (1) illustrates an intimate connection between the theory of continuous quantum measurement and quantum field theory, (2) gives an explicit construction of the boundary field allowing the extension of real-space renormalization group methods to arbitrary dimensional quantum field theories without the introduction of a lattice parameter, and (3) yields a novel interpretation of recent cavity QED experiments in terms of quantum field theory, and hence paves the way toward observing genuine quantum phase transitions in such zero-dimensional driven quantum systems.

An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group

International Nuclear Information System (INIS)

Wang, S.J.

1993-04-01

An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group is formulated for the first time. One dimensional problem is treated explicitly in detail for both the finite dimensional and infinite dimensional Hilbert spaces. For the finite dimensional Hilbert space, the su(2) algebraic representation is used; while for the infinite dimensional Hilbert space, the Heisenberg-Weyl algebraic representation is employed. Fourier expansion technique is generalized to the generator space, which is suitable for analysis of irregular spectra. The polynormial operator basis is also used for complement, which is appropriate for analysis of some simple Hamiltonians. The proposed new approach is applied to solve the classical inverse Sturn-Liouville problem and to study the problems of quantum regular and irregular spectra. (orig.)

Galois quantum systems

International Nuclear Information System (INIS)

Vourdas, A

2005-01-01

A finite quantum system in which the position and momentum take values in the Galois field GF(p l ) is constructed from a smaller quantum system in which the position and momentum take values in Z p , using field extension. The Galois trace is used in the definition of the Fourier transform. The Heisenberg-Weyl group of displacements and the Sp(2, GF(p l )) group of symplectic transformations are studied. A class of transformations inspired by the Frobenius maps in Galois fields is introduced. The relationship of this 'Galois quantum system' with its subsystems in which the position and momentum take values in subfields of GF(p l ) is discussed

Boundary actions in Ponzano-Regge discretization, Quantum groups and AdS(3)

OpenAIRE

O'Loughlin, Martin

2000-01-01

Boundary actions for three-dimensional quantum gravity in the discretized formalism of Ponzano-Regge are studied with a view towards understanding the boundary degrees of freedom. These degrees of freedom postulated in the holography hypothesis are supposed to be characteristic of quantum gravity theories. In particular it is expected that some of these degrees of freedom reside on black hole horizons. This paper is a study of these ideas in the context of a theory of quantum gravity that req...

Logical independence and quantum randomness

International Nuclear Information System (INIS)

Paterek, T; Kofler, J; Aspelmeyer, M; Zeilinger, A; Brukner, C; Prevedel, R; Klimek, P

2010-01-01

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.

Group theoretical methods in Physics

International Nuclear Information System (INIS)

Olmo, M.A. del; Santander, M.; Mateos Guilarte, J.M.

1993-01-01

The meeting had 102 papers. These was distributed in following areas: -Quantum groups,-Integrable systems,-Physical Applications of Group Theory,-Mathematical Results,-Geometry, Topology and Quantum Field Theory,-Super physics,-Super mathematics,-Atomic, Molecular and Condensed Matter Physics. Nuclear and Particle Physics,-Symmetry and Foundations of classical and Quantum mechanics

Bicovariant quantum algebras and quantum Lie algebras

International Nuclear Information System (INIS)

Schupp, P.; Watts, P.; Zumino, B.

1993-01-01

A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond L + SL - being a special case - generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N). (orig.)

Logical independence and quantum randomness

Energy Technology Data Exchange (ETDEWEB)

Paterek, T; Kofler, J; Aspelmeyer, M; Zeilinger, A; Brukner, C [Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna (Austria); Prevedel, R; Klimek, P [Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)], E-mail: tomasz.paterek@univie.ac.at

2010-01-15

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.

The synthesis of CdSe quantum dots with carboxyl group and study on their optical characteristics

International Nuclear Information System (INIS)

Ye, Chen; Park, Sangjoon; Kim, Jongsung

2009-01-01

Quantum dots are nanocrystal semiconductors which attract lots of research interests due to their peculiar optical properties. CdSe/ZnS quantum dots have been synthesized via pyrolysis of organometallic reagents. The color of the quantum dot changes from yellow-green to red as their size increases with reaction time. Photoluminescence quantum efficiency of CdSe quantum dots have been enhanced by passivating the surface of CdSe quantum dots with ZnS layers. Quantum dots are nanocrystal semiconductors which attract lots of research interests due to their peculiar optical properties. CdSe/ZnS quantum dots have been synthesized via pyrolysis of organometallic reagents. The color of the quantum dot changes from yellow-green to red as their size increases with reaction time. Photoluminescence quantum efficiency of CdSe quantum dots have been enhanced by passivating the surface of CdSe quantum dots with ZnS layers. (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Quantum mechanics a fundamental approach

CERN Document Server

Wan, K Kong

2018-01-01

The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning. This makes it difficult to appreciate the mathematical formalism and hampers the understanding of quantum mechanics. This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics. Quantum mechanics is presented in six groups of postulates. A chapter is devoted to each group of postulates with a detailed discussion. Systems with superselection rules, and some conceptual issues such as quantum paradoxes and measurement, are also discussed. The book conc...

Quantum quaternion spheres

Indian Academy of Sciences (India)

The theory of quantum groups was first studied in the topological setting ... and relations based on quantum R-matrix of a simple Lie algebra to define ..... We refer the reader to [10] for a proof of the following theorem that gives a dual pairing.

Topics in quantum groups and finite-type invariants mathematics at the independent University of Moscow

CERN Document Server

Arkhipov, S M; Odesskii, A V; Feigin, B; Vassiliev, V

1998-01-01

This volume presents the first collection of articles consisting entirely of work by faculty and students of the Higher Mathematics College of the Independent University of Moscow (IUM). This unique institution was established to train elite students to become research scientists. Covered in the book are two main topics: quantum groups and low-dimensional topology. The articles were written by participants of the Feigin and Vassiliev seminars, two of the most active seminars at the IUM.

The quantum symmetry of rational conformal field theories

Directory of Open Access Journals (Sweden)

César Gómez

1991-04-01

Full Text Available The quantum group symmetry of the c ˇ1 Rational Conformal Field Theory, in its Coulomb gas version, is formulated in terms of a new type of screened vertex operators, which define the representation spaces of a quantum group Q. The conformal properties of these operators show a deep interplay between the quantum group Q and the Virasoro algebra.The R-matrix, the comultiplication rules and the quantum Clebsch-Gordan coefficients of Q are obtained using contour deformation techniques. Finally, the relation between the chiral vertex operators and the quantum Clebsch-Gordan coefficients is shown.

Topology-preserving quantum deformation with non-numerical parameter

Science.gov (United States)

Aukhadiev, Marat; Grigoryan, Suren; Lipacheva, Ekaterina

2013-11-01

We introduce a class of compact quantum semigroups, that we call semigroup deformations of compact Abelian qroups. These objects arise from reduced semigroup -algebras, the generalization of the Toeplitz algebra. We study quantum subgroups, quantum projective spaces and quantum quotient groups for such objects, and show that the group is contained as a compact quantum subgroup in the deformation of itself. The connection with the weak Hopf algebra notion is described. We give a grading on the -algebra of the compact quantum semigroups constructed.

Quantum Nanostructures by Droplet Epitaxy

Directory of Open Access Journals (Sweden)

Somsak Panyakeow

2009-02-01

Full Text Available Droplet epitaxy is an alternative growth technique for several quantum nanostructures. Indium droplets are distributed randomly on GaAs substrates at low temperatures (120-350'C. Under background pressure of group V elements, Arsenic and Phosphorous, InAs and InP nanostructures are created. Quantum rings with isotropic shape are obtained at low temperature range. When the growth thickness is increased, quantum rings are transformed to quantum dot rings. At high temperature range, anisotropic strain gives rise to quantum rings with square holes and non-uniform ring stripe. Regrowth of quantum dots on these anisotropic quantum rings, Quadra-Quantum Dots (QQDs could be realized. Potential applications of these quantum nanostructures are also discussed.

Spin networks and quantum computation

International Nuclear Information System (INIS)

Kauffman, L.; Lomonaco, S. Jr.

2008-01-01

We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. The simplest case of these models is the Fibonacci model, itself universal for quantum computation. We here formulate these braid group representations in a form suitable for computation and algebraic work. (authors)

Fermion-induced quantum critical points.

Science.gov (United States)

Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong

2017-08-22

A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.

Quantum scaling in many-body systems an approach to quantum phase transitions

CERN Document Server

Continentino, Mucio

2017-01-01

Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.

Mathematical foundation of quantum mechanics

CERN Document Server

Parthasarathy, K R

2005-01-01

This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations ...

On structure of quantum super groups GLq(m/n)

International Nuclear Information System (INIS)

Phung Ho Hai

1998-02-01

We show that a quantum super matrix in standard format is invertible if and only if its block matrices of even entries are invertible. We prove the q-analogue of the well-known formula for the Berezinian. (author)

Connections among quantum logics

International Nuclear Information System (INIS)

Lock, P.F.; Hardegree, G.M.

1985-01-01

In this paper, a theory of quantum logics is proposed which is general enough to enable us to reexamine a previous work on quantum logics in the context of this theory. It is then easy to assess the differences between the different systems studied. The quantum logical systems which are incorporated are divided into two groups which we call ''quantum propositional logics'' and ''quantum event logics''. The work of Kochen and Specker (partial Boolean algebras) is included and so is that of Greechie and Gudder (orthomodular partially ordered sets), Domotar (quantum mechanical systems), and Foulis and Randall (operational logics) in quantum propositional logics; and Abbott (semi-Boolean algebras) and Foulis and Randall (manuals) in quantum event logics, In this part of the paper, an axiom system for quantum propositional logics is developed and the above structures in the context of this system examined. (author)

Scaling of the local quantum uncertainty at quantum phase transitions

International Nuclear Information System (INIS)

Coulamy, I.B.; Warnes, J.H.; Sarandy, M.S.; Saguia, A.

2016-01-01

We investigate the local quantum uncertainty (LQU) between a block of L qubits and one single qubit in a composite system of n qubits driven through a quantum phase transition (QPT). A first-order QPT is analytically considered through a Hamiltonian implementation of the quantum search. In the case of second-order QPTs, we consider the transverse-field Ising chain via a numerical analysis through density matrix renormalization group. For both cases, we compute the LQU for finite-sizes as a function of L and of the coupling parameter, analyzing its pronounced behavior at the QPT. - Highlights: • LQU is suitable for the analysis of block correlations. • LQU exhibits pronounced behavior at quantum phase transitions. • LQU exponentially saturates in the quantum search. • Concavity of LQU indicates criticality in the Ising chain.

Does an Emphasis on the Concept of Quantum States Enhance Students' Understanding of Quantum Mechanics?

Science.gov (United States)

Greca, Ileana Maria; Freire, Olival

Teaching physics implies making choices. In the case of teaching quantum physics, besides an educational choice - the didactic strategy - another choice must be made, an epistemological one, concerning the interpretation of quantum theory itself. These two choices are closely connected. We have chosen a didactic strategy that privileges the phenomenological-conceptual approach, with emphasis upon quantum features of the systems, instead of searching for classical analogies. This choice has led us to present quantum theory associated with an orthodox, yet realistic, interpretation of the concept of quantum state, considered as the key concept of quantum theory, representing the physical reality of a system, independent of measurement processes. The results of the mplementation of this strategy, with three groups of engineering students, showed that more than a half of them attained a reasonable understanding of the basics of quantum mechanics (QM) for this level. In addition, a high degree of satisfaction was attained with the classes as 80% of the students of the experimental groups claimed to have liked it and to be interested in learning more about QM.

Associated quantum vector bundles and symplectic structure on a quantum space

International Nuclear Information System (INIS)

Coquereaux, R.; Garcia, A.O.; Trinchero, R.

2000-01-01

We define a quantum generalization of the algebra of functions over an associated vector bundle of a principal bundle. Here the role of a quantum principal bundle is played by a Hopf-Galois extension. Smash products of an algebra times a Hopf algebra H are particular instances of these extensions, and in these cases we are able to define a differential calculus over their associated vector bundles without requiring the use of a (bicovariant) differential structure over H. Moreover, if H is coquasitriangular, it coacts naturally on the associated bundle, and the differential structure is covariant. We apply this construction to the case of the finite quotient of the SL q (2) function Hopf algebra at a root of unity (q 3 = 1) as the structure group, and a reduced 2-dimensional quantum plane as both the 'base manifold' and fibre, getting an algebra which generalizes the notion of classical phase space for this quantum space. We also build explicitly a differential complex for this phase space algebra, and find that levels 0 and 2 support a (co)representation of the quantum symplectic group. On this phase space we define vector fields, and with the help of the Sp q structure we introduce a symplectic form relating 1-forms to vector fields. This leads naturally to the introduction of Poisson brackets, a necessary step to do 'classical' mechanics on a quantum space, the quantum plane. (author)

Quantum Dialogue by Using Non-Symmetric Quantum Channel

International Nuclear Information System (INIS)

Zhan Youbang; Zhang Lingling; Zhang Qunyong; Wang Yuwu

2010-01-01

A protocol for quantum dialogue is proposed to exchange directly the communicator's secret messages by using a three-dimensional Bell state and a two-dimensional Bell state as quantum channel with quantum superdence coding, local collective unitary operations, and entanglement swapping. In this protocol, during the process of transmission of particles, the transmitted particles do not carry any secret messages and are transmitted only one time. The protocol has higher source capacity than protocols using symmetric two-dimensional states. The security is ensured by the unitary operations randomly performed on all checking groups before the particle sequence is transmitted and the application of entanglement swapping. (general)

Spin networks, quantum automata and link invariants

International Nuclear Information System (INIS)

Garnerone, Silvano; Marzuoli, Annalisa; Rasetti, Mario

2006-01-01

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum automata which in turn represent discrete versions of topological quantum computation models. Such a quantum combinatorial scheme, which essentially encodes SU(2) Racah-Wigner algebra and its braided counterpart, is particularly suitable to address problems in topology and group theory and we discuss here a finite states-quantum automaton able to accept the language of braid group in view of applications to the problem of estimating link polynomials in Chern-Simons field theory

Non-linear entropy functionals and a characteristic invariant of symmetry group actions on infinite quantum systems

International Nuclear Information System (INIS)

Hudetz, T.

1989-01-01

We review the development of the non-Abelian generalization of the Kolmogorov-Sinai(KS) entropy invariant, as initated by Connes and Stormer and completed by Connes, Narnhofer and Thirring only recently. As an introduction and motivation, the classical KS theory is reformulated in terms of Abelian W * -algebras. Finally, we describe simple physical applications of the developed characteristic invariant to space-time symmetry group actions on infinite quantum systems. 42 refs. (Author)

Quantum control and representation theory

International Nuclear Information System (INIS)

Ibort, A; Perez-Pardo, J M

2009-01-01

A new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced. We call such a notion von Neumann controllability, and it is shown that it is strictly weaker than the usual notion of pure state and operator controllability. We provide a simple and effective characterization of it by using tools from the theory of unitary representations of Lie groups. In this sense, we are able to approach the problem of control of quantum states from a new perspective, that of the theory of unitary representations of Lie groups. A few examples of physical interest and the particular instances of compact and nilpotent dynamical Lie groups are discussed

Finite and profinite quantum systems

CERN Document Server

Vourdas, Apostolos

2017-01-01

This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics. The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers. Applications of the formalism include quantum optics and ...

Quantum Nanostructures by Droplet Epitaxy

OpenAIRE

Somsak Panyakeow

2009-01-01

Droplet epitaxy is an alternative growth technique for several quantum nanostructures. Indium droplets are distributed randomly on GaAs substrates at low temperatures (120-350'C). Under background pressure of group V elements, Arsenic and Phosphorous, InAs and InP nanostructures are created. Quantum rings with isotropic shape are obtained at low temperature range. When the growth thickness is increased, quantum rings are transformed to quantum dot rings. At high temperature range, anisotropic...

Deformation quantization of the Heisenberg group

International Nuclear Information System (INIS)

Bonechi, F.

1994-01-01

After reviewing the way the quantization of Poisson Lie Groups naturally leads to Quantum Groups, the existing quantum version H(1) q of the Heisenberg algebra is used to give an explicit example of this quantization on the Heisenberg group. (author) 6 refs

Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.

Science.gov (United States)

Sahlmann, Hanno; Thiemann, Thomas

2012-03-16

We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups.

Quantum symmetry for pedestrians

International Nuclear Information System (INIS)

Mack, G.; Schomerus, V.

1992-03-01

Symmetries more general than groups are possible in quantum therory. Quantum symmetries in the narrow sense are compatible with braid statistics. They are theoretically consistent much as supersymmetry is, and they could lead to degenerate multiplets of excitations with fractional spin in thin films. (orig.)

Quantum mechanical alternative to Arrhenius equation in the interpretation of proton spin-lattice relaxation data for the methyl groups in solids

KAUST Repository

Bernatowicz, Piotr; Shkurenko, Aleksander; Osior, Agnieszka; Kamieński, Bohdan; Szymański, Sławomir

2015-01-01

Theory of nuclear spin-lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum

Current algebras, measures quasi-invariant under diffeomorphism groups, and infinite quantum systems with accumulation points

Science.gov (United States)

Sakuraba, Takao

The approach to quantum physics via current algebra and unitary representations of the diffeomorphism group is established. This thesis studies possible infinite Bose gas systems using this approach. Systems of locally finite configurations and systems of configurations with accumulation points are considered, with the main emphasis on the latter. In Chapter 2, canonical quantization, quantization via current algebra and unitary representations of the diffeomorphism group are reviewed. In Chapter 3, a new definition of the space of configurations is proposed and an axiom for general configuration spaces is abstracted. Various subsets of the configuration space, including those specifying the number of points in a Borel set and those specifying the number of accumulation points in a Borel set are proved to be measurable using this axiom. In Chapter 4, known results on the space of locally finite configurations and Poisson measure are reviewed in the light of the approach developed in Chapter 3, including the approach to current algebra in the Poisson space by Albeverio, Kondratiev, and Rockner. Goldin and Moschella considered unitary representations of the group of diffeomorphisms of the line based on self-similar random processes, which may describe infinite quantum gas systems with clusters. In Chapter 5, the Goldin-Moschella theory is developed further. Their construction of measures quasi-invariant under diffeomorphisms is reviewed, and a rigorous proof of their conjectures is given. It is proved that their measures with distinct correlation parameters are mutually singular. A quasi-invariant measure constructed by Ismagilov on the space of configurations with accumulation points on the circle is proved to be singular with respect to the Goldin-Moschella measures. Finally a generalization of the Goldin-Moschella measures to the higher-dimensional case is studied, where the notion of covariance matrix and the notion of condition number play important roles. A

Quantum mechanics and the psyche

Science.gov (United States)

Galli Carminati, G.; Martin, F.

2008-07-01

In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.

Integrability and nonintegrability of quantum systems. II. Dynamics in quantum phase space

Science.gov (United States)

Zhang, Wei-Min; Feng, Da Hsuan; Yuan, Jian-Min

1990-12-01

Based on the concepts of integrability and nonintegrability of a quantum system presented in a previous paper [Zhang, Feng, Yuan, and Wang, Phys. Rev. A 40, 438 (1989)], a realization of the dynamics in the quantum phase space is now presented. For a quantum system with dynamical group scrG and in one of its unitary irreducible-representation carrier spaces gerhΛ, the quantum phase space is a 2MΛ-dimensional topological space, where MΛ is the quantum-dynamical degrees of freedom. This quantum phase space is isomorphic to a coset space scrG/scrH via the unitary exponential mapping of the elementary excitation operator subspace of scrg (algebra of scrG), where scrH (⊂scrG) is the maximal stability subgroup of a fixed state in gerhΛ. The phase-space representation of the system is realized on scrG/scrH, and its classical analogy can be obtained naturally. It is also shown that there is consistency between quantum and classical integrability. Finally, a general algorithm for seeking the manifestation of ``quantum chaos'' via the classical analogy is provided. Illustrations of this formulation in several important quantum systems are presented.

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.

Science.gov (United States)

Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic

2010-01-14

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).

Quantum complexity of graph and algebraic problems

International Nuclear Information System (INIS)

Doern, Sebastian

2008-01-01

This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)

Quantum complexity of graph and algebraic problems

Energy Technology Data Exchange (ETDEWEB)

Doern, Sebastian

2008-02-04

This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)

Quantum centipedes: collective dynamics of interacting quantum walkers

International Nuclear Information System (INIS)

Krapivsky, P L; Luck, J M; Mallick, K

2016-01-01

We consider the quantum centipede made of N fermionic quantum walkers on the one-dimensional lattice interacting by means of the simplest of all hard-bound constraints: the distance between two consecutive fermions is either one or two lattice spacings. This composite quantum walker spreads ballistically, just as the simple quantum walk. However, because of the interactions between the internal degrees of freedom, the distribution of its center-of-mass velocity displays numerous ballistic fronts in the long-time limit, corresponding to singularities in the empirical velocity distribution. The spectrum of the centipede and the corresponding group velocities are analyzed by direct means for the first few values of N . Some analytical results are obtained for arbitrary N by exploiting an exact mapping of the problem onto a free-fermion system. We thus derive the maximal velocity describing the ballistic spreading of the two extremal fronts of the centipede wavefunction, including its non-trivial value in the large- N limit. (paper)

The many faces of the quantum Liouville exponentials

Science.gov (United States)

Gervais, Jean-Loup; Schnittger, Jens

1994-01-01

First, it is proven that the three main operator approaches to the quantum Liouville exponentials—that is the one of Gervais-Neveu (more recently developed further by Gervais), Braaten-Curtright-Ghandour-Thorn, and Otto-Weigt—are equivalent since they are related by simple basis transformations in the Fock space of the free field depending upon the zero-mode only. Second, the GN-G expressions for quantum Liouville exponentials, where the U q( sl(2)) quantum-group structure is manifest, are shown to be given by q-binomial sums over powers of the chiral fields in the J = {1}/{2} representation. Third, the Liouville exponentials are expressed as operator tau functions, whose chiral expansion exhibits a q Gauss decomposition, which is the direct quantum analogue of the classical solution of Leznov and Saveliev. It involves q exponentials of quantum-group generators with group "parameters" equal to chiral components of the quantum metric. Fourth, we point out that the OPE of the J = {1}/{2} Liouville exponential provides the quantum version of the Hirota bilinear equation.

Quantum critical matter. Quantum phase transitions with multiple dynamics and Weyl superconductors

International Nuclear Information System (INIS)

Meng, Tobias

2012-01-01

In this PhD thesis, the physics of quantum critical matter and exotic quantum state close to quantum phase transitions is investigated. We will focus on three different examples that highlight some of the interesting phenomena related to quantum phase transitions. Firstly, we discuss the physics of quantum phase transitions in quantum wires as a function of an external gate voltage when new subbands are activated. We find that at these transitions, strong correlations lead to the formation of an impenetrable gas of polarons, and identify criteria for possible instabilities in the spin- and charge sectors of the model. Our analysis is based on the combination of exact resummations, renormalization group techniques and Luttinger liquid approaches. Secondly, we turn to the physics of multiple divergent time scales close to a quantum critical point. Using an appropriately generalized renormalization group approach, we identify that the presence of multiple dynamics at a quantum phase transition can lead to the emergence of new critical scaling exponents and thus to the breakdown of the usual scaling schemes. We calculate the critical behavior of various thermodynamic properties and detail how unusual physics can arise. It is hoped that these results might be helpful for the interpretation of experimental scaling puzzles close to quantum critical points. Thirdly, we turn to the physics of topological transitions, and more precisely the physics of Weyl superconductors. The latter are the superconducting variant of the topologically non-trivial Weyl semimetals, and emerge at the quantum phase transition between a topological superconductor and a normal insulator upon perturbing the transition with a time reversal symmetry breaking perturbation, such as magnetism. We characterize the topological properties of Weyl superconductors and establish a topological phase diagram for a particular realization in heterostructures. We discuss the physics of vortices in Weyl

Towards quantum gravity via quantum field theory. Problems and perspectives

Energy Technology Data Exchange (ETDEWEB)

Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)

2016-07-01

General Relativity is a classical field theory; the standard methods for constructing a corresponding quantum field theory, however, meet severe difficulties, in particular perturbative non-renormalizability and the problem of background independence. Nevertheless, modern approaches to quantum field theory have significantly lowered these obstacles. On the side of non-renormalizability, this is the concept of effective theories, together with indications for better non-perturbative features of the renormalization group flow. On the side of background independence the main progress comes from an improved understanding of quantum field theories on generic curved spacetimes. Combining these informations, a promising approach to quantum gravity is an expansion around a classical solution which then is a quantum field theory on a given background, augmented by an identity which expresses independence against infinitesimal shifts of the background. The arising theory is expected to describe small corrections to classical general relativity. Inflationary cosmology is expected to arise as a lowest order approximation.

Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C

OpenAIRE

Blaha, Stephen

2002-01-01

We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.

BRST-operator for quantum Lie algebra and differential calculus on quantum groups

International Nuclear Information System (INIS)

Isaev, A.P.; Ogievetskij, O.V.

2001-01-01

For A Hopf algebra one determined structure of differential complex in two dual external Hopf algebras: A external expansion and in A* dual algebra external expansion. The Heisenberg double of these two Hopf algebras governs the differential algebra for the Cartan differential calculus on A algebra. The forst differential complex is the analog of the de Rame complex. The second complex coincide with the standard complex. Differential is realized as (anti)commutator with Q BRST-operator. Paper contains recursion relation that determines unequivocally Q operator. For U q (gl(N)) Lie quantum algebra one constructed BRST- and anti-BRST-operators and formulated the theorem of the Hodge expansion [ru

Towards topological quantum computer

Science.gov (United States)

Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

2018-01-01

Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

Towards topological quantum computer

Directory of Open Access Journals (Sweden)

D. Melnikov

2018-01-01

Full Text Available Quantum R-matrices, the entangling deformations of non-entangling (classical permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern–Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

Quantum resonances and regularity islands in quantum maps

Science.gov (United States)

Sokolov; Zhirov; Alonso; Casati

2000-05-01

We study analytically as well as numerically the dynamics of a quantum map near a quantum resonance of an order q. The map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. Such a Hamiltonian generates at the very point of the resonance a local gauge transformation described by the unitary unimodular group SU(q). The resonant energy growth is attributed to the zero Liouville eigenmodes of the generator in the adjoint representation of the group while the nonzero modes yield saturating with time contribution. In a vicinity of a given resonance, the quasi-Hamiltonian is then found in the form of power expansion with respect to the detuning from the resonance. The problem is related in this way to the motion along a circle in a (q2 - 1)-component inhomogeneous "magnetic" field of a quantum particle with q intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a nonlinear resonance. The most important role is played by the resonances with the orders much smaller than the typical localization length q < l. Such resonances master for exponentially long though finite times the motion in some domains around them. Explicit analytical solution is possible for a few lowest and strongest resonances.

Quantum entanglement and quantum phase transitions in frustrated Majumdar-Ghosh model

International Nuclear Information System (INIS)

Liu Guanghua; Wang Chunhai; Deng Xiaoyan

2011-01-01

By using the density matrix renormalization group technique, the quantum phase transitions in the frustrated Majumdar-Ghosh model are investigated. The behaviors of the conventional order parameter and the quantum entanglement entropy are analyzed in detail. The order parameter is found to peak at J 2 ∼0.58, but not at the Majumdar-Ghosh point (J 2 =0.5). Although, the quantum entanglements calculated with different subsystems display dissimilarly, the extremes of their first derivatives approach to the same critical point. By finite size scaling, this quantum critical point J C 2 converges to around 0.301 in the thermodynamic limit, which is consistent with those predicted previously by some authors (Tonegawa and Harada, 1987 ; Kuboki and Fukuyama, 1987 ; Chitra et al., 1995 ). Across the J C 2 , the system undergoes a quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase.

Some quantum Lie algebras of type Dn positive

International Nuclear Information System (INIS)

Bautista, Cesar; Juarez-Ramirez, Maria Araceli

2003-01-01

A quantum Lie algebra is constructed within the positive part of the Drinfeld-Jimbo quantum group of type D n . Our quantum Lie algebra structure includes a generalized antisymmetry property and a generalized Jacobi identity closely related to the braid equation. A generalized universal enveloping algebra of our quantum Lie algebra of type D n positive is proved to be the Drinfeld-Jimbo quantum group of the same type. The existence of such a generalized Lie algebra is reduced to an integer programming problem. Moreover, when the integer programming problem is feasible we show, by means of the generalized Jacobi identity, that the Poincare-Birkhoff-Witt theorem (basis) is still true

Fixed points of quantum gravity

OpenAIRE

Litim, D F

2003-01-01

Euclidean quantum gravity is studied with renormalisation group methods. Analytical results for a non-trivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameter in the Einstein-Hilbert truncation. Implications for quantum gravity in four dimensions are discussed.

Fractional statistics and quantum theory

CERN Document Server

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

Classification of quantum relativistic orientable objects

Energy Technology Data Exchange (ETDEWEB)

Gitman, D M [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970, Sao Paulo, SP (Brazil); Shelepin, A L, E-mail: gitman@dfn.if.usp.br, E-mail: alex@shelepin.msk.ru [Moscow Institute of Radio Engineering, Electronics and Automation, Prospect Vernadskogo, 78, 117454 Moscow (Russian Federation)

2011-01-15

Extending our previous work 'Fields on the Poincare group and quantum description of orientable objects' (Gitman and Shelepin 2009 Eur. Phys. J. C 61 111-39), we consider here a classification of orientable relativistic quantum objects in 3+1 dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.

Classification of quantum relativistic orientable objects

International Nuclear Information System (INIS)

Gitman, D M; Shelepin, A L

2011-01-01

Extending our previous work 'Fields on the Poincare group and quantum description of orientable objects' (Gitman and Shelepin 2009 Eur. Phys. J. C 61 111-39), we consider here a classification of orientable relativistic quantum objects in 3+1 dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.

Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C Language

OpenAIRE

Blaha, Stephen

2002-01-01

We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.

Quantum walks, quantum gates, and quantum computers

International Nuclear Information System (INIS)

Hines, Andrew P.; Stamp, P. C. E.

2007-01-01

The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between quantum walk Hamiltonians and Hamiltonians for qubit systems and quantum circuits; this is done for both single-excitation and multiexcitation encodings. Specific examples of spin chains, as well as static and dynamic systems of qubits, are mapped to quantum walks, and walks on hyperlattices and hypercubes are mapped to various gate systems. We also show how to map a quantum circuit performing the quantum Fourier transform, the key element of Shor's algorithm, to a quantum walk system doing the same. The results herein are an essential preliminary to a Hamiltonian formulation of quantum walks in which coupling to a dynamic quantum environment is included

Optically Controlled Quantum Dot Spins for Scaleable Quantum Computing

National Research Council Canada - National Science Library

Steel, Duncan G

2006-01-01

.... Sham is responsible for theoretical support & concept development. The group at Michigan along with this QuaCGR student are responsible for experimental demonstration of key experimental demonstrations for quantum computing...

A Quantum Non-Demolition Parity measurement in a mixed-species trapped-ion quantum processor

Science.gov (United States)

Marinelli, Matteo; Negnevitsky, Vlad; Lo, Hsiang-Yu; Flühmann, Christa; Mehta, Karan; Home, Jonathan

2017-04-01

Quantum non-demolition measurements of multi-qubit systems are an important tool in quantum information processing, in particular for syndrome extraction in quantum error correction. We have recently demonstrated a protocol for quantum non-demolition measurement of the parity of two beryllium ions by detection of a co-trapped calcium ion. The measurement requires a sequence of quantum gates between the three ions, using mixed-species gates between beryllium hyperfine qubits and a calcium optical qubit. Our work takes place in a multi-zone segmented trap setup in which we have demonstrated high fidelity control of both species and multi-well ion shuttling. The advantage of using two species of ion is that we can individually manipulate and read out the state of each ion species without disturbing the internal state of the other. The methods demonstrated here can be used for quantum error correcting codes as well as quantum metrology and are key ingredients for realizing a hybrid universal quantum computer based on trapped ions. Mixed-species control may also enable the investigation of new avenues in quantum simulation and quantum state control. left the group and working in a company now.

Therapeutic Effects of Oligonol, Acupuncture, and Quantum Light Therapy in Chronic Nonbacterial Prostatitis.

Science.gov (United States)

Öztekin, İlhan; Akdere, Hakan; Can, Nuray; Aktoz, Tevfik; Arda, Ersan; Turan, Fatma Nesrin

2015-01-01

This research aimed to compare anti-inflammatory effects of oligonol, acupuncture, and quantum light therapy in rat models of estrogen-induced prostatitis. Adult male Wistar albino rats were grouped as follows: Group I, control (n = 10); Group II, chronic prostatitis (n = 10); Group III, oligonol (n = 10); Group IV, acupuncture (n = 10); Group V, quantum (n = 10); Group VI, oligonol plus quantum (n = 10); Group VII, acupuncture plus oligonol (n = 10); Group VIII, quantum plus acupuncture (n = 10); and Group IX, acupuncture plus quantum plus oligonol (n = 10). Chronic prostatitis (CP) was induced by the administration of 17-beta-estradiol (E2) and dihydrotestosterone (DHT). Oligonol was given for 6 weeks at a dose of 60 mg/day. Acupuncture needles were inserted at CV 3/4 and bilaterally B 32/35 points with 1-hour manual stimulation. Quantum therapy was administered in 5-minute sessions three times weekly for 6 weeks. Lateral lobes of prostates were dissected for histopathologic evaluation. Although all of the treatment modalities tested in this study showed anti-inflammatory effects in the treatment of CP in male rats, a synergistic effect was observed for oligonol plus quantum light combination. Monotherapy with oligonol showed a superior anti-inflammatory efficacy as compared to quantum light and acupuncture monotherapies.

Therapeutic Effects of Oligonol, Acupuncture, and Quantum Light Therapy in Chronic Nonbacterial Prostatitis

Directory of Open Access Journals (Sweden)

İlhan Öztekin

2015-01-01

Full Text Available This research aimed to compare anti-inflammatory effects of oligonol, acupuncture, and quantum light therapy in rat models of estrogen-induced prostatitis. Adult male Wistar albino rats were grouped as follows: Group I, control (n = 10; Group II, chronic prostatitis (n = 10; Group III, oligonol (n = 10; Group IV, acupuncture (n = 10; Group V, quantum (n = 10; Group VI, oligonol plus quantum (n = 10; Group VII, acupuncture plus oligonol (n = 10; Group VIII, quantum plus acupuncture (n = 10; and Group IX, acupuncture plus quantum plus oligonol (n = 10. Chronic prostatitis (CP was induced by the administration of 17-beta-estradiol (E2 and dihydrotestosterone (DHT. Oligonol was given for 6 weeks at a dose of 60 mg/day. Acupuncture needles were inserted at CV 3/4 and bilaterally B 32/35 points with 1-hour manual stimulation. Quantum therapy was administered in 5-minute sessions three times weekly for 6 weeks. Lateral lobes of prostates were dissected for histopathologic evaluation. Although all of the treatment modalities tested in this study showed anti-inflammatory effects in the treatment of CP in male rats, a synergistic effect was observed for oligonol plus quantum light combination. Monotherapy with oligonol showed a superior anti-inflammatory efficacy as compared to quantum light and acupuncture monotherapies.

Quantum walks on quotient graphs

International Nuclear Information System (INIS)

Krovi, Hari; Brun, Todd A.

2007-01-01

A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup

Divide and conquer approach to quantum Hamiltonian simulation

Science.gov (United States)

Hadfield, Stuart; Papageorgiou, Anargyros

2018-04-01

We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.

Geometry of Quantum Principal Bundles. Pt. 1

International Nuclear Information System (INIS)

Durdevic, M.

1996-01-01

A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential forms on the base manifold with an appropriate differential calculus on the structure quantum group. Relations between the calculus on the group and the calculus on the bundle are investigated. A concept of (pseudo)tensoriality is formulated. The formalism of connections is developed. In particular, operators of horizontal projection, covariant derivative and curvature are constructed and analyzed. Generalizations of the first Structure Equation and of the Bianchi identity are found. Illustrative examples are presented. (orig.)

Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire

Science.gov (United States)

Horing, Norman J. M.

2017-06-01

This work is concerned with the derivation of the Green's function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green's function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green's function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function). The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ (x ) -potential profile. This retarded Green's function for propagation directly along the wire is determined exactly in terms of the corresponding Green's function for the system without the δ (x ) -potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green's function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.

Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire

Directory of Open Access Journals (Sweden)

Norman J. M. Horing

2017-06-01

Full Text Available This work is concerned with the derivation of the Green’s function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green’s function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green’s function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function. The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ(x-potential profile. This retarded Green’s function for propagation directly along the wire is determined exactly in terms of the corresponding Green’s function for the system without the δ(x-potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green’s function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.

Weakly interacting topological insulators: Quantum criticality and the renormalization group approach

Science.gov (United States)

Chen, Wei

2018-03-01

For D -dimensional weakly interacting topological insulators in certain symmetry classes, the topological invariant can be calculated from a D - or (D +1 ) -dimensional integration over a certain curvature function that is expressed in terms of single-particle Green's functions. Based on the divergence of curvature function at the topological phase transition, we demonstrate how a renormalization group approach circumvents these integrations and reduces the necessary calculation to that for the Green's function alone, rendering a numerically efficient tool to identify topological phase transitions in a large parameter space. The method further unveils a number of statistical aspects related to the quantum criticality in weakly interacting topological insulators, including correlation function, critical exponents, and scaling laws, that can be used to characterize the topological phase transitions driven by either interacting or noninteracting parameters. We use 1D class BDI and 2D class A Dirac models with electron-electron and electron-phonon interactions to demonstrate these principles and find that interactions may change the critical exponents of the topological insulators.

Trapped atomic ions for quantum-limited metrology

Science.gov (United States)

Wineland, David

2017-04-01

Laser-beam-manipulated trapped ions are a candidate for large-scale quantum information processing and quantum simulation but the basic techniques used can also be applied to quantum-limited metrology and sensing. Some examples being explored at NIST are: 1) As charged harmonic oscillators, trapped ions can be used to sense electric fields; this can be used to characterize the electrode-surface-based noisy electric fields that compromise logic-gate fidelities and may eventually be used as a tool in surface science. 2) Since typical qubit logic gates depend on state-dependent forces, we can adapt the gate dynamics to sensitively detect additional forces. 3) We can use extensions of Bell inequality measurements to further restrict the degree of local realism possessed by Bell states. 4) We also briefly describe experiments for creation of Bell states using Hilbert space engineering. This work is a joint effort including the Ion-Storage group, the Quantum processing group, and the Computing and Communications Theory group at NIST, Boulder. Supported by IARPA, ONR, and the NIST Quantum Information Program.

Representations of quantum algebras and combinatorics of Young tableaux

CERN Document Server

Ariki, Susumu

2002-01-01

Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and to apply the theory to representations of Hecke algebras. The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type A_{r-1}^{(1)} as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be the combinatorics of Young tableaux. The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type. The book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the stu...

Quantum memories: emerging applications and recent advances

Science.gov (United States)

Heshami, Khabat; England, Duncan G.; Humphreys, Peter C.; Bustard, Philip J.; Acosta, Victor M.; Nunn, Joshua; Sussman, Benjamin J.

2016-01-01

Quantum light–matter interfaces are at the heart of photonic quantum technologies. Quantum memories for photons, where non-classical states of photons are mapped onto stationary matter states and preserved for subsequent retrieval, are technical realizations enabled by exquisite control over interactions between light and matter. The ability of quantum memories to synchronize probabilistic events makes them a key component in quantum repeaters and quantum computation based on linear optics. This critical feature has motivated many groups to dedicate theoretical and experimental research to develop quantum memory devices. In recent years, exciting new applications, and more advanced developments of quantum memories, have proliferated. In this review, we outline some of the emerging applications of quantum memories in optical signal processing, quantum computation and non-linear optics. We review recent experimental and theoretical developments, and their impacts on more advanced photonic quantum technologies based on quantum memories. PMID:27695198

Knots, topology and quantum field theories

International Nuclear Information System (INIS)

Lusanna, L.

1989-01-01

The title of the workshop, Knots, Topology and Quantum Field Theory, accurate reflected the topics discussed. There have been important developments in mathematical and quantum field theory in the past few years, which had a large impact on physicist thinking. It is historically unusual and pleasing that these developments are taking place as a result of an intense interaction between mathematical physicists and mathematician. On the one hand, topological concepts and methods are playing an increasingly important lead to novel mathematical concepts: for instance, the study of quantum groups open a new chapter in the deformation theory of Lie algebras. These developments at present will lead to new insights into the theory of elementary particles and their interactions. In essence, the talks dealt with three, broadly defined areas of theoretical physics. One was topological quantum field theories, the other the problem of quantum groups and the third one certain aspects of more traditional field theories, such as, for instance, quantum gravity. These topics, however, are interrelated and the general theme of the workshop defies rigid classification; this was evident from the cross references to be found in almo all the talks

Remarks on unitary representations of Poincare group

International Nuclear Information System (INIS)

Burzynski, A.

1979-01-01

In this paper the elementary review of methods and notions using in the theory of unitary representations of Poincare group is included. The Poincare group is a basic group for relativistic quantum mechanics. Our aim is to introduce the reader into some problems of quantum physics, which are difficult approachable for beginners. (author)

Quantum principles in field interactions

International Nuclear Information System (INIS)

Shirkov, D.V.

1986-01-01

The concept of quantum principle is intruduced as a principle whosee formulation is based on specific quantum ideas and notions. We consider three such principles, viz. those of quantizability, local gauge symmetry, and supersymmetry, and their role in the development of the quantum field theory (QFT). Concerning the first of these, we analyze the formal aspects and physical contents of the renormalization procedure in QFT and its relation to ultraviolet divergences and the renorm group. The quantizability principle is formulated as an existence condition of a self-consistent quantum version with a given mechanism of the field interaction. It is shown that the consecutive (from a historial point of view) use of these quantum principles puts still larger limitations on possible forms of field interactions

Statistical algebraic approach to quantum mechanics

International Nuclear Information System (INIS)

Slavnov, D.A.

2001-01-01

The scheme for plotting the quantum theory with application of the statistical algebraic approach is proposed. The noncommutative algebra elements (observed ones) and nonlinear functionals on this algebra (physical state) are used as the primary constituents. The latter ones are associated with the single-unit measurement results. Certain physical state groups are proposed to consider as quantum states of the standard quantum mechanics. It is shown that the mathematical apparatus of the standard quantum mechanics may be reproduced in such a scheme in full volume [ru

Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems

Science.gov (United States)

Rück, Marlon; Reuther, Johannes

2018-04-01

We implement an extension of the pseudofermion functional renormalization group method for quantum spin systems that takes into account two-loop diagrammatic contributions. An efficient numerical treatment of the additional terms is achieved within a nested graph construction which recombines different one-loop interaction channels. In order to be fully self-consistent with respect to self-energy corrections, we also include certain three-loop terms of Katanin type. We first apply this formalism to the antiferromagnetic J1-J2 Heisenberg model on the square lattice and benchmark our results against the previous one-loop plus Katanin approach. Even though the renormalization group (RG) equations undergo significant modifications when including the two-loop terms, the magnetic phase diagram, comprising Néel ordered and collinear ordered phases separated by a magnetically disordered regime, remains remarkably unchanged. Only the boundary position between the disordered and the collinear phases is found to be moderately affected by two-loop terms. On the other hand, critical RG scales, which we associate with critical temperatures Tc, are reduced by a factor of ˜2 indicating that the two-loop diagrams play a significant role in enforcing the Mermin-Wagner theorem. Improved estimates for critical temperatures are also obtained for the Heisenberg ferromagnet on the three-dimensional simple cubic lattice where errors in Tc are reduced by ˜34 % . These findings have important implications for the quantum phase diagrams calculated within the previous one-loop plus Katanin approach which turn out to be already well converged.

A linearization of quantum channels

Science.gov (United States)

Crowder, Tanner

2015-06-01

Because the quantum channels form a compact, convex set, we can express any quantum channel as a convex combination of extremal channels. We give a Euclidean representation for the channels whose inverses are also valid channels; these are a subset of the extreme points. They form a compact, connected Lie group, and we calculate its Lie algebra. Lastly, we calculate a maximal torus for the group and provide a constructive approach to decomposing any invertible channel into a product of elementary channels.

I, Quantum Robot: Quantum Mind control on a Quantum Computer

OpenAIRE

Zizzi, Paola

2008-01-01

The logic which describes quantum robots is not orthodox quantum logic, but a deductive calculus which reproduces the quantum tasks (computational processes, and actions) taking into account quantum superposition and quantum entanglement. A way toward the realization of intelligent quantum robots is to adopt a quantum metalanguage to control quantum robots. A physical implementation of a quantum metalanguage might be the use of coherent states in brain signals.

Time Asymmetric Quantum Mechanics

Directory of Open Access Journals (Sweden)

Arno R. Bohm

2011-09-01

Full Text Available The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1 for states or the Heisenberg equation (6a for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus and observables (defined by a registration apparatus (detector. If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t_0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Quantum coherence and quantum phase transition in the XY model with staggered Dzyaloshinsky-Moriya interaction

Energy Technology Data Exchange (ETDEWEB)

Hui, Ning-Ju [Department of Applied Physics, Xi' an University of Technology, Xi' an 710054 (China); Xu, Yang-Yang; Wang, Jicheng; Zhang, Yixin [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China); Hu, Zheng-Da, E-mail: huyuanda1112@jiangnan.edu.cn [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China)

2017-04-01

We investigate the properties of geometric quantum coherence in the XY spin-1/2 chain with staggered Dzyaloshinsky-Moriya interaction via the quantum renormalization-group approach. It is shown that the geometric quantum coherence and its coherence susceptibility are effective to detect the quantum phase transition. In the thermodynamic limit, the geometric quantum coherence exhibits a sudden jump. The coherence susceptibilities versus the anisotropy parameter and the Dzyaloshinsky-Moriya interaction are infinite and vanishing, respectively, illustrating the distinct roles of the anisotropy parameter and the Dzyaloshinsky-Moriya interaction in quantum phase transition. Moreover, we also explore the finite-size scaling behaviors of the coherence susceptibilities. For a finite-size chain, the coherence susceptibility versus the phase-transition parameter is always maximal at the critical point, indicating the dramatic quantum fluctuation. Besides, we show that the correlation length can be revealed by the scaling exponent for the coherence susceptibility versus the Dzyaloshinsky-Moriya interaction.

Damped Quantum Rotation of the Methyl Group in 9-Methyltriptycene Derivatives. The Magnitude of The Effect vs. The Activation Energy

International Nuclear Information System (INIS)

Czerski, I.; Szymanski, S.

2005-01-01

According to the damped quantum rotation (DQR) theory, hindered rotation of methyl groups, reflected in NMR spectra, is a quantum mechanical process controlled by two quantum mechanical rate constants k t and k K . The subscripts t and K, designating '' tunneling '' and '' Kramers '', refer to two specific, long-lived quantum coherence in the methyl rotor system each of which engages the space and spin coordinates of the three protons, correlated by the Pauli principle. Only in the instances where k t and k K happen to be equal, the NMR picture will be the same as for a hypothetical CH 3 group undergoing classical jumps between its three equivalent orientations, described by single rate constant k '. Departure of the ratio c = k t /k K from 1 can thus serve as a quick measure of the degree of non classicality in the stochastic dynamics of the methyl group or, in other words, of the magnitude of the DQR effect. When the Arrhenius activation energy, Ea, for k K is about 12 kJmol -1 , the non classicality factor c can exceed 5. This is an inference from our recent single-crystal NMR studies at temperatures 60 - 110 K. On an intuitive ground, there should be an inverse (but hardly linear) correlation between E a and c. Indeed, for strongly hindered methyl group in 9-methyltripticene derivatives for which the activation energies can exceed 37 kJmol -1 , the DQR effect proves to be much smaller, with the corresponding values of c not exceeding 1.20. Nonetheless, for the values of c above 1.10 it can still be clearly seen in liquid-phase NMR spectra. Here we report on our recent liquid-phase NMR experiments with a series of 9-methyltriptycene derivatives for which the values of E a for k K span the range 37.4 - 44.8 kJmol -1 while the respective, average values of c vary between 1.04 and 1.20. It comes out that, within such a narrow variability range of E a , the correlation between c and E a no longer holds. For example, for 1,2,3,4-tetrabromo-9,10-dimethyltriptycene

Quantum Optics Initiative

Science.gov (United States)

2007-06-30

the choice for the specificity parameter (S), which is the area around the 51(±3) cm 1 frequency in the Fourier plane (right in Fig...1). The HOMO is believed to be entirely of phthalocyanine character in Alu symmetry of the D4h group [6]. The full-width-at- half - maximum (FWHM) of...quantum Lyapunov exponents or by examining the corresponding Poincare sections in this limit. Since the Bohmian formulation of quantum theory is based

Renormalization and asymptotic freedom in quantum gravity

International Nuclear Information System (INIS)

Tomboulis, E.T.

1984-01-01

The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)

Electron Liquids in Semiconductor Quantum Structures

International Nuclear Information System (INIS)

Pinczuk, Aron

2009-01-01

The groups led by Stormer and Pinczuk have focused this project on goals that seek the elucidation of novel many-particle effects that emerge in two-dimensional electron systems (2DES) as the result from fundamental quantum interactions. This experimental research is conducted under extreme conditions of temperature and magnetic field. From the materials point of view, the ultra-high mobility systems in GaAs/AlGaAs quantum structures continue to be at the forefront of this research. The newcomer materials are based on graphene, a single atomic layer of graphite. The graphene research is attracting enormous attention from many communities involved in condensed matter research. The investigated many-particle phenomena include the integer and fractional quantum Hall effect, composite fermions, and Dirac fermions, and a diverse group of electron solid and liquid crystal phases. The Stormer group performed magneto-transport experiments and far-infrared spectroscopy, while the Pinczuk group explores manifestations of such phases in optical spectra.

Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control

Science.gov (United States)

Deffner, Sebastian; Campbell, Steve

2017-11-01

One of the most widely known building blocks of modern physics is Heisenberg’s indeterminacy principle. Among the different statements of this fundamental property of the full quantum mechanical nature of physical reality, the uncertainty relation for energy and time has a special place. Its interpretation and its consequences have inspired continued research efforts for almost a century. In its modern formulation, the uncertainty relation is understood as setting a fundamental bound on how fast any quantum system can evolve. In this topical review we describe important milestones, such as the Mandelstam-Tamm and the Margolus-Levitin bounds on the quantum speed limit, and summarise recent applications in a variety of current research fields—including quantum information theory, quantum computing, and quantum thermodynamics amongst several others. To bring order and to provide an access point into the many different notions and concepts, we have grouped the various approaches into the minimal time approach and the geometric approach, where the former relies on quantum control theory, and the latter arises from measuring the distinguishability of quantum states. Due to the volume of the literature, this topical review can only present a snapshot of the current state-of-the-art and can never be fully comprehensive. Therefore, we highlight but a few works hoping that our selection can serve as a representative starting point for the interested reader.

Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control

International Nuclear Information System (INIS)

Deffner, Sebastian; Campbell, Steve

2017-01-01

One of the most widely known building blocks of modern physics is Heisenberg’s indeterminacy principle. Among the different statements of this fundamental property of the full quantum mechanical nature of physical reality, the uncertainty relation for energy and time has a special place. Its interpretation and its consequences have inspired continued research efforts for almost a century. In its modern formulation, the uncertainty relation is understood as setting a fundamental bound on how fast any quantum system can evolve. In this topical review we describe important milestones, such as the Mandelstam–Tamm and the Margolus–Levitin bounds on the quantum speed limit , and summarise recent applications in a variety of current research fields—including quantum information theory, quantum computing, and quantum thermodynamics amongst several others. To bring order and to provide an access point into the many different notions and concepts, we have grouped the various approaches into the minimal time approach and the geometric approach , where the former relies on quantum control theory, and the latter arises from measuring the distinguishability of quantum states. Due to the volume of the literature, this topical review can only present a snapshot of the current state-of-the-art and can never be fully comprehensive. Therefore, we highlight but a few works hoping that our selection can serve as a representative starting point for the interested reader. (topical review)

Quantum electrodynamics of strong fields

International Nuclear Information System (INIS)

Greiner, W.

1983-01-01

Quantum Electrodynamics of Strong Fields provides a broad survey of the theoretical and experimental work accomplished, presenting papers by a group of international researchers who have made significant contributions to this developing area. Exploring the quantum theory of strong fields, the volume focuses on the phase transition to a charged vacuum in strong electric fields. The contributors also discuss such related topics as QED at short distances, precision tests of QED, nonperturbative QCD and confinement, pion condensation, and strong gravitational fields In addition, the volume features a historical paper on the roots of quantum field theory in the history of quantum physics by noted researcher Friedrich Hund

Conditional expectations associated with quantum states

International Nuclear Information System (INIS)

Niestegge, Gerd

2005-01-01

An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations always exist; in the quantum case, however, they exist only if a certain weak compatibility criterion is satisfied. This compatibility criterion was introduced among others in a recent paper by the author. Then, state-independent conditional expectations and quantum Markov processes are studied. A classical Markov process is a probability measure, together with a system of random variables, satisfying the Markov property and can equivalently be described by a system of Markovian kernels (often forming a semigroup). This equivalence is partly extended to quantum probabilities. It is shown that a dynamical (semi)group can be derived from a given system of quantum observables satisfying the Markov property, and the group generators are studied. The results are presented in the framework of Jordan operator algebras, and a very general type of observables (including the usual real-valued observables or self-adjoint operators) is considered

A quantum causal discovery algorithm

Science.gov (United States)

Giarmatzi, Christina; Costa, Fabio

2018-03-01

Finding a causal model for a set of classical variables is now a well-established task—but what about the quantum equivalent? Even the notion of a quantum causal model is controversial. Here, we present a causal discovery algorithm for quantum systems. The input to the algorithm is a process matrix describing correlations between quantum events. Its output consists of different levels of information about the underlying causal model. Our algorithm determines whether the process is causally ordered by grouping the events into causally ordered non-signaling sets. It detects if all relevant common causes are included in the process, which we label Markovian, or alternatively if some causal relations are mediated through some external memory. For a Markovian process, it outputs a causal model, namely the causal relations and the corresponding mechanisms, represented as quantum states and channels. Our algorithm opens the route to more general quantum causal discovery methods.

Principles and methods of quantum information technologies

CERN Document Server

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 symplectic geometry. 1. The matrix Hamiltonian formalism

International Nuclear Information System (INIS)

Djemai, A.E.F.

1994-07-01

The main purpose of this work is to describe the quantum analogue of the usual classical symplectic geometry and then to formulate the quantum mechanics as a (quantum) non-commutative symplectic geometry. In this first part, we define the quantum symplectic structure in the context of the matrix differential geometry by using the discrete Weyl-Schwinger realization of the Heisenberg group. We also discuss the continuous limit and give an expression of the quantum structure constants. (author). 42 refs

Quantum Cybernetics and Complex Quantum Systems Science - A Quantum Connectionist Exploration

OpenAIRE

Gonçalves, Carlos Pedro

2014-01-01

Quantum cybernetics and its connections to complex quantum systems science is addressed from the perspective of complex quantum computing systems. In this way, the notion of an autonomous quantum computing system is introduced in regards to quantum artificial intelligence, and applied to quantum artificial neural networks, considered as autonomous quantum computing systems, which leads to a quantum connectionist framework within quantum cybernetics for complex quantum computing systems. Sever...

Toward protocols for quantum-ensured privacy and secure voting

International Nuclear Information System (INIS)

Bonanome, Marianna; Buzek, Vladimir; Ziman, Mario; Hillery, Mark

2011-01-01

We present a number of schemes that use quantum mechanics to preserve privacy, in particular, we show that entangled quantum states can be useful in maintaining privacy. We further develop our original proposal [see M. Hillery, M. Ziman, V. Buzek, and M. Bielikova, Phys. Lett. A 349, 75 (2006)] for protecting privacy in voting, and examine its security under certain types of attacks, in particular dishonest voters and external eavesdroppers. A variation of these quantum-based schemes can be used for multiparty function evaluation. We consider functions corresponding to group multiplication of N group elements, with each element chosen by a different party. We show how quantum mechanics can be useful in maintaining the privacy of the choices group elements.

Toward protocols for quantum-ensured privacy and secure voting

Energy Technology Data Exchange (ETDEWEB)

Bonanome, Marianna [Department of Applied Mathematics and Computer Science, New York City College of Technology, 300 Jay Street, Brooklyn, New York 11201 (United States); Buzek, Vladimir; Ziman, Mario [Research Center for Quantum Information, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia); Faculty of Informatics, Masaryk University, Botanicka 68a, 602 00 Brno (Czech Republic); Hillery, Mark [Department of Physics, Hunter College of CUNY, 695 Park Avenue, New York, New York 10021 (United States)

2011-08-15

We present a number of schemes that use quantum mechanics to preserve privacy, in particular, we show that entangled quantum states can be useful in maintaining privacy. We further develop our original proposal [see M. Hillery, M. Ziman, V. Buzek, and M. Bielikova, Phys. Lett. A 349, 75 (2006)] for protecting privacy in voting, and examine its security under certain types of attacks, in particular dishonest voters and external eavesdroppers. A variation of these quantum-based schemes can be used for multiparty function evaluation. We consider functions corresponding to group multiplication of N group elements, with each element chosen by a different party. We show how quantum mechanics can be useful in maintaining the privacy of the choices group elements.

Private quantum subsystems and quasiorthogonal operator algebras

International Nuclear Information System (INIS)

Levick, Jeremy; Kribs, David W; Pereira, Rajesh; Jochym-O’Connor, Tomas; Laflamme, Raymond

2016-01-01

We generalize a recently discovered example of a private quantum subsystem to find private subsystems for Abelian subgroups of the n-qubit Pauli group, which exist in the absence of private subspaces. In doing so, we also connect these quantum privacy investigations with the theory of quasiorthogonal operator algebras through the use of tools from group theory and operator theory. (paper)

Quantum group spin nets: Refinement limit and relation to spin foams

Science.gov (United States)

Dittrich, Bianca; Martin-Benito, Mercedes; Steinhaus, Sebastian

2014-07-01

So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so-called "spin nets," for quantum groups SU(2)k and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse-graining procedure, we find a vast nontrivial fixed-point structure beyond the degenerate and the BF phase. In comparison to previous work, we use fixed-point intertwiners, inspired by Reisenberger's construction principle [M. P. Reisenberger, J. Math. Phys. (N.Y.) 40, 2046 (1999)] and the recent work [B. Dittrich and W. Kaminski, arXiv:1311.1798], as the initial parametrization. In this new parametrization fine-tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse-graining flow of spin nets can thus be interpreted as describing the effective coupling between two spin foam vertices or space time atoms.

Loop Quantum Gravity.

Science.gov (United States)

Rovelli, Carlo

2008-01-01

The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime , is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n -point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

Relativistic quantum mechanics

CERN Document Server

Horwitz, Lawrence P

2015-01-01

This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...

Quantum theory from questions

Energy Technology Data Exchange (ETDEWEB)

Hoehn, Philipp [Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Vienna (Austria); Wever, Christopher [Institute for Theoretical Particle Physics, Karlsruhe (Germany)

2016-07-01

In contrast to relativity, quantum theory has evaded a commonly accepted apprehension, in part because of the lack of physical statements that fully characterize it. In an attempt to remedy the situation, we summarize a novel reconstruction of the explicit formalism of quantum theory (for arbitrarily many qubits) 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, one can derive, among other things, the state spaces, the unitary group, the von Neumann evolution and show that the binary questions correspond to Pauli operators. The reconstruction also offers new structural insights in the form of novel informational charges and informational complementarity relations which define the state spaces and the unitary group. This reconstruction permits a new perspective on quantum theory.

Quantum Erasure: Quantum Interference Revisited

OpenAIRE

Walborn, Stephen P.; Cunha, Marcelo O. Terra; Pádua, Sebastião; Monken, Carlos H.

2005-01-01

Recent experiments in quantum optics have shed light on the foundations of quantum physics. Quantum erasers - modified quantum interference experiments - show that quantum entanglement is responsible for the complementarity principle.

Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing

Science.gov (United States)

Mazzola, Guglielmo; Smelyanskiy, Vadim N.; Troyer, Matthias

2017-10-01

Quantum tunneling is ubiquitous across different fields, from quantum chemical reactions and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum dynamics of tunneling is infeasible for high-dimensional systems, quantum tunneling also shows up in quantum Monte Carlo (QMC) simulations, which aim to simulate quantum statistics with resources growing only polynomially with the system size. Here we extend the recent results obtained for quantum spin models [Phys. Rev. Lett. 117, 180402 (2016), 10.1103/PhysRevLett.117.180402], and we study continuous-variable models for proton transfer reactions. We demonstrate that QMC simulations efficiently recover the scaling of ground-state tunneling rates due to the existence of an instanton path, which always connects the reactant state with the product. We discuss the implications of our results in the context of quantum chemical reactions and quantum annealing, where quantum tunneling is expected to be a valuable resource for solving combinatorial optimization problems.

Covariant differential calculus on the quantum hyperplane

International Nuclear Information System (INIS)

Wess, J.

1991-01-01

We develop a differential calculus on the quantum hyperplane covariant with respect to the action of the quantum group GL q (n). This is a concrete example of noncommutative differential geometry. We describe the general constraints for a noncommutative differential calculus and verify that the example given here satisfies all these constraints. We also discuss briefly the integration over the quantum plane. (orig.)

Intrinsic Time Quantum Geometrodynamics

OpenAIRE

Ita III, Eyo Eyo; Soo, Chopin; Yu, Hoi-Lai

2015-01-01

Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl Curvature Hypothesis, and thermodynamic and gravitational `arrows of tim...

An Improved Quantum Information Hiding Protocol Based on Entanglement Swapping of χ-type Quantum States

International Nuclear Information System (INIS)

Xu Shu-Jiang; Wang Lian-Hai; Ding Qing-Yan; Zhang Shu-Hui; Chen Xiu-Bo

2016-01-01

In 2011, Qu et al. proposed a quantum information hiding protocol based on the entanglement swapping of χ-type quantum states. Because a χ-type state can be described by the 4-particle cat states which have good symmetry, the possible output results of the entanglement swapping between a given χ-type state and all of the 16 χ-type states are divided into 8 groups instead of 16 groups of different results when the global phase is not considered. So it is difficult to read out the secret messages since each result occurs twice in each line (column) of the secret messages encoding rule for the original protocol. In fact, a 3-bit instead of a 4-bit secret message can be encoded by performing two unitary transformations on 2 particles of a χ-type quantum state in the original protocol. To overcome this defect, we propose an improved quantum information hiding protocol based on the general term formulas of the entanglement swapping among χ-type states. (paper)

Analgesic effects of oligonol, acupuncture and quantum light therapy on chronic nonbacterial prostatitis.

Science.gov (United States)

Akdere, Hakan; Oztekin, Ilhan; Arda, Ersan; Aktoz, Tevfik; Turan, Fatma Nesrin; Burgazli, Kamil Mehmet

2015-04-01

Chronic Nonbacterial Prostatitis (CNBP) is a condition that frequently causes long-term pain and a significant decrease in the quality of life. The present study aimed to examine the analgesic effects of oligonol, acupuncture, quantum light therapy and their combinations on estrogen-induced CNBP in rats. This experimental study was conducted in Edirne, Turkey, using a simple randomized allocation. A total of 90 adult male Wistar rats were randomized into 9 groups of 10 rats each: Group I, control; Group II, CNBP, Group III, oligonol only, Group IV, acupuncture only; Group V, quantum only; Group VI, oligonol + quantum; Group VII, acupuncture + oligonol; Group VIII, quantum + acupuncture; Group IX, acupuncture + quantum + oligonol. Oligonol treatment was given at a dose of 60 mg/day for 6 weeks. Conceptual vessels (CV) 3 and 4, and bilaterally urinary bladder (Bl) 32 and 34 points were targeted with 1-hour acupuncture stimulation. The quantum light therapy was applied in 5-minute sessions for 6 weeks (3-times/a week). For pain measurements, mechanical pressure was applied to a point 2 cm distal to the root of the tail to elicit pain and consequent parameters (peak force, latency time of response and total length of measurement) were assessed. Analgesic effects were observed with all treatment regimens; however, the most prominent median analgesic effect was shown in the quantum light therapy in combination with acupuncture for estrogen-induced CNBP (PF1 = 663.9, PF2 = 403.4) (P = 0.012). Furthermore, we observed that monotherapy with quantum light showed a better analgesic efficacy as compared to oligonol and acupuncture monotherapies (PF1 = 1044.6, PF2 = 661.2) (P = 0.018, P = 0.008, P = 0.018; respectively). All treatment modalities showed a significant analgesic effect on CNBP in rats, being most prominent with the quantum light therapy.

Regularization ambiguities in loop quantum gravity

International Nuclear Information System (INIS)

Perez, Alejandro

2006-01-01

One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultraviolet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem--the existence of well-behaved regularization of the constraints--is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities is the one associated to the SU(2) unitary representation used in the diffeomorphism covariant 'point-splitting' regularization of the nonlinear functionals of the connection. This ambiguity is labeled by a half-integer m and, here, it is referred to as the m ambiguity. The aim of this paper is to investigate the important implications of this ambiguity. We first study 2+1 gravity (and more generally BF theory) quantized in the canonical formulation of loop quantum gravity. Only when the regularization of the quantum constraints is performed in terms of the fundamental representation of the gauge group does one obtain the usual topological quantum field theory as a result. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear-cut choice in the quantization of the constraints in 2+1 loop quantum gravity. We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher representation quantizations of the Hamiltonian constraint. Although the analysis is not complete in 3+1 dimensions - due to the difficulties associated to the definition of the physical inner product - it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find

Steganalysis and improvement of a quantum steganography protocol via a GHZ4 state

International Nuclear Information System (INIS)

Xu Shu-Jiang; Chen Xiu-Bo; Niu Xin-Xin; Yang Yi-Xian

2013-01-01

Quantum steganography that utilizes the quantum mechanical effect to achieve the purpose of information hiding is a popular topic of quantum information. Recently, El Allati et al. proposed a new quantum steganography using the GHZ 4 state. Since all of the 8 groups of unitary transformations used in the secret message encoding rule change the GHZ 4 state into 6 instead of 8 different quantum states when the global phase is not considered, we point out that a 2-bit instead of a 3-bit secret message can be encoded by one group of the given unitary transformations. To encode a 3-bit secret message by performing a group of unitary transformations on the GHZ 4 state, we give another 8 groups of unitary transformations that can change the GHZ 4 state into 8 different quantum states. Due to the symmetry of the GHZ 4 state, all the possible 16 groups of unitary transformations change the GHZ 4 state into 8 different quantum states, so the improved protocol achieves a high efficiency

On the epistemic view of quantum states

International Nuclear Information System (INIS)

Skotiniotis, Michael; Roy, Aidan; Sanders, Barry C.

2008-01-01

We investigate the strengths and limitations of the Spekkens toy model, which is a local hidden variable model that replicates many important properties of quantum dynamics. First, we present a set of five axioms that fully encapsulate Spekkens' toy model. We then test whether these axioms can be extended to capture more quantum phenomena by allowing operations on epistemic as well as ontic states. We discover that the resulting group of operations is isomorphic to the projective extended Clifford group for two qubits. This larger group of operations results in a physically unreasonable model; consequently, we claim that a relaxed definition of valid operations in Spekkens' toy model cannot produce an equivalence with the Clifford group for two qubits. However, the new operations do serve as tests for correlation in a two toy bit model, analogous to the well known Horodecki criterion for the separability of quantum states

Fixed points of quantum gravity in extra dimensions

International Nuclear Information System (INIS)

Fischer, Peter; Litim, Daniel F.

2006-01-01

We study quantum gravity in more than four dimensions with renormalisation group methods. We find a non-trivial ultraviolet fixed point in the Einstein-Hilbert action. The fixed point connects with the perturbative infrared domain through finite renormalisation group trajectories. We show that our results for fixed points and related scaling exponents are stable. If this picture persists at higher order, quantum gravity in the metric field is asymptotically safe. We discuss signatures of the gravitational fixed point in models with low scale quantum gravity and compact extra dimensions

Quantum localisation on the circle

Science.gov (United States)

Fresneda, Rodrigo; Gazeau, Jean Pierre; Noguera, Diego

2018-05-01

Covariant integral quantisation using coherent states for semi-direct product groups is implemented for the motion of a particle on the circle. In this case, the phase space is the cylinder, which is viewed as a left coset of the Euclidean group E(2). Coherent states issued from fiducial vectors are labeled by points in the cylinder and depend also on extra parameters. We carry out the corresponding quantisations of the basic classical observables, particularly the angular momentum and the 2π-periodic discontinuous angle function. We compute their corresponding lower symbols. The quantum localisation on the circle is examined through the properties of the angle operator yielded by our procedure, its spectrum and lower symbol, its commutator with the quantum angular momentum, and the resulting Heisenberg inequality. Comparison with other approaches to the long-standing question of the quantum angle is discussed.

Quantum games as quantum types

Science.gov (United States)

Delbecque, Yannick

In this thesis, we present a new model for higher-order quantum programming languages. The proposed model is an adaptation of the probabilistic game semantics developed by Danos and Harmer [DH02]: we expand it with quantum strategies which enable one to represent quantum states and quantum operations. Some of the basic properties of these strategies are established and then used to construct denotational semantics for three quantum programming languages. The first of these languages is a formalisation of the measurement calculus proposed by Danos et al. [DKP07]. The other two are new: they are higher-order quantum programming languages. Previous attempts to define a denotational semantics for higher-order quantum programming languages have failed. We identify some of the key reasons for this and base the design of our higher-order languages on these observations. The game semantics proposed in this thesis is the first denotational semantics for a lambda-calculus equipped with quantum types and with extra operations which allow one to program quantum algorithms. The results presented validate the two different approaches used in the design of these two new higher-order languages: a first one where quantum states are used through references and a second one where they are introduced as constants in the language. The quantum strategies presented in this thesis allow one to understand the constraints that must be imposed on quantum type systems with higher-order types. The most significant constraint is the fact that abstraction over part of the tensor product of many unknown quantum states must not be allowed. Quantum strategies are a new mathematical model which describes the interaction between classical and quantum data using system-environment dialogues. The interactions between the different parts of a quantum system are described using the rich structure generated by composition of strategies. This approach has enough generality to be put in relation with other

Performing quantum computing experiments in the cloud

Science.gov (United States)

Devitt, Simon J.

2016-09-01

Quantum computing technology has reached a second renaissance in the past five years. Increased interest from both the private and public sector combined with extraordinary theoretical and experimental progress has solidified this technology as a major advancement in the 21st century. As anticipated my many, some of the first realizations of quantum computing technology has occured over the cloud, with users logging onto dedicated hardware over the classical internet. Recently, IBM has released the Quantum Experience, which allows users to access a five-qubit quantum processor. In this paper we take advantage of this online availability of actual quantum hardware and present four quantum information experiments. We utilize the IBM chip to realize protocols in quantum error correction, quantum arithmetic, quantum graph theory, and fault-tolerant quantum computation by accessing the device remotely through the cloud. While the results are subject to significant noise, the correct results are returned from the chip. This demonstrates the power of experimental groups opening up their technology to a wider audience and will hopefully allow for the next stage of development in quantum information technology.

Loop Quantum Gravity

Directory of Open Access Journals (Sweden)

Rovelli Carlo

2008-07-01

Full Text Available The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler’s “spacetime foam” intuition. (iii Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv A derivation of the Bekenstein–Hawking black-hole entropy. (v Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method.

Science.gov (United States)

Yao, Yao; Sun, Ke-Wei; Luo, Zhen; Ma, Haibo

2018-01-18

The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.

Authentication Protocol using Quantum Superposition States

Energy Technology Data Exchange (ETDEWEB)

Kanamori, Yoshito [University of Alaska; Yoo, Seong-Moo [University of Alabama, Huntsville; Gregory, Don A. [University of Alabama, Huntsville; Sheldon, Frederick T [ORNL

2009-01-01

When it became known that quantum computers could break the RSA (named for its creators - Rivest, Shamir, and Adleman) encryption algorithm within a polynomial-time, quantum cryptography began to be actively studied. Other classical cryptographic algorithms are only secure when malicious users do not have sufficient computational power to break security within a practical amount of time. Recently, many quantum authentication protocols sharing quantum entangled particles between communicators have been proposed, providing unconditional security. An issue caused by sharing quantum entangled particles is that it may not be simple to apply these protocols to authenticate a specific user in a group of many users. An authentication protocol using quantum superposition states instead of quantum entangled particles is proposed. The random number shared between a sender and a receiver can be used for classical encryption after the authentication has succeeded. The proposed protocol can be implemented with the current technologies we introduce in this paper.

Quantum Field Theory A Modern Perspective

CERN Document Server

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...

PREFACE: Quantum Optics III

Science.gov (United States)

Orszag, M.; Retamal, J. C.; Saavedra, C.; Wallentowitz, S.

2007-06-01

All the 50 years of conscious pondering did not bring me nearer to an answer to the question `what is light quanta?'. Nowadays, every rascal believes, he knows it, however, he is mistaken. (A Einstein, 1951 in a letter to M Besso) Quantum optics has played a key role in physics in the last several decades. On the other hand, in these early decades of the information age, the flow of information is becoming more and more central to our daily life. Thus, the related fields of quantum information theory as well as Bose-Einstein condensation have acquired tremendous importance in the last couple of decades. In Quantum Optics III, a fusion of these fields appears in a natural way. Quantum Optics III was held in Pucón, Chile, in 27-30 of November, 2006. This beautiful location in the south of Chile is near the lake Villarrica and below the snow covered volcano of the same name. This fantastic environment contributed to a relaxed atmosphere, suitable for informal discussion and for the students to have a chance to meet the key figures in the field. The previous Quantum Optics conferences took place in Santiago, Chile (Quantum Optics I, 2000) and Cozumel, Mexico (Quantum Optics II, 2004). About 115 participants from 19 countries attended and participated in the meeting to discuss a wide variety of topics such as quantum-information processing, experiments related to non-linear optics and squeezing, various aspects of entanglement including its sudden death, correlated twin-photon experiments, light storage, decoherence-free subspaces, Bose-Einstein condensation, discrete Wigner functions and many more. There was a strong Latin-American participation from Argentina, Brazil, Chile, Colombia, Peru, Uruguay, Venezuela and Mexico, as well as from Europe, USA, China, and Australia. New experimental and theoretical results were presented at the conference. In Latin-America a quiet revolution has taken place in the last twenty years. Several groups working in quantum optics and

Quantum information. Teleporation - cryptography - quantum computer

International Nuclear Information System (INIS)

Breuer, Reinhard

2010-01-01

The following topics are dealt with: Reality in the test house, quantum teleportation, 100 years of quantum theory, the reality of quanta, interactionless quantum measurement, rules for quantum computers, quantum computers with ions, spintronics with diamond, the limits of the quantum computers, a view into the future of quantum optics. (HSI)

Discrete quantum geometries and their effective dimension

International Nuclear Information System (INIS)

Thuerigen, Johannes

2015-01-01

In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.

Some quantum Lie algebras of type D{sub n} positive

Energy Technology Data Exchange (ETDEWEB)

Bautista, Cesar [Facultad de Ciencias de la Computacion, Benemerita Universidad Autonoma de Puebla, Edif 135, 14 sur y Av San Claudio, Ciudad Universitaria, Puebla Pue. CP 72570 (Mexico); Juarez-Ramirez, Maria Araceli [Facultad de Ciencias Fisico-Matematicas, Benemerita Universidad Autonoma de Puebla, Edif 158 Av San Claudio y Rio Verde sn Ciudad Universitaria, Puebla Pue. CP 72570 (Mexico)

2003-03-07

A quantum Lie algebra is constructed within the positive part of the Drinfeld-Jimbo quantum group of type D{sub n}. Our quantum Lie algebra structure includes a generalized antisymmetry property and a generalized Jacobi identity closely related to the braid equation. A generalized universal enveloping algebra of our quantum Lie algebra of type D{sub n} positive is proved to be the Drinfeld-Jimbo quantum group of the same type. The existence of such a generalized Lie algebra is reduced to an integer programming problem. Moreover, when the integer programming problem is feasible we show, by means of the generalized Jacobi identity, that the Poincare-Birkhoff-Witt theorem (basis) is still true.

Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations

Directory of Open Access Journals (Sweden)

Hitoshi Konno

2006-12-01

Full Text Available For any affine Lie algebra ${mathfrak g}$, we show that any finite dimensional representation of the universal dynamical $R$ matrix ${cal R}(lambda$ of the elliptic quantum group ${cal B}_{q,lambda}({mathfrak g}$ coincides with a corresponding connection matrix for the solutions of the $q$-KZ equation associated with $U_q({mathfrak g}$. This provides a general connection between ${cal B}_{q,lambda}({mathfrak g}$ and the elliptic face (IRF or SOS models. In particular, we construct vector representations of ${cal R}(lambda$ for ${mathfrak g}=A_n^{(1}$, $B_n^{(1}$, $C_n^{(1}$, $D_n^{(1}$, and show that they coincide with the face weights derived by Jimbo, Miwa and Okado. We hence confirm the conjecture by Frenkel and Reshetikhin.

Simplicial quantum gravity

International Nuclear Information System (INIS)

Hartle, J.B.

1985-01-01

Simplicial approximation and the ideas associated with the Regge calculus provide a concrete way of implementing a sum over histories formulation of quantum gravity. A simplicial geometry is made up of flat simplices joined together in a prescribed way together with an assignment of lengths to their edges. A sum over simplicial geometries is a sum over the different ways the simplices can be joined together with an integral over their edge lengths. The construction of the simplicial Euclidean action for this approach to quantum general relativity is illustrated. The recovery of the diffeomorphism group in the continuum limit is discussed. Some possible classes of simplicial complexes with which to define a sum over topologies are described. In two dimensional quantum gravity it is argued that a reasonable class is the class of pseudomanifolds

Quantum space and quantum completeness

Science.gov (United States)

Jurić, Tajron

2018-05-01

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

Optimal signal states for quantum detectors

International Nuclear Information System (INIS)

Oreshkov, Ognyan; Calsamiglia, John; Munoz-Tapia, Ramon; Bagan, Emili

2011-01-01

Quantum detectors provide information about the microscopic properties of quantum systems by establishing correlations between those properties and a set of macroscopically distinct events that we observe. The question of how much information a quantum detector can extract from a system is therefore of fundamental significance. In this paper, we address this question within a precise framework: given a measurement apparatus implementing a specific POVM measurement, what is the optimal performance achievable with it for a specific information readout task and what is the optimal way to encode information in the quantum system in order to achieve this performance? We consider some of the most common information transmission tasks-the Bayes cost problem, unambiguous message discrimination and the maximal mutual information. We provide general solutions to the Bayesian and unambiguous discrimination problems. We also show that the maximal mutual information is equal to the classical capacity of the quantum-to-classical channel describing the measurement, and study its properties in certain special cases. For a group covariant measurement, we show that the problem is equivalent to the problem of accessible information of a group covariant ensemble of states. We give analytical proofs of optimality in some relevant cases. The framework presented here provides a natural way to characterize generalized quantum measurements in terms of their information readout capabilities.

Controlling the emission wavelength in group III-V semiconductor laser diodes

KAUST Repository

Ooi, Boon S.

2016-12-29

Methods are provided for modifying the emission wavelength of a semiconductor quantum well laser diode, e.g. by blue shifting the emission wavelength. The methods can be applied to a variety of semiconductor quantum well laser diodes, e.g. group III-V semiconductor quantum wells. The group III-V semiconductor can include AlSb, AlAs, Aln, AlP, BN, GaSb, GaAs, GaN, GaP, InSb, InAs, InN, and InP, and group III-V ternary semiconductors alloys such as AlxGai.xAs. The methods can results in a blue shifting of about 20 meV to 350 meV, which can be used for example to make group III-V semiconductor quantum well laser diodes with an emission that is orange or yellow. Methods of making semiconductor quantum well laser diodes and semiconductor quantum well laser diodes made therefrom are also provided.

Quantum correlations in multipartite quantum systems

Science.gov (United States)

Jafarizadeh, M. A.; Heshmati, A.; Karimi, N.; Yahyavi, M.

2018-03-01

Quantum entanglement is the most famous type of quantum correlation between elements of a quantum system that has a basic role in quantum communication protocols like quantum cryptography, teleportation and Bell inequality detection. However, it has already been shown that various applications in quantum information theory do not require entanglement. Quantum discord as a new kind of quantum correlations beyond entanglement, is the most popular candidate for general quantum correlations. In this paper, first we find the entanglement witness in a particular multipartite quantum system which consists of a N-partite system in 2 n -dimensional space. Then we give an exact analytical formula for the quantum discord of this system. At the end of the paper, we investigate the additivity relation of the quantum correlation and show that this relation is satisfied for a N-partite system with 2 n -dimensional space.

Renormalisation in Quantum Mechanics, Quantum Instantons and Quantum Chaos

OpenAIRE

Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.

2001-01-01

We suggest how to construct non-perturbatively a renormalized action in quantum mechanics. We discuss similarties and differences with the standard effective action. We propose that the new quantum action is suitable to define and compute quantum instantons and quantum chaos.

Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review

Directory of Open Access Journals (Sweden)

Ion C. Baianu

2009-04-01

Full Text Available A novel algebraic topology approach to supersymmetry (SUSY and symmetry breaking in quantum field and quantum gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear fusion and other nuclear reaction studies in quantum chromodynamics, nonlinear physics at high energy densities, dynamic Jahn-Teller effects, superfluidity, high temperature superconductors, multiple scattering by molecular systems, molecular or atomic paracrystal structures, nanomaterials, ferromagnetism in glassy materials, spin glasses, quantum phase transitions and supergravity. This approach requires a unified conceptual framework that utilizes extended symmetries and quantum groupoid, algebroid and functorial representations of non-Abelian higher dimensional structures pertinent to quantized spacetime topology and state space geometry of quantum operator algebras. Fourier transforms, generalized Fourier-Stieltjes transforms, and duality relations link, respectively, the quantum groups and quantum groupoids with their dual algebraic structures; quantum double constructions are also discussed in this context in relation to quasi-triangular, quasi-Hopf algebras, bialgebroids, Grassmann-Hopf algebras and higher dimensional algebra. On the one hand, this quantum algebraic approach is known to provide solutions to the quantum Yang-Baxter equation. On the other hand, our novel approach to extended quantum symmetries and their associated representations is shown to be relevant to locally covariant general relativity theories that are consistent with either nonlocal quantum field theories or local bosonic (spin models with the extended quantum symmetry of entangled, 'string-net condensed' (ground states.

Quantum conserved charges in N=1 and N=2 supersymmetric sine-Gordon theories

International Nuclear Information System (INIS)

Kobayashi, Ken-ichiro; Uematsu, Tsuneo; Yu Yangzheng

1993-01-01

We investigate quantum conservation laws in the N=1 and N=2 supersymmetric sine-Gordon theories. We study conserved charges at the quantum level based on perturbation theory formulated in superspace. It will turn out that there exist extra conserved charges of the vertex operator type at the quantum level and they generate a quantum group symmetry in supersymmetric sine-Gordon systems. We also discuss the implication of the quantum group symmetry on the S-matrix structure. (orig.)

Correlation effects in side-coupled quantum dots

International Nuclear Information System (INIS)

Zitko, R; Bonca, J

2007-01-01

Using Wilson's numerical renormalization group (NRG) technique, we compute zero-bias conductance and various correlation functions of a double quantum dot (DQD) system. We present different regimes within a phase diagram of the DQD system. By introducing a negative Hubbard U on one of the quantum dots, we simulate the effect of electron-phonon coupling and explore the properties of the coexisting spin and charge Kondo state. In a triple quantum dot (TQD) system, a multi-stage Kondo effect appears where localized moments on quantum dots are screened successively at exponentially distinct Kondo temperatures

Double quantum dot as a minimal thermoelectric generator

OpenAIRE

Donsa, S.; Andergassen, S.; Held, K.

2014-01-01

Based on numerical renormalization group calculations, we demonstrate that experimentally realized double quantum dots constitute a minimal thermoelectric generator. In the Kondo regime, one quantum dot acts as an n-type and the other one as a p-type thermoelectric device. Properly connected the double quantum dot provides a miniature power supply utilizing the thermal energy of the environment.

Quantum Kinematics of Bosonic Vortex Loops

International Nuclear Information System (INIS)

Goldin, G.A.; Owczarek, R.; Sharp, D.H.

1999-01-01

Poisson structure for vortex filaments (loops and arcs) in 2D ideal incompressible fluid is analyzed in detail. Canonical coordinates and momenta on coadjoint orbits of the area-preserving diffeomorphism group, associated with such vortices, are found. The quantum space of states in the simplest case of ''bosonic'' vortex loops is built within a geometric quantization approach to the description of a quantum fluid. Fock-like structure and non-local creation and annihilation operators of quantum vortex filaments are introduced

Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons

OpenAIRE

Kröger, H.

2003-01-01

We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.

Quantum dynamics of quantum bits

International Nuclear Information System (INIS)

Nguyen, Bich Ha

2011-01-01

The theory of coherent oscillations of the matrix elements of the density matrix of the two-state system as a quantum bit is presented. Different calculation methods are elaborated in the case of a free quantum bit. Then the most appropriate methods are applied to the study of the density matrices of the quantum bits interacting with a classical pumping radiation field as well as with the quantum electromagnetic field in a single-mode microcavity. The theory of decoherence of a quantum bit in Markovian approximation is presented. The decoherence of a quantum bit interacting with monoenergetic photons in a microcavity is also discussed. The content of the present work can be considered as an introduction to the study of the quantum dynamics of quantum bits. (review)

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

International Nuclear Information System (INIS)

Yoshida, Beni

2011-01-01

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.

Hybrid quantum systems: Outsourcing superconducting qubits

Science.gov (United States)

Cleland, Andrew

Superconducting qubits offer excellent prospects for manipulating quantum information, with good qubit lifetimes, high fidelity single- and two-qubit gates, and straightforward scalability (admittedly with multi-dimensional interconnect challenges). One interesting route for experimental development is the exploration of hybrid systems, i.e. coupling superconducting qubits to other systems. I will report on our group's efforts to develop approaches that will allow interfacing superconducting qubits in a quantum-coherent fashion to spin defects in solids, to optomechanical devices, and to resonant nanomechanical structures. The longer term goals of these efforts include transferring quantum states between different qubit systems; generating and receiving ``flying'' acoustic phonon-based as well as optical photon-based qubits; and ultimately developing systems that can be used for quantum memory, quantum computation and quantum communication, the last in both the microwave and fiber telecommunications bands. Work is supported by Grants from AFOSR, ARO, DOE and NSF.

Quantum information. Teleportation - cryptography - quantum computer

International Nuclear Information System (INIS)

Koenneker, Carsten

2012-01-01

The following topics are dealt with: Reality in the test facility, quantum teleportation, the reality of quanta, interaction-free quantum measurement, rules for quantum computers, quantum computers with ions, spintronics with diamond, the limits of the quantum computers, a view in the future of quantum optics. (HSI)

Double-partition Quantum Cluster Algebras

DEFF Research Database (Denmark)

Jakobsen, Hans Plesner; Zhang, Hechun

2012-01-01

A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti- tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping...... together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis....

Quantumness-generating capability of quantum dynamics

Science.gov (United States)

Li, Nan; Luo, Shunlong; Mao, Yuanyuan

2018-04-01

We study quantumness-generating capability of quantum dynamics, where quantumness refers to the noncommutativity between the initial state and the evolving state. In terms of the commutator of the square roots of the initial state and the evolving state, we define a measure to quantify the quantumness-generating capability of quantum dynamics with respect to initial states. Quantumness-generating capability is absent in classical dynamics and hence is a fundamental characteristic of quantum dynamics. For qubit systems, we present an analytical form for this measure, by virtue of which we analyze several prototypical dynamics such as unitary dynamics, phase damping dynamics, amplitude damping dynamics, and random unitary dynamics (Pauli channels). Necessary and sufficient conditions for the monotonicity of quantumness-generating capability are also identified. Finally, we compare these conditions for the monotonicity of quantumness-generating capability with those for various Markovianities and illustrate that quantumness-generating capability and quantum Markovianity are closely related, although they capture different aspects of quantum dynamics.

Supersymmetric symplectic quantum mechanics

Science.gov (United States)

de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.

2018-02-01

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

Light fermions in quantum gravity

International Nuclear Information System (INIS)

Eichhorn, Astrid; Gies, Holger

2011-01-01

We study the impact of quantum gravity, formulated as a quantum field theory of the metric, on chiral symmetry in a fermionic matter sector. Specifically we address the question of whether metric fluctuations can induce chiral symmetry breaking and bound state formation. Our results based on the functional renormalization group indicate that chiral symmetry is left intact even at strong gravitational coupling. In particular, we found that asymptotically safe quantum gravity where the gravitational couplings approach a non-Gaußian fixed point generically admits universes with light fermions. Our results thus further support quantum gravity theories built on fluctuations of the metric field such as the asymptotic-safety scenario. A study of chiral symmetry breaking through gravitational quantum effects may also serve as a significant benchmark test for other quantum gravity scenarios, since a completely broken chiral symmetry at the Planck scale would not be in accordance with the observation of light fermions in our universe. We demonstrate that this elementary observation already imposes constraints on a generic UV completion of gravity. (paper)

Differential calculus on deformed E(2) group

International Nuclear Information System (INIS)

Giller, S.; Gonera, C.; Kosinski, P.; Maslanka, P.

1997-01-01

Four dimensional bi-covariant differential *-calculus on quantum E(2) group is constructed. The relevant Lie algebra is obtained and covariant differential calculus on quantum plane is found. (author)

Black holes as quantum gravity condensates

Science.gov (United States)

Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo

2018-03-01

We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalized condensate states, involving sums over arbitrarily refined graphs (dual to three-dimensional triangulations). The construction relies heavily on both the combinatorial tools of random tensor models and the quantum geometric data of loop quantum gravity, both part of the group field theory formalism. Armed with the detailed microscopic structure, we compute the entropy associated with the black hole horizon, which turns out to be equivalently the Boltzmann entropy of its microscopic degrees of freedom and the entanglement entropy between the inside and outside regions. We recover the area law under very general conditions, as well as the Bekenstein-Hawking formula. The result is also shown to be generically independent of any specific value of the Immirzi parameter.

Algebraic quantization, good operators and fractional quantum numbers

International Nuclear Information System (INIS)

Aldaya, V.; Calixto, M.; Guerrero, J.

1996-01-01

The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the failure of the Ehrenfest theorem is clarified in terms of the already defined notion of good (and bad) operators. The analysis of constrained Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for quantum operators without classical analogue and for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring anomalous operators, non-equivalent quantization and the latter, fractional quantum numbers. These provide the rationale behind flux quantization in superconducting rings and Fractional Quantum Hall Effect, respectively. (orig.)

Quantum entanglement and quantum teleportation

International Nuclear Information System (INIS)

Shih, Y.H.

2001-01-01

One of the most surprising consequences of quantum mechanics is the entanglement of two or more distance particles. The ''ghost'' interference and the ''ghost'' image experiments demonstrated the astonishing nonlocal behavior of an entangled photon pair. Even though we still have questions in regard to fundamental issues of the entangled quantum systems, quantum entanglement has started to play important roles in quantum information and quantum computation. Quantum teleportation is one of the hot topics. We have demonstrated a quantum teleportation experiment recently. The experimental results proved the working principle of irreversibly teleporting an unknown arbitrary quantum state from one system to another distant system by disassembling into and then later reconstructing from purely classical information and nonclassical EPR correlations. The distinct feature of this experiment is that the complete set of Bell states can be distinguished in the Bell state measurement. Teleportation of a quantum state can thus occur with certainty in principle. (orig.)

Quantum ensembles of quantum classifiers.

Science.gov (United States)

Schuld, Maria; Petruccione, Francesco

2018-02-09

Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which - similar to Bayesian learning - the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.

Quantum computer games: quantum minesweeper

Science.gov (United States)

Gordon, Michal; Gordon, Goren

2010-07-01

The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical minesweeper the goal of the game is to discover all the mines laid out on a board without triggering them, in the quantum version there are several classical boards in superposition. The goal is to know the exact quantum state, i.e. the precise layout of all the mines in all the superposed classical boards. The player can perform three types of measurement: a classical measurement that probabilistically collapses the superposition; a quantum interaction-free measurement that can detect a mine without triggering it; and an entanglement measurement that provides non-local information. The application of the concepts taught by quantum minesweeper to one-way quantum computing are also presented.

Coherent states associated to the Jacobi group

International Nuclear Information System (INIS)

Berceanu, S.

2007-01-01

.The coherent states (CS) offer a useful connection between classical and quantum mechanics. In several previous works we have constructed CS attached to the Jacobi group. It is well known that the Jacobi group appears in Quantum Mechanics, Geometric Quantization, Optics. The mathematicians have given the name 'Jacobi group' to the semidirect product of the Heisenberg-Weyl group and the symplectic group. The same group is known to physicists under other names, as the Schroedinger group. Also the name 'Weyl-symplectic' group is used for the same semi-direct product of the Heisenberg-Weyl group and the symplectic group. In this paper we review and discuss some properties of the coherent states associated to the Jacobi group. (author)

On the embedding of quantum field theory on curved spacetimes into loop quantum gravity

International Nuclear Information System (INIS)

Stottmeister, Alexander

2015-01-01

The main theme of this thesis is an investigation into possible connections between loop quantum gravity and quantum field theory on curved spacetimes: On the one hand, we aim for the formulation of a general framework that allows for a derivation of quantum field theory on curved spacetimes in a semi-classical limit. On the other hand, we discuss representation-theoretical aspects of loop quantum gravity and quantum field theory on curved spacetimes as both of the latter presumably influence each other in the aforesaid semi-classical limit. Regarding the first point, we investigate the possible implementation of the Born-Oppenheimer approximation in the sense of space-adiabatic perturbation theory in models of loop quantum gravity-type. In the course of this, we argue for the need of a Weyl quantisation and an associated symbolic calculus for loop quantum gravity, which we then successfully define, at least to a certain extent. The compactness of the Lie groups, which models a la loop quantum gravity are based on, turns out to be a main obstacle to a fully satisfactory definition of a Weyl quantisation. Finally, we apply our findings to some toy models of linear scalar quantum fields on quantum cosmological spacetimes and discuss the implementation of space-adiabatic perturbation theory therein. In view of the second point, we start with a discussion of the microlocal spectrum condition for quantum fields on curved spacetimes and how it might be translated to a background-independent Hamiltonian quantum theory of gravity, like loop quantum gravity. The relevance of this lies in the fact that the microlocal spectrum condition selects a class of physically relevant states of the quantum matter fields and is, therefore, expected to play an important role in the aforesaid semi-classical limit of gravity-matter systems. Following this, we switch our perspective and analyse the representation theory of loop quantum gravity. We find some intriguing relations between the

Deformed quantum double realization of the toric code and beyond

Science.gov (United States)

Padmanabhan, Pramod; Ibieta-Jimenez, Juan Pablo; Bernabe Ferreira, Miguel Jorge; Teotonio-Sobrinho, Paulo

2016-09-01

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Zn and S3. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z2 phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.

Quantum control limited by quantum decoherence

International Nuclear Information System (INIS)

Xue, Fei; Sun, C. P.; Yu, S. X.

2006-01-01

We describe quantum controllability under the influences of the quantum decoherence induced by the quantum control itself. It is shown that, when the controller is considered as a quantum system, it will entangle with its controlled system and then cause quantum decoherence in the controlled system. In competition with this induced decoherence, the controllability will be limited by some uncertainty relation in a well-armed quantum control process. In association with the phase uncertainty and the standard quantum limit, a general model is studied to demonstrate the possibility of realizing a decoherence-free quantum control with a finite energy within a finite time. It is also shown that if the operations of quantum control are to be determined by the initial state of the controller, then due to the decoherence which results from the quantum control itself, there exists a low bound for quantum controllability

Quantum memory Quantum memory

Science.gov (United States)

Le Gouët, Jean-Louis; Moiseev, Sergey

2012-06-01

Interaction of quantum radiation with multi-particle ensembles has sparked off intense research efforts during the past decade. Emblematic of this field is the quantum memory scheme, where a quantum state of light is mapped onto an ensemble of atoms and then recovered in its original shape. While opening new access to the basics of light-atom interaction, quantum memory also appears as a key element for information processing applications, such as linear optics quantum computation and long-distance quantum communication via quantum repeaters. Not surprisingly, it is far from trivial to practically recover a stored quantum state of light and, although impressive progress has already been accomplished, researchers are still struggling to reach this ambitious objective. This special issue provides an account of the state-of-the-art in a fast-moving research area that makes physicists, engineers and chemists work together at the forefront of their discipline, involving quantum fields and atoms in different media, magnetic resonance techniques and material science. Various strategies have been considered to store and retrieve quantum light. The explored designs belong to three main—while still overlapping—classes. In architectures derived from photon echo, information is mapped over the spectral components of inhomogeneously broadened absorption bands, such as those encountered in rare earth ion doped crystals and atomic gases in external gradient magnetic field. Protocols based on electromagnetic induced transparency also rely on resonant excitation and are ideally suited to the homogeneous absorption lines offered by laser cooled atomic clouds or ion Coulomb crystals. Finally off-resonance approaches are illustrated by Faraday and Raman processes. Coupling with an optical cavity may enhance the storage process, even for negligibly small atom number. Multiple scattering is also proposed as a way to enlarge the quantum interaction distance of light with matter. The

From quantum coherence to quantum correlations

Science.gov (United States)

Sun, Yuan; Mao, Yuanyuan; Luo, Shunlong

2017-06-01

In quantum mechanics, quantum coherence of a state relative to a quantum measurement can be identified with the quantumness that has to be destroyed by the measurement. In particular, quantum coherence of a bipartite state relative to a local quantum measurement encodes quantum correlations in the state. If one takes minimization with respect to the local measurements, then one is led to quantifiers which capture quantum correlations from the perspective of coherence. In this vein, quantum discord, which quantifies the minimal correlations that have to be destroyed by quantum measurements, can be identified as the minimal coherence, with the coherence measured by the relative entropy of coherence. To advocate and formulate this idea in a general context, we first review coherence relative to Lüders measurements which extends the notion of coherence relative to von Neumann measurements (or equivalently, orthonomal bases), and highlight the observation that quantum discord arises as minimal coherence through two prototypical examples. Then, we introduce some novel measures of quantum correlations in terms of coherence, illustrate them through examples, investigate their fundamental properties and implications, and indicate their applications to quantum metrology.

Lattice quantum phase space and Yang-Baxter equation

International Nuclear Information System (INIS)

Djemai, A.E.F.

1995-04-01

In this work, we show that it is possible to construct the quantum group which preserves the quantum symplectic structure introduced in the context of the matrix Hamiltonian formalism. We also study the braiding existing behind the lattice quantum phase space, and present another type of non-trivial solution to the resulting Yang-Baxter equation. (author). 20 refs, 1 fig

Electronic states in a quantum lens

International Nuclear Information System (INIS)

Rodriguez, Arezky H.; Trallero-Giner, C.; Ulloa, S. E.; Marin-Antuna, J.

2001-01-01

We present a model to find analytically the electronic states in self-assembled quantum dots with a truncated spherical cap (''lens'') geometry. A conformal analytical image is designed to map the quantum dot boundary into a dot with semispherical shape. The Hamiltonian for a carrier confined in the quantum lens is correspondingly mapped into an equivalent operator and its eigenvalues and eigenfunctions for the corresponding Dirichlet problem are analyzed. A modified Rayleigh-Schro''dinger perturbation theory is presented to obtain analytical expressions for the energy levels and wave functions as a function of the spherical cap height b and radius a of the circular cross section. Calculations for a hard wall confinement potential are presented, and the effect of decreasing symmetry on the energy values and eigenfunctions of the lens-shape quantum dot is studied. As the degeneracies of a semicircular geometry are broken for b≠a, our perturbation approach allows tracking of the split states. Energy states and electronic wave functions with m=0 present the most pronounced influence on the reduction of the lens height. The method and expressions presented here can be straightforwardly extended to deal with more general Hamiltonians, including strains and valence-band coupling effects in Group III--V and Group II--VI self-assembled quantum dots

Quantum Instantons and Quantum Chaos

OpenAIRE

Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.; Rubin, S. G.

1999-01-01

Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.

[Studies in quantum field theory

International Nuclear Information System (INIS)

1990-01-01

During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity

Duality Quantum Information and Duality Quantum Communication

International Nuclear Information System (INIS)

Li, C. Y.; Wang, W. Y.; Wang, C.; Song, S. Y.; Long, G. L.

2011-01-01

Quantum mechanical systems exhibit particle wave duality property. This duality property has been exploited for information processing. A duality quantum computer is a quantum computer on the move and passing through a multi-slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a duality quantum computer, and a duality quantum computer with n qubits and d-slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so-called duality quantum computing mode. The quantum particle-wave duality can be used in providing secure communication. In this paper, we will review duality quantum computing and duality quantum key distribution.

Quantum computers and quantum computations

International Nuclear Information System (INIS)

Valiev, Kamil' A

2005-01-01

This review outlines the principles of operation of quantum computers and their elements. The theory of ideal computers that do not interact with the environment and are immune to quantum decohering processes is presented. Decohering processes in quantum computers are investigated. The review considers methods for correcting quantum computing errors arising from the decoherence of the state of the quantum computer, as well as possible methods for the suppression of the decohering processes. A brief enumeration of proposed quantum computer realizations concludes the review. (reviews of topical problems)

States of maximum polarization for a quantum light field and states of a maximum sensitivity in quantum interferometry

International Nuclear Information System (INIS)

Peřinová, Vlasta; Lukš, Antonín

2015-01-01

The SU(2) group is used in two different fields of quantum optics, the quantum polarization and quantum interferometry. Quantum degrees of polarization may be based on distances of a polarization state from the set of unpolarized states. The maximum polarization is achieved in the case where the state is pure and then the distribution of the photon-number sums is optimized. In quantum interferometry, the SU(2) intelligent states have also the property that the Fisher measure of information is equal to the inverse minimum detectable phase shift on the usual simplifying condition. Previously, the optimization of the Fisher information under a constraint was studied. Now, in the framework of constraint optimization, states similar to the SU(2) intelligent states are treated. (paper)

Quantum Computation and Quantum Spin Dynamics

NARCIS (Netherlands)

Raedt, Hans De; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji

2001-01-01

We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum

Effective quantum field theories

International Nuclear Information System (INIS)

Georgi, H.M.

1989-01-01

Certain dimensional parameters play a crucial role in the understanding of weak and strong interactions based on SU(2) x U(1) and SU(3) symmetry group theories and of grand unified theories (GUT's) based on SU(5). These parameters are the confinement scale of quantum chromodynamics and the breaking scales of SU(2) x U(1) and SU(5). The concepts of effective quantum field theories and renormalisability are discussed with reference to the economics and ethics of research. (U.K.)

What is quantum in quantum randomness?

Science.gov (United States)

Grangier, P; Auffèves, A

2018-07-13

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of 'What is quantum in quantum randomness?', i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to be answered. In a first part, we make explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programmes inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyse quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness that have opened up in the emerging field of quantum thermodynamics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Quantum robots and quantum computers

Energy Technology Data Exchange (ETDEWEB)

Benioff, P.

1998-07-01

Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.

On the τ(2)-model in the chiral Potts model and cyclic representation of the quantum group Uq(sl2)

International Nuclear Information System (INIS)

Roan Shishyr

2009-01-01

We identify the precise relationship between the five-parameter τ (2) -family in the N-state chiral Potts model and XXZ chains with U q (sl 2 )-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover a one-parameter family of L-operators in terms of the quantum group U q (sl 2 ). When N is odd, the N-state τ (2) -model can be regarded as the XXZ chain of U q (sl 2 ) cyclic representations with q N =1. The symmetry algebra of the τ (2) -model is described by the quantum affine algebra U q (sl 2 -hat) via the canonical representation. In general, for an arbitrary N, we show that the XXZ chain with a U q (sl 2 )-cyclic representation for q 2N = 1 is equivalent to two copies of the same N-state τ (2) -model. (fast track communication)

Quantum Hurwitz numbers and Macdonald polynomials

Science.gov (United States)

Harnad, J.

2016-11-01

Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.

Quantum double actions on operator algebras and orbifold quantum field theories

International Nuclear Information System (INIS)

Mueger, M.

1996-06-01

Starting from a local quantum field theory with an unbroken compact symmetry group G in 1+1 dimensional spacetime we construct disorder fields implementing gauge transformations on the fields (order variables) localized in a wedge region. Enlarging the local algebras by these disorder fields we obtain a nonlocal field theory, the fixpoint algebras of which under the appropriately extended action of the group G are shown to satisfy Haag duality in every simple sector. The specifically 1+1 dimensional phenomenon of violation of Haag duality of fixpoint nets is thereby clarified. In the case of a finite group G the extended theory is acted upon in a completely canonical way by the quantum double D(G) and satisfies R-matrix commutation relations as well as a Verlinde algebra. Furthermore, our methods are suitable for a concise and transparent approach to bosonization. The main technical ingredient is a strengthened version of the split property which should hold in all reasonable massive theories. In the appendices (part of) the results are extended to arbitary locally compact groups and our methods are adapted to chiral theories on the circle. (orig.)

De Rham complexes of q-analogue of general linear group GLq(N)

International Nuclear Information System (INIS)

Sun Xiaodong; Wang Shikun

1993-07-01

In this paper we give a set of De Rham complexes of quantum group GL q (N) determined by one parameter r, and prove that the differential calculi on the quantum group GL q (N) given in this paper are bicovariant. The noncommutative differential calculi on the quantum groups SL q (N) and SU q (N) are also discussed. (author). 15 refs

Quantum relativity theory and quantum space-time

International Nuclear Information System (INIS)

Banai, M.

1984-01-01

A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis's quantum relativity. The recently proposed classical relativistic quantum theory of Prugovecki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (''elementary particles''). The main new aspect of this quantum mechanics is that it provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that ''quarks'' should be considered as quantum relativistic particles. (author)

Quantum Correlations Evolution Asymmetry in Quantum Channels

International Nuclear Information System (INIS)

Li Meng; Huang Yun-Feng; Guo Guang-Can

2017-01-01

It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entanglement and quantum discord, evolution asymmetry to various quantum channels. We found that the asymmetry of entanglement and quantum discord only occurs in some special quantum channels, and the behavior of the entanglement evolution may be quite different from the behavior of the quantum discord evolution. To quantum entanglement, in some channels it decreases monotonously with the increase of the quantum channel intensity. In some other channels, when we increase the intensity of the quantum channel, it decreases at first, then keeps zero for some time, and then rises up. To quantum discord, the evolution becomes more complex and you may find that it evolutes unsmoothly at some points. These results illustrate the strong dependence of the quantum correlations evolution on the property of the quantum channels. (paper)

Quantum Secure Dialogue with Quantum Encryption

International Nuclear Information System (INIS)

Ye Tian-Yu

2014-01-01

How to solve the information leakage problem has become the research focus of quantum dialogue. In this paper, in order to overcome the information leakage problem in quantum dialogue, a novel approach for sharing the initial quantum state privately between communicators, i.e., quantum encryption sharing, is proposed by utilizing the idea of quantum encryption. The proposed protocol uses EPR pairs as the private quantum key to encrypt and decrypt the traveling photons, which can be repeatedly used after rotation. Due to quantum encryption sharing, the public announcement on the state of the initial quantum state is omitted, thus the information leakage problem is overcome. The information-theoretical efficiency of the proposed protocol is nearly 100%, much higher than previous information leakage resistant quantum dialogue protocols. Moreover, the proposed protocol only needs single-photon measurements and nearly uses single photons as quantum resource so that it is convenient to implement in practice. (general)

Trading quantum for classical resources in quantum data compression

International Nuclear Information System (INIS)

Hayden, Patrick; Jozsa, Richard; Winter, Andreas

2002-01-01

We study the visible compression of a source E={|φ i >,p i } of pure quantum signal states or, more formally, the minimal resources per signal required to represent arbitrarily long strings of signals with arbitrarily high fidelity, when the compressor is given the identity of the input state sequence as classical information. According to the quantum source coding theorem, the optimal quantum rate is the von Neumann entropy S(E) qubits per signal. We develop a refinement of this theorem in order to analyze the situation in which the states are coded into classical and quantum bits that are quantified separately. This leads to a trade-off curve Q * (R), where Q * (R) qubits per signal is the optimal quantum rate for a given classical rate of R bits per signal. Our main result is an explicit characterization of this trade-off function by a simple formula in terms of only single-signal, perfect fidelity encodings of the source. We give a thorough discussion of many further mathematical properties of our formula, including an analysis of its behavior for group covariant sources and a generalization to sources with continuously parametrized states. We also show that our result leads to a number of corollaries characterizing the trade-off between information gain and state disturbance for quantum sources. In addition, we indicate how our techniques also provide a solution to the so-called remote state preparation problem. Finally, we develop a probability-free version of our main result which may be interpreted as an answer to the question: ''How many classical bits does a qubit cost?'' This theorem provides a type of dual to Holevo's theorem, insofar as the latter characterizes the cost of coding classical bits into qubits

Feynman propagator for spin foam quantum gravity.

Science.gov (United States)

Oriti, Daniele

2005-03-25

We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".

Twisted traces of quantum intertwiners and quantum dynamical R-matrices corresponding to generalized Belavin-Drinfeld triples

International Nuclear Information System (INIS)

Etingof, P.; Massachusetts Inst. of Tech., Cambridge, MA; Schiffmann, O.

2001-01-01

We consider weighted traces of products of intertwining operators for quantum groups U q (g), suitably twisted by a ''generalized Belavin-Drinfeld triple''. We derive two commuting sets of difference equations - the (twisted) Macdonald-Ruijsenaars system and the (twisted) quantum Knizhnik-Zamolodchikov-Bernard (qKZB) system. These systems involve the nonstandard quantum R-matrices defined in a previous joint work with T. Schedler (2000). When the generalized Belavin-Drinfeld triple comes from an automorphism of the Lie algebra g, we also derive two additional sets of difference equations, the dual Macdonald-Ruijsenaars system and the dual qKZB equations. (orig.)

Reconstruction of abstract quantum theory

International Nuclear Information System (INIS)

Drieschner, M.; Goernitz, T.; von Weizsaecker, C.F.

1988-01-01

Understanding quantum theory as a general theory of prediction, we reconstruct abstract quantum theory. Abstract means the general frame of quantum theory, without reference to a three-dimensional position space, to concepts like particle or field, or to special laws of dynamics. Reconstruction is the attempt to do this by formulating simple and plausible postulates on prediction in order to derive the basic concepts of quantum theory from them. Thereby no law of classical physics is presupposed which would then have to be quantized. We briefly discuss the relationship of theory and interpretation in physics and the fundamental role of time as a basic concept for physics. Then a number of assertions are given, formulated as succinctly as possible in order to make them easily quotable and comparable. The assertations are arranged in four groups: heuristic principles, verbal definitions of some terms, three basic postulates, and consequences. The three postulates of separable alternatives, indeterminism, and kinematics are the central points of this work. These brief assertions are commented upon, and their relationship with the interpretation of quantum theory is discussed. Also given are an outlook on the further development into concrete quantum theory and some philosophical reflections

Quantum Computer Games: Quantum Minesweeper

Science.gov (United States)

Gordon, Michal; Gordon, Goren

2010-01-01

The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…

Quantum Chess: Making Quantum Phenomena Accessible

Science.gov (United States)

Cantwell, Christopher

Quantum phenomena have remained largely inaccessible to the general public. There tends to be a scare factor associated with the word ``Quantum''. This is in large part due to the alien nature of phenomena such as superposition and entanglement. However, Quantum Computing is a very active area of research and one day we will have games that run on those quantum computers. Quantum phenomena such as superposition and entanglement will seem as normal as gravity. Is it possible to create such games today? Can we make games that are built on top of a realistic quantum simulation and introduce players of any background to quantum concepts in a fun and mentally stimulating way? One of the difficulties with any quantum simulation run on a classical computer is that the Hilbert space grows exponentially, making simulations of an appreciable size physically impossible due largely to memory restrictions. Here we will discuss the conception and development of Quantum Chess, and how to overcome some of the difficulties faced. We can then ask the question, ``What's next?'' What are some of the difficulties Quantum Chess still faces, and what is the future of quantum games?

GLq(N)-covariant quantum algebras and covariant differential calculus

International Nuclear Information System (INIS)

Isaev, A.P.; Pyatov, P.N.

1993-01-01

We consider GL q (N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. The connection with the bicovariant differential calculus on the linear quantum groups is discussed. (orig.)

The renormalization-group flux of the conformally reduced quantum gravity; Der Renormierungsgruppen-Fluss der konform-reduzierten Quantengravitation

Energy Technology Data Exchange (ETDEWEB)

Weyer, Holger

2010-12-17

We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent nonperturbative renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG ow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a non-Gaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of Quantum Einstein Gravity (QEG) in the ''conformally reduced'' theory which discards all degrees of freedom contained in the metric except the conformal one. The conformally reduced Einstein-Hilbert approximation has exactly the same qualitative properties as in the full Einstein-Hilbert truncation. In particular it possesses the non-Gaussian fixed point which is necessary for asymptotic safety. Without the extra field dependence the resulting RG flow is that of a simple {phi}{sup 4}-theory. We employ the Local Potential Approximation for the conformal factor to generalize the RG flow on an infinite dimensional theory space. Again we find a Gaussian as well as a non-Gaussian fixed point which provides further evidence for the viability of the asymptotic safety scenario. The analog of the invariant cubic in the curvature which spoils perturbative renormalizability is seen to be unproblematic for the asymptotic safety of the conformally reduced theory. The scaling fields and dimensions of both fixed points are obtained explicitly and possible implications for the predictivity of the theory are discussed. Since the RG flow depends on the topology of the

Quantum signature scheme for known quantum messages

International Nuclear Information System (INIS)

Kim, Taewan; Lee, Hyang-Sook

2015-01-01

When we want to sign a quantum message that we create, we can use arbitrated quantum signature schemes which are possible to sign for not only known quantum messages but also unknown quantum messages. However, since the arbitrated quantum signature schemes need the help of a trusted arbitrator in each verification of the signature, it is known that the schemes are not convenient in practical use. If we consider only known quantum messages such as the above situation, there can exist a quantum signature scheme with more efficient structure. In this paper, we present a new quantum signature scheme for known quantum messages without the help of an arbitrator. Differing from arbitrated quantum signature schemes based on the quantum one-time pad with the symmetric key, since our scheme is based on quantum public-key cryptosystems, the validity of the signature can be verified by a receiver without the help of an arbitrator. Moreover, we show that our scheme provides the functions of quantum message integrity, user authentication and non-repudiation of the origin as in digital signature schemes. (paper)

Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

Science.gov (United States)

Merker, L.; Costi, T. A.

2012-08-01

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat Cimp to be calculated accurately from local static correlation functions; specifically via Cimp=(∂Eionic)/(∂T)+(1)/(2)(∂Ehyb)/(∂T), where Eionic and Ehyb are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to Cimp. For the nondegenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high-temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two-state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The approach could also be of interest within other impurity solvers, for example, within quantum Monte Carlo techniques.

Quantum master equation for QED in exact renormalization group

International Nuclear Information System (INIS)

Igarashi, Yuji; Itoh, Katsumi; Sonoda, Hidenori

2007-01-01

Recently, one of us (H. S.) gave an explicit form of the Ward-Takahashi identity for the Wilson action of QED. We first rederive the identity using a functional method. The identity makes it possible to realize the gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the nilpotency of the BRS transformation is lost. Using the Batalin-Vilkovisky formalism, we extend the Wilson action by including the antifield contributions. Then, the Ward-Takahashi identity for the Wilson action is lifted to a quantum master equation, and the modified BRS transformation regains nilpotency. We also obtain a flow equation for the extended Wilson action. (author)

Expected number of quantum channels in quantum networks

Science.gov (United States)

Chen, Xi; Wang, He-Ming; Ji, Dan-Tong; Mu, Liang-Zhu; Fan, Heng

2015-07-01

Quantum communication between nodes in quantum networks plays an important role in quantum information processing. Here, we proposed the use of the expected number of quantum channels as a measure of the efficiency of quantum communication for quantum networks. This measure quantified the amount of quantum information that can be teleported between nodes in a quantum network, which differs from classical case in that the quantum channels will be consumed if teleportation is performed. We further demonstrated that the expected number of quantum channels represents local correlations depicted by effective circles. Significantly, capacity of quantum communication of quantum networks quantified by ENQC is independent of distance for the communicating nodes, if the effective circles of communication nodes are not overlapped. The expected number of quantum channels can be enhanced through transformations of the lattice configurations of quantum networks via entanglement swapping. Our results can shed lights on the study of quantum communication in quantum networks.

Blind Quantum Signature with Blind Quantum Computation

Science.gov (United States)

Li, Wei; Shi, Ronghua; Guo, Ying

2017-04-01

Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.

Quantum memory for images: A quantum hologram

International Nuclear Information System (INIS)

Vasilyev, Denis V.; Sokolov, Ivan V.; Polzik, Eugene S.

2008-01-01

Matter-light quantum interface and quantum memory for light are important ingredients of quantum information protocols, such as quantum networks, distributed quantum computation, etc. [P. Zoller et al., Eur. Phys. J. D 36, 203 (2005)]. In this paper we present a spatially multimode scheme for quantum memory for light, which we call a quantum hologram. Our approach uses a multiatom ensemble which has been shown to be efficient for a single spatial mode quantum memory. Due to the multiatom nature of the ensemble and to the optical parallelism it is capable of storing many spatial modes, a feature critical for the present proposal. A quantum hologram with the fidelity exceeding that of classical hologram will be able to store quantum features of an image, such as multimode superposition and entangled quantum states, something that a standard hologram is unable to achieve

Fermion-induced quantum critical points

OpenAIRE

Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong

2017-01-01

A unified theory of quantum critical points beyond the conventional Landau?Ginzburg?Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau?Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such t...

Mathematical aspects of quantum field theory

CERN Document Server

de Faria, Edson

2010-01-01

Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

Quantum correlations and distinguishability of quantum states

Energy Technology Data Exchange (ETDEWEB)

Spehner, Dominique [Université Grenoble Alpes and CNRS, Institut Fourier, F-38000 Grenoble, France and Laboratoire de Physique et Modélisation des Milieux Condensés, F-38000 Grenoble (France)

2014-07-15

A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature.

Quantum correlations and distinguishability of quantum states

International Nuclear Information System (INIS)

Spehner, Dominique

2014-01-01

A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature

Invariant measures on multimode quantum Gaussian states

Science.gov (United States)

Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.

2012-12-01

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Invariant measures on multimode quantum Gaussian states

International Nuclear Information System (INIS)

Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.

2012-01-01

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Invariant measures on multimode quantum Gaussian states

Energy Technology Data Exchange (ETDEWEB)

Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)

2012-12-15

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Matrix product state calculations for one-dimensional quantum chains and quantum impurity models

Energy Technology Data Exchange (ETDEWEB)

Muender, Wolfgang

2011-09-28

This thesis contributes to the field of strongly correlated electron systems with studies in two distinct fields thereof: the specific nature of correlations between electrons in one dimension and quantum quenches in quantum impurity problems. In general, strongly correlated systems are characterized in that their physical behaviour needs to be described in terms of a many-body description, i.e. interactions correlate all particles in a complex way. The challenge is that the Hilbert space in a many-body theory is exponentially large in the number of particles. Thus, when no analytic solution is available - which is typically the case - it is necessary to find a way to somehow circumvent the problem of such huge Hilbert spaces. Therefore, the connection between the two studies comes from our numerical treatment: they are tackled by the density matrix renormalization group (DMRG) and the numerical renormalization group (NRG), respectively, both based on matrix product states. The first project presented in this thesis addresses the problem of numerically finding the dominant correlations in quantum lattice models in an unbiased way, i.e. without using prior knowledge of the model at hand. A useful concept for this task is the correlation density matrix (CDM) which contains all correlations between two clusters of lattice sites. We show how to extract from the CDM, a survey of the relative strengths of the system's correlations in different symmetry sectors as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. We demonstrate this by a DMRG study of a one-dimensional spinless extended Hubbard model, while emphasizing that the proposed analysis of the CDM is not restricted to one dimension. The second project presented in this thesis is motivated by two phenomena under ongoing experimental and theoretical investigation in the context of quantum impurity models: optical absorption

Matrix product state calculations for one-dimensional quantum chains and quantum impurity models

International Nuclear Information System (INIS)

Muender, Wolfgang

2011-01-01

This thesis contributes to the field of strongly correlated electron systems with studies in two distinct fields thereof: the specific nature of correlations between electrons in one dimension and quantum quenches in quantum impurity problems. In general, strongly correlated systems are characterized in that their physical behaviour needs to be described in terms of a many-body description, i.e. interactions correlate all particles in a complex way. The challenge is that the Hilbert space in a many-body theory is exponentially large in the number of particles. Thus, when no analytic solution is available - which is typically the case - it is necessary to find a way to somehow circumvent the problem of such huge Hilbert spaces. Therefore, the connection between the two studies comes from our numerical treatment: they are tackled by the density matrix renormalization group (DMRG) and the numerical renormalization group (NRG), respectively, both based on matrix product states. The first project presented in this thesis addresses the problem of numerically finding the dominant correlations in quantum lattice models in an unbiased way, i.e. without using prior knowledge of the model at hand. A useful concept for this task is the correlation density matrix (CDM) which contains all correlations between two clusters of lattice sites. We show how to extract from the CDM, a survey of the relative strengths of the system's correlations in different symmetry sectors as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. We demonstrate this by a DMRG study of a one-dimensional spinless extended Hubbard model, while emphasizing that the proposed analysis of the CDM is not restricted to one dimension. The second project presented in this thesis is motivated by two phenomena under ongoing experimental and theoretical investigation in the context of quantum impurity models: optical absorption

Mathematical concepts of quantum mechanics. 2. ed.

International Nuclear Information System (INIS)

Gustafson, Stephen J.; Sigal, Israel Michael

2011-01-01

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory. (orig.)

Introduction to quantized LIE groups and algebras

International Nuclear Information System (INIS)

Tjin, T.

1992-01-01

In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl 2 is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxter equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl 2 algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory

Self-tallying quantum anonymous voting

Science.gov (United States)

Wang, Qingle; Yu, Chaohua; Gao, Fei; Qi, Haoyu; Wen, Qiaoyan

2016-08-01

Anonymous voting is a voting method of hiding the link between a vote and a voter, the context of which ranges from governmental elections to decision making in small groups like councils and companies. In this paper, we propose a quantum anonymous voting protocol assisted by two kinds of entangled quantum states. Particularly, we provide a mechanism of opening and permuting the ordered votes of all the voters in an anonymous manner; any party who is interested in the voting results can acquire a permutation copy and then obtains the voting result through a simple calculation. Unlike all previous quantum works on anonymous voting, our quantum anonymous protocol possesses the properties of privacy, self-tallying, nonreusability, verifiability, and fairness at the same time. In addition, we demonstrate that the entanglement of the quantum states used in our protocol makes an attack from an outside eavesdropper and inside dishonest voters impossible. We also generalize our protocol to execute the task of anonymous multiparty computation, such as anonymous broadcast and anonymous ranking.

Symmetries and groups in particle physics

International Nuclear Information System (INIS)

Scherer, Stefan

2016-01-01

The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to

Quantum dynamics in open quantum-classical systems.

Science.gov (United States)

Kapral, Raymond

2015-02-25

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

Quantum machine learning for quantum anomaly detection

Science.gov (United States)

Liu, Nana; Rebentrost, Patrick

2018-04-01

Anomaly detection is used for identifying data that deviate from "normal" data patterns. Its usage on classical data finds diverse applications in many important areas such as finance, fraud detection, medical diagnoses, data cleaning, and surveillance. With the advent of quantum technologies, anomaly detection of quantum data, in the form of quantum states, may become an important component of quantum applications. Machine-learning algorithms are playing pivotal roles in anomaly detection using classical data. Two widely used algorithms are the kernel principal component analysis and the one-class support vector machine. We find corresponding quantum algorithms to detect anomalies in quantum states. We show that these two quantum algorithms can be performed using resources that are logarithmic in the dimensionality of quantum states. For pure quantum states, these resources can also be logarithmic in the number of quantum states used for training the machine-learning algorithm. This makes these algorithms potentially applicable to big quantum data applications.

2-point functions in quantum cosmology

International Nuclear Information System (INIS)

Gielen, Steffen

2012-01-01

We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories, with particular reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, deriving vertex expansions and composition laws they satisfy. We clarify the tie between definitions using a group averaging procedure and those in a deparametrised framework. We draw some conclusions about the physics of a single quantum universe and multiverse field theories where the role of these sectors and the inner product are reinterpreted.

Quantum information processing with graph states

International Nuclear Information System (INIS)

Schlingemann, Dirk-Michael

2005-04-01

Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)

Matroids and quantum-secret-sharing schemes

International Nuclear Information System (INIS)

Sarvepalli, Pradeep; Raussendorf, Robert

2010-01-01

A secret-sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret-sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret-sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum-secret-sharing schemes. In addition to providing a new perspective on quantum-secret-sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum-secret-sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum-secret-sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure-state quantum-secret-sharing scheme with information rate 1.

Quantum quincunx in cavity quantum electrodynamics

International Nuclear Information System (INIS)

Sanders, Barry C.; Bartlett, Stephen D.; Tregenna, Ben; Knight, Peter L.

2003-01-01

We introduce the quantum quincunx, which physically demonstrates the quantum walk and is analogous to Galton's quincunx for demonstrating the random walk by employing gravity to draw pellets through pegs on a board, thereby yielding a binomial distribution of final peg locations. In contradistinction to the theoretical studies of quantum walks over orthogonal lattice states, we introduce quantum walks over nonorthogonal lattice states (specifically, coherent states on a circle) to demonstrate that the key features of a quantum walk are observable albeit for strict parameter ranges. A quantum quincunx may be realized with current cavity quantum electrodynamics capabilities, and precise control over decoherence in such experiments allows a remarkable decrease in the position noise, or spread, with increasing decoherence

Quantum conductance in silicon quantum wires

CERN Document Server

Bagraev, N T; Klyachkin, L E; Malyarenko, A M; Gehlhoff, W; Ivanov, V K; Shelykh, I A

2002-01-01

The results of investigations of electron and hole quantum conductance staircase in silicon quantum wires are presented. The characteristics of self-ordering quantum wells of n- and p-types, which from on the silicon (100) surface in the nonequilibrium boron diffusion process, are analyzed. The results of investigations of the quantum conductance as the function of temperature, carrier concentration and modulation degree of silicon quantum wires are given. It is found out, that the quantum conductance of the one-dimensional channels is observed, for the first time, at an elevated temperature (T >= 77 K)

Quantum key distribution via quantum encryption

CERN Document Server

Yong Sheng Zhang; Guang Can Guo

2001-01-01

A quantum key distribution protocol based on quantum encryption is presented in this Brief Report. In this protocol, the previously shared Einstein-Podolsky-Rosen pairs act as the quantum key to encode and decode the classical cryptography key. The quantum key is reusable and the eavesdropper cannot elicit any information from the particle Alice sends to Bob. The concept of quantum encryption is also discussed. (21 refs).

Quantum mechanics on Riemannian manifold in Schwinger's quantization approach II

International Nuclear Information System (INIS)

Chepilko, N.M.; Romanenko, A.V.

2001-01-01

The extended Schwinger quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold M is a homogeneous Riemannian space with the given action of an isometry transformation group. Using the identification of M with the quotient space G/H, where H is the isotropy group of an arbitrary fixed point of M, we show that quantum mechanics on G/H possesses a gauge structure, described by a gauge potential that is the connection 1-form of the principal fiber bundle G(G/H, H). The coordinate representation of quantum mechanics and the procedure for selecting the physical sector of the states are developed. (orig.)

Reality and dimension of space and the complexity of quantum mechanics

International Nuclear Information System (INIS)

Mirman, R.

1988-01-01

The dimension (and signature) of space is a result of distances being real numbers and quantum mechanical state functions being complex ones; it is an inescapable consequence of quantum mechanics and group theory. So nonrelativistic quantum mechanics cannot be complete (it requires ad hoc additional assumptions) and consistent (nor can classical physics), leading to relativity, quantum mechanics, and field theory. Implications of the constraints of consistency and physical reasonableness and of group theory for the structure of these theories are considered. It appears that there are simple, perhaps unavoidable reasons for the laws of physics, the nature of the world they describe, and the space in which they act