Nonlinear Temporal Dynamics of Strongly Coupled Quantum Dot-Cavity System
Majumdar, Arka; Bajcsy, Michal; Vuckovic, Jelena
2011-01-01
We theoretically analyze and simulate the temporal dynamics of strongly coupled quantum dot-cavity system driven by a resonant laser pulse. We observe the signature of Rabi oscillation in the time resolved response of the system (i.e., in the numerically calculated cavity output), derive simplified linear and non-linear semi-classical models that approximate well the system's behavior in the limits of high and low power drive pulse, and describe the role of quantum coherence in the exact dynamics of the system. Finally, we also present experimental data showing the signature of the Rabi oscillation in time domain.
Nielsen, Per Kær; Nielsen, Torben Roland; Lodahl, Peter;
2010-01-01
treatments. A pronounced consequence is the emergence of a phonon induced spectral asymmetry when detuning the cavity from the quantum-dot resonance. The asymmetry can only be explained when considering the polaritonic quasiparticle nature of the quantum-dot-cavity system. Furthermore, a temperature induced......We investigate the influence of electron-phonon interactions on the dynamical properties of a quantum-dot-cavity QED system. We show that non-Markovian effects in the phonon reservoir lead to strong changes in the dynamics, arising from photon-assisted dephasing processes, not present in Markovian...
Quantum Interference Induced Photon Blockade in a Coupled Single Quantum Dot-Cavity System
Tang, Jing; Xu, Xiulai
2015-01-01
We propose an experimental scheme to implement a strong photon blockade with a single quantum dot coupled to a nanocavity. The photon blockade effect can be tremendously enhanced by driving the cavity and the quantum dot simultaneously with two classical laser fields. This enhancement of photon blockade is ascribed to the quantum interference effect to avoid two-photon excitation of the cavity field. Comparing with Jaynes-Cummings model, the second-order correlation function at zero time delay $g^{(2)}(0)$ in our scheme can be reduced by two orders of magnitude and the system sustains a large intracavity photon number. A red (blue) cavity-light detuning asymmetry for photon quantum statistics with bunching or antibunching characteristics is also observed. The photon blockade effect has a controllable flexibility by tuning the relative phase between the two pumping laser fields and the Rabi coupling strength between the quantum dot and the pumping field. Moreover, the photon blockade scheme based on quantum in...
Sub-Poissonian photon emission in coupled double quantum dots-cavity system
Ye, Han; Peng, Yi-Wei; Yu, Zhong-Yuan; Zhang, Wen; Liu, Yu-Min
2015-11-01
In this work, we theoretically analyze the few-photon emissions generated in a coupled double quantum dots (CDQDs)-single mode microcavity system, under continuous wave and pulse excitation. Compared with the uncoupled case, strong sub-Poissonian character is achieved in a CDQDs-cavity system at a certain laser frequency. Based on the proposed scheme, single photon generation can be obtained separately under QD-cavity resonant condition and off-resonant condition. For different cavity decay rates, we reveal that laser frequency detunings of minimum second-order autocorrelation function are discrete and can be divided into three regions. Moreover, the non-ideal situation where two QDs are not identical is discussed, indicating the robustness of the proposed scheme, which possesses sub-Poissonian character in a large QD difference variation range. Project supported by the National Natural Science Foundation of China (Grant Nos. 61372037 and 61401035), the Beijing Excellent Ph.D. Thesis Guidance Foundation, China (Grant No. 20131001301), and the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (Grant No. IPOC2015ZC05).
Bright single photon source based on self-aligned quantum dot-cavity systems
Maier, Sebastian; Gold, Peter; Forchel, Alfred; Gregersen, Niels; Mørk, Jesper; Höfling, Sven; Schneider, Christian; Kamp, Martin
2014-01-01
We report on a quasi-planar quantum-dot-based single-photon source that shows an unprecedented high extraction efficiency of 42% without complex photonic resonator geometries or post-growth nanofabrication. This very high efficiency originates from the coupling of the photons emitted by a quantum dot to a Gaussian shaped nanohill defect that naturally arises during epitaxial growth in a self-aligned manner. We investigate the morphology of these defects and characterize the photonic operation...
Bright single photon source based on self-aligned quantum dot-cavity systems.
Maier, Sebastian; Gold, Peter; Forchel, Alfred; Gregersen, Niels; Mørk, Jesper; Höfling, Sven; Schneider, Christian; Kamp, Martin
2014-04-01
We report on a quasi-planar quantum-dot-based single-photon source that shows an unprecedented high extraction efficiency of 42% without complex photonic resonator geometries or post-growth nanofabrication. This very high efficiency originates from the coupling of the photons emitted by a quantum dot to a Gaussian shaped nanohill defect that naturally arises during epitaxial growth in a self-aligned manner. We investigate the morphology of these defects and characterize the photonic operation mechanism. Our results show that these naturally arising coupled quantum dot-defects provide a new avenue for efficient (up to 42% demonstrated) and pure (g(2)(0) value of 0.023) single-photon emission. PMID:24718190
Rabi oscillations in a quantum dot-cavity system coupled to a nonzero temperature phonon bath
Larson, Jonas [ICFO-Institut de Ciencies Fotoniques, E-08860 Castelldefels, Barcelona (Spain); Moya-Cessa, Hector [INAOE, Coordinacion de Optica, Apdo. Postal 51 y 216, 72000 Puebla, Pue (Mexico)], E-mail: jolarson@kth.se
2008-06-15
We study a quantum dot strongly coupled to a single high-finesse optical microcavity mode. We use a rotating wave approximation (RWA) method, commonly used in ion-laser interactions, together with the Lamb-Dicke approximation to obtain an analytic solution of this problem. The decay of Rabi oscillations because of the electron-phonon coupling is studied at arbitrary temperature and analytical expressions for the collapse and revival times are presented. Analyses without the RWA are presented as means of investigating the energy spectrum.
Transport Spectroscopy of a Spin-Coherent Dot-Cavity System.
Rössler, C; Oehri, D; Zilberberg, O; Blatter, G; Karalic, M; Pijnenburg, J; Hofmann, A; Ihn, T; Ensslin, K; Reichl, C; Wegscheider, W
2015-10-16
Quantum engineering requires controllable artificial systems with quantum coherence exceeding the device size and operation time. This can be achieved with geometrically confined low-dimensional electronic structures embedded within ultraclean materials, with prominent examples being artificial atoms (quantum dots) and quantum corrals (electronic cavities). Combining the two structures, we implement a mesoscopic coupled dot-cavity system in a high-mobility two-dimensional electron gas, and obtain an extended spin-singlet state in the regime of strong dot-cavity coupling. Engineering such extended quantum states presents a viable route for nonlocal spin coupling that is applicable for quantum information processing. PMID:26550890
Quantum Dot Cavity-QED in the Presence of Strong Electron-Phonon Interactions
Wilson-Rae, I
2001-01-01
A quantum dot strongly coupled to a single high finesse optical microcavity mode constitutes a new fundamental system for quantum optics. Here, the effect of exciton-phonon interactions on reversible quantum-dot cavity coupling is analysed without making Born-Markov approximation. The analysis is based on techniques that have been used to study the ``spin boson'' Hamiltonian. Observability of vacuum-Rabi splitting depends on the strength and the frequency dependence of the spectral density function characterizing the interactions with phonons, both of which can be influenced by phonon confinement.
Coupling and single-photon purity of a quantum dot-cavity system studied using hydrostatic pressure
Zhou, P. Y.; Wu, X. F.; Ding, K.; Dou, X. M.; Zha, G. W.; Ni, H. Q.; Niu, Z. C.; Zhu, H. J.; Jiang, D. S. [State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); Zhao, C. L. [College of Physics and Electronic Information, Inner Mongolia University for Nationalities, Tongliao 028043 (China); Sun, B. Q., E-mail: bqsun@semi.ac.cn [State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); College of Physics and Electronic Information, Inner Mongolia University for Nationalities, Tongliao 028043 (China)
2015-01-07
We propose an approach to tune the emission of a single semiconductor quantum dot (QD) to couple with a planar cavity using hydrostatic pressure without inducing temperature variation during the process of measurement. Based on this approach, we studied the influence of cavity mode on the single-photon purity of an InAs/GaAs QD. Our measurement demonstrates that the single-photon purity degrades when the QD emission resonates with the cavity mode. This negative influence of the planar cavity is mainly caused by the cavity feeding effect.
Nielsen, Per Kær; Lodahl, Peter; Jauho, Antti-Pekka;
2013-01-01
We study the fundamental limit on single-photon indistinguishability imposed by decoherence due to phonon interactions in semiconductor quantum dot-cavity quantum electrodynamics systems. Employing an exact diagonalization approach we find large differences compared to standard methods. An...
All-optical tailoring of single-photon spectra in a quantum-dot microcavity system
Breddermann, Dominik; Heinze, Dirk; Binder, Rolf; Zrenner, Artur; Schumacher, Stefan
2016-01-01
Semiconductor quantum-dot cavity systems are promising sources for solid-state based on-demand generation of single photons for quantum communication. Commonly, the spectral characteristics of the emitted single photon are fixed by system properties such as electronic transition energies and spectral properties of the cavity. In the present work we study single-photon generation from the quantum-dot biexciton through a partly stimulated non-degenerate two-photon emission. We show that frequen...
All-optical tailoring of single-photon spectra in a quantum-dot microcavity system
Breddermann, Dominik; Binder, Rolf; Zrenner, Artur; Schumacher, Stefan
2016-01-01
Semiconductor quantum-dot cavity systems are promising sources for solid-state based on-demand generation of single photons for quantum communication. Commonly, the spectral characteristics of the emitted single photon are fixed by system properties such as electronic transition energies and spectral properties of the cavity. In the present work we study single-photon generation from the quantum-dot biexciton through a partly stimulated non-degenerate two-photon emission. We show that frequency and linewidth of the single photon can be fully controlled by the stimulating laser pulse, ultimately allowing for efficient all-optical spectral shaping of the single photon.
Fundamental properties of devices for quantum information technology
Nielsen, Per Kær
system, the effect of the phonon interaction is very pronounced. A simple approximate analytical expression for the quantum dot decay rate is derived, which predicts a strong asymmetry with respect to the quantum dot-cavity detuning at low temperatures, and allows for a clear interpretation of the...
Hughes, S
2011-01-01
The input/output characteristics of coherent photon transport through a semiconductor cavity system containing a single quantum dot is presented. The nonlinear quantum optics formalism uses a master equation approach and focuses on a waveguide-cavity system containing a semiconductor quantum dot; our general technique also applies to studying coherent reflection from a micropillar cavity. We investigate the effects of light propagation and show the need for quantized multiphoton effects for various dot-cavity systems, including weakly-coupled, intermediately-coupled, and strongly-coupled regimes. We demonstrate that for mean photon numbers much less than 0.1, the commonly adopted weak excitation (single quantum) approximation breaks down---even in the weak coupling regime. As a measure of the photon correlations, we compute the Fano factor and the error associated with making a semiclassical approximation. We also investigate the role of electron--acoustic-phonon scattering and show that phonon-mediated scatt...
Complete Coherent Control of a Quantum Dot Strongly Coupled to a Nanocavity
Dory, Constantin; Fischer, Kevin A.; Müller, Kai; Lagoudakis, Konstantinos G.; Sarmiento, Tomas; Rundquist, Armand; Zhang, Jingyuan L.; Kelaita, Yousif; Vučković, Jelena
2016-04-01
Strongly coupled quantum dot-cavity systems provide a non-linear configuration of hybridized light-matter states with promising quantum-optical applications. Here, we investigate the coherent interaction between strong laser pulses and quantum dot-cavity polaritons. Resonant excitation of polaritonic states and their interaction with phonons allow us to observe coherent Rabi oscillations and Ramsey fringes. Furthermore, we demonstrate complete coherent control of a quantum dot-photonic crystal cavity based quantum-bit. By controlling the excitation power and phase in a two-pulse excitation scheme we achieve access to the full Bloch sphere. Quantum-optical simulations are in good agreement with our experiments and provide insight into the decoherence mechanisms.
Complete Coherent Control of a Quantum Dot Strongly Coupled to a Nanocavity
Dory, Constantin; Fischer, Kevin A.; Müller, Kai; Lagoudakis, Konstantinos G.; Sarmiento, Tomas; Rundquist, Armand; Zhang, Jingyuan L.; Kelaita, Yousif; Vučković, Jelena
2016-01-01
Strongly coupled quantum dot-cavity systems provide a non-linear configuration of hybridized light-matter states with promising quantum-optical applications. Here, we investigate the coherent interaction between strong laser pulses and quantum dot-cavity polaritons. Resonant excitation of polaritonic states and their interaction with phonons allow us to observe coherent Rabi oscillations and Ramsey fringes. Furthermore, we demonstrate complete coherent control of a quantum dot-photonic crystal cavity based quantum-bit. By controlling the excitation power and phase in a two-pulse excitation scheme we achieve access to the full Bloch sphere. Quantum-optical simulations are in good agreement with our experiments and provide insight into the decoherence mechanisms. PMID:27112420
Ren, Bao-Cang; Wei, Hai-Rui; Hua, Ming; Li, Tao; Deng, Fu-Guo
2012-10-22
Bell-state analysis (BSA) is essential in quantum communication, but it is impossible to distinguish unambiguously the four Bell states in the polarization degree of freedom (DOF) of two-photon systems with only linear optical elements, except for the case in which the BSA is assisted with hyperentangled states, the simultaneous entanglement in more than one DOF. Here, we propose a scheme to distinguish completely the 16 hyperentangled Bell states in both the polarization and the spatial-mode DOFs of two-photon systems, by using the giant nonlinear optics in quantum dot-cavity systems. This scheme can be applied to increase the channel capacity of long-distance quantum communication based on hyperentanglement, such as entanglement swapping, teleportation, and superdense coding. We use hyperentanglement swapping as an example to show the application of this HBSA. PMID:23187229
Nielsen, Per Kær; Lodahl, Peter; Jauho, Antti-Pekka; Mørk, Jesper
2013-01-01
We study the fundamental limit on single-photon indistinguishability imposed by decoherence due to phonon interactions in semiconductor quantum dot-cavity quantum electrodynamics systems. Employing an exact diagonalization approach we find large differences compared to standard methods. An important finding is that short-time non-Markovian effects limit the maximal attainable indistinguishability. The results are explained using a polariton picture that yields valuable insight into the phonon...
Controlled Quantum Open Systems
Alicki, R
2003-01-01
The theory of controlled quantum open systems describes quantum systems interacting with quantum environments and influenced by external forces varying according to given algorithms. It is aimed, for instance, to model quantum devices which can find applications in the future technology based on quantum information processing. One of the main problems making difficult the practical implementations of quantum information theory is the fragility of quantum states under external perturbations. The aim of this note is to present the relevant results concerning ergodic properties of open quantum systems which are useful for the optimization of quantum devices and noise (errors) reduction. In particular we present mathematical characterization of the so-called "decoherence-free subspaces" for discrete and continuous-time quantum dynamical semigroups in terms of $C^*$-algebras and group representations. We analyze the non-Markovian models also, presenting the formulas for errors in the Born approximation. The obtain...
Characterization of strong light-matter coupling in semiconductor quantum-dot microcavities
Schneebeli, L.; Kira, M.; Koch, S.W. [Department of Physics and Material Sciences Center, Philipps-University, Marburg (Germany)
2009-02-15
Maxwell-Bloch and luminescence equations are presented which describe vacuum Rabi splitting and the quantum rungs on the Jaynes-Cummings ladder for strongly-coupled dot-cavity systems. Resonance fluorescence conditions are considered where an optical pump is exciting the dot-cavity system while the re-emitted light is detected. An analytical formula for the vacuum Rabi splitting is derived and a pumping mechanism for the direct generation of the second rung is presented and analyzed. An optimum pumping frequency and optimum pumping intensity are identified for the generation of the second rung. (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Pillet, Claude-Alain
2006-01-01
This notes are an expanded version of the lectures given by the author at the Grenoble "Open Quantum Systems" summer school in 2003. They provide a short introduction to quantum dynamical systems and their ergodic properties with particular emphasis on the quantum Koopman–von Neumann spectral theory.
Sorting quantum systems efficiently
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) – which direct photons according to their polarization – and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
Sorting quantum systems efficiently.
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) - which direct photons according to their polarization - and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
Quantum Games and Programmable Quantum Systems
Piotrowski, E W; Piotrowski, Edward W.; Sladkowski, Jan
2005-01-01
Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum description of the system provides advantages over the classical approach. Game theory, the study of decision making in conflict situation has already been extended to the quantum domain. We would like to review the latest development in quantum game theory that is relevant to information processing. We will begin by illustrating the general idea of a quantum game and methods of gaining an advantage over "classical opponent". Then we review the most important game theoretical aspects of quantum information processing. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is explained.
Solenov, Dmitry; Economou, Sophia E.; Reinecke, T. L.
2013-01-01
Implementations for quantum computing require fast single- and multiqubit quantum gate operations. In the case of optically controlled quantum dot qubits, theoretical designs for long-range two- or multiqubit operations satisfying all the requirements in quantum computing are not yet available. We have developed a design for a fast, long-range two-qubit gate mediated by a photonic microcavity mode using excited states of the quantum-dot-cavity system that addresses these needs. This design does not require identical qubits, it is compatible with available optically induced single-qubit operations, and it advances opportunities for scalable architectures. We show that the gate fidelity can exceed 90% in experimentally accessible systems.
Weiss, Ulrich
2008-01-01
Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book - originally published in 1990 and republished in 1999 as an enlarged second edition - delves much deeper than ever before into the fundamental concepts, methods, and applications of quantum dissipative systems, including the most recent developments. In this third edi
Rivasseau, Vincent [Paris-Sud Univ. Orsay (France). Laboratoire de Physique Theorique; Seiringer, Robert [McGill Univ., Montreal, QC (Canada). Dept. of Mathematics and Statistics; Solovej, Jan Philip [Copenhagen Univ. (Denmark). Dept. of Mathematics; Spencer, Thomas [Institute for Advanced Study, Princeton, NJ (United States). School of Mathematics
2012-11-01
The book is based on the lectures given at the CIME school ''Quantum many body systems'' held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.
Danilov, Viatcheslav; /Oak Ridge; Nagaitsev, Sergei; /Fermilab
2011-11-01
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and nonlinear integrable plasma traps. Now, all classical results are carried over to a nonrelativistic quantum case. In this paper we have described an extension of the Ermakov-like transformation to the Schroedinger and Pauli equations. It is shown that these newly found transformations create a vast variety of time dependent quantum equations that can be solved in analytic functions, or, at least, can be reduced to time-independent ones.
We generalize the classical notion of a K-system to a non-commutative dynamical system by requiring that an invariantly defined memory loss be 100%. We give some examples of quantum K-systems and show that they cannot contain any quasi-periodic subsystem. 13 refs. (Author)
Magmatic "Quantum-Like" Systems
Rosinger, Elemer E
2008-01-01
Quantum computation has suggested, among others, the consideration of "non-quantum" systems which in certain respects may behave "quantum-like". Here, what algebraically appears to be the most general possible known setup, namely, of {\\it magmas} is used in order to construct "quantum-like" systems. The resulting magmatic composition of systems has as a well known particular case the tensor products.
Micheli, Fiorenza de [Centro de Estudios Cientificos, Arturo Prat 514, Valdivia (Chile); Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Zanelli, Jorge [Centro de Estudios Cientificos, Arturo Prat 514, Valdivia (Chile); Universidad Andres Bello, Av. Republica 440, Santiago (Chile)
2012-10-15
A degenerate dynamical system is characterized by a symplectic structure whose rank is not constant throughout phase space. Its phase space is divided into causally disconnected, nonoverlapping regions in each of which the rank of the symplectic matrix is constant, and there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems-in which the degeneracy cannot be eliminated by redefining variables in the action-the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated.
Scheme of thinking quantum systems
V. I. YUKALOV; Sornette, D.
2009-01-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of p...
Scheme of thinking quantum systems
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field
Scheme of thinking quantum systems
Yukalov, V I
2009-01-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
Scheme of thinking quantum systems
Yukalov, V. I.; Sornette, D.
2009-11-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
Quantum Cybernetics and Complex Quantum Systems Science - A Quantum Connectionist Exploration
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...
Quantum systems as classical systems
Cassa, A
2001-01-01
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several values with only a predictable probability. However, even in the classical case, when an observer is intrinsically unable to distinguish between some distinct states he can convince himself that the measure of its ''observables'' can have several values in a random way with a statistical character. What kind of statistical theory is obtainable in this way? It is possible, for example, to obtain exactly the statistical previsions of quantum mechanics? Or, in other words, can a physical system showing a classical behaviour appear to be a quantum system to a confusing observer? We show that from a mathematical viewpoint it is not difficult to produce a theory with hidden variables having this property. We don't even try to justify in physical terms the artificial construction ...
Asymptotically open quantum systems
In the present thesis we investigate the structure of time-dependent equations of motion in quantum mechanics.We start from two coupled systems with an autonomous equation of motion. A limit, in which the dynamics of one of the two systems has a decoupled evolution and imposes a non-autonomous evolution for the second system is identified. A result due to K. Hepp that provides a classical limit for dynamics turns out to be part and parcel for this limit and is generalized in our work. The method introduced by J.S. Howland for the solution of the time-dependent Schroedinger equation is interpreted as such a limit. Moreover, we associate our limit with the modern theory of quantization. (orig.)
Quantum Effects in Biological Systems
2016-01-01
Since the last decade the study of quantum mechanical phenomena in biological systems has become a vibrant field of research. Initially sparked by evidence of quantum effects in energy transport that is instrumental for photosynthesis, quantum biology asks the question of how methods and models from quantum theory can help us to understand fundamental mechanisms in living organisms. This approach entails a paradigm change challenging the related disciplines: The successful framework of quantum theory is taken out of its low-temperature, microscopic regimes and applied to hot and dense macroscopic environments, thereby extending the toolbox of biology and biochemistry at the same time. The Quantum Effects in Biological Systems conference is a platform for researchers from biology, chemistry and physics to present and discuss the latest developments in the field of quantum biology. After meetings in Lisbon (2009), Harvard (2010), Ulm (2011), Berkeley (2012), Vienna (2013), Singapore (2014) and Florence (2015),...
Quantum trajectories and open many-body quantum systems
Daley, Andrew J.
2014-01-01
The study of open quantum systems has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the syst...
Feedback control of quantum system
DONG Dao-yi; CHEN Zong-hai; ZHANG Chen-bin; CHEN Chun-lin
2006-01-01
Feedback is a significant strategy for the control of quantum system.Information acquisition is the greatest difficulty in quantum feedback applications.After discussing several basic methods for information acquisition,we review three kinds of quantum feedback control strategies:quantum feedback control with measurement,coherent quantum feedback,and quantum feedback control based on cloning and recognition.The first feedback strategy can effectively acquire information,but it destroys the coherence in feedback loop.On the contrary,coherent quantum feedback does not destroy the coherence,but the capability of information acquisition is limited.However,the third feedback scheme gives a compromise between information acquisition and measurement disturbance.
Quantum Effects in Biological Systems
Roy, Sisir
2014-07-01
The debates about the trivial and non-trivial effects in biological systems have drawn much attention during the last decade or so. What might these non-trivial sorts of quantum effects be? There is no consensus so far among the physicists and biologists regarding the meaning of "non-trivial quantum effects". However, there is no doubt about the implications of the challenging research into quantum effects relevant to biology such as coherent excitations of biomolecules and photosynthesis, quantum tunneling of protons, van der Waals forces, ultrafast dynamics through conical intersections, and phonon-assisted electron tunneling as the basis for our sense of smell, environment assisted transport of ions and entanglement in ion channels, role of quantum vacuum in consciousness. Several authors have discussed the non-trivial quantum effects and classified them into four broad categories: (a) Quantum life principle; (b) Quantum computing in the brain; (c) Quantum computing in genetics; and (d) Quantum consciousness. First, I will review the above developments. I will then discuss in detail the ion transport in the ion channel and the relevance of quantum theory in brain function. The ion transport in the ion channel plays a key role in information processing by the brain.
Open quantum systems recent developments
Joye, Alain; Pillet, Claude-Alain
2006-01-01
Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. From a mathematical point of view, it involves a large body of knowledge. Significant progress in the understanding of such systems has been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. In Volume I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems. Volume II is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential...
Noncommutative mathematics for quantum systems
Franz, Uwe
2016-01-01
Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physi...
Fault Tolerant Quantum Filtering and Fault Detection for Quantum Systems
Gao, Qing; Dong, Daoyi; Petersen, Ian R.
2015-01-01
This paper aims to determine the fault tolerant quantum filter and fault detection equation for a class of open quantum systems coupled to a laser field that is subject to stochastic faults. In order to analyze this class of open quantum systems, we propose a quantum-classical Bayesian inference method based on the definition of a so-called quantum-classical conditional expectation. It is shown that the proposed Bayesian inference approach provides a convenient tool to simultaneously derive t...
Information in individual quantum systems
A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems, the only feature known before an experiment is performed are the probabilities for various events to occur. The sum of the individual measures of information for mutually complementary observations is invariant under the choice of the particular set of complementary observations and conserved in time if there is no information exchange with an environment unitary transformation. This operational quantum information invariant results in k bits of information for a system consisting of $k$ qubits. For a composite system, maximal entanglement results if the total information carried by the system is exhausted in specifying joint properties, with no individual qubit carrying any information on its own. We interpret our results as implying that information is the most fundamental notion in quantum mechanics. Based on this observation we suggest ideas for a foundational principle for quantum theory. It is proposed here that the foundational principle for quantum theory may be identified through the assumption that the most elementary system carries one bit of information only. Therefore an elementary system can only give a definite answer in one specific measurement. The irreducible randomness of individual outcomes in other measurements and quantum complementarity are then necessary consequences. The most natural function between probabilities for outcomes to occur and the experimental parameters, consistent with the foundational principle proposed, is the well-known sinusoidal dependence. (author)
A prototype quantum cryptography system
In this work we have constructed a new secure quantum key distribution system based on the BB84 protocol. Many current state-of-the-art quantum cryptography systems encounter major problems concerning low bit rate, synchronization, and stabilization. Our quantum cryptography system utilizes only laser diodes and standard passive optical components, to enhance the stability and also to decrease the space requirements. The development of this demonstration for a practical quantum key distribution system is a consequence of our previous work on the quantum cryptographic system using optical fiber components for the transmitter and receiver. There we found that the optical fiber couplers should not be used due to the problems with space, stability and alignment. The goal of the synchronization is to use as little transmission capacities as possible. The experimental results of our quantum key distribution system show the feasibility of getting more than 90 % transmission capacities with the approaches developed in this work. Therefore it becomes feasible to securely establish a random key sequence at a rate of 1 to ∼ 5K bit/s by using our stable, compact, cheap, and user-friendly modules for quantum cryptography. (author)
Preconditioned quantum linear system algorithm.
Clader, B D; Jacobs, B C; Sprouse, C R
2013-06-21
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers. To demonstrate the algorithm's applicability, we show how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm. PMID:23829722
Mechanism for quantum speedup in open quantum systems
Liu, Hai-Bin; Yang, W. L.; An, Jun-Hong; Xu, Zhen-Yu
2016-02-01
The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interest in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.
Quantum walk public-key cryptographic system
Vlachou, C.; Rodrigues, J.; Mateus, P.; Paunković, N.; Souto, A.
2015-12-01
Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for quantum information processing. In this paper, we present a quantum public-key cryptographic system based on quantum walks. In particular, in the proposed protocol the public-key is given by a quantum state generated by performing a quantum walk. We show that the protocol is secure and analyze the complexity of public key generation and encryption/decryption procedures.
Design of coherent quantum observers for linear quantum systems
Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum H∞ optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent quantum observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent quantum observers avoid measurements of the plant outputs. We compare our coherent quantum observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs. (paper)
Quantum energy teleportation in a quantum Hall system
Yusa, Go; Izumida, Wataru; Hotta, Masahiro [Department of Physics, Tohoku University, Sendai 980-8578 (Japan)
2011-09-15
We propose an experimental method for a quantum protocol termed quantum energy teleportation (QET), which allows energy transportation to a remote location without physical carriers. Using a quantum Hall system as a realistic model, we discuss the physical significance of QET and estimate the order of energy gain using reasonable experimental parameters.
Hypothesis testing with open quantum systems
Molmer, Klaus
2014-01-01
Using a quantum circuit model we derive the maximal ability to distinguish which of several candidate Hamiltonians describe an open quantum system. This theory, in particular, provides the maximum information retrievable from continuous quantum measurement records, available when a quantum system is perturbatively coupled to a broadband quantized environment.
Quantum variance: A measure of quantum coherence and quantum correlations for many-body systems
Frérot, Irénée; Roscilde, Tommaso
2016-08-01
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed many-body quantum states remains a formidable challenge, with fundamental implications in areas as broad as quantum condensed matter, quantum information, quantum metrology, and quantum biology. Here, we provide a quantitative definition of the variance of quantum coherent fluctuations (the quantum variance) of any observable on generic quantum states. The quantum variance generalizes the concept of thermal de Broglie wavelength (for the position of a free quantum particle) to the space of eigenvalues of any observable, quantifying the degree of coherent delocalization in that space. The quantum variance is generically measurable and computable as the difference between the static fluctuations and the static susceptibility of the observable; despite its simplicity, it is found to provide a tight lower bound to most widely accepted estimators of "quantumness" of observables (both as a feature as well as a resource), such as the Wigner-Yanase skew information and the quantum Fisher information. When considering bipartite fluctuations in an extended quantum system, the quantum variance expresses genuine quantum correlations among the two parts. In the case of many-body systems, it is found to obey an area law at finite temperature, extending therefore area laws of entanglement and quantum fluctuations of pure states to the mixed-state context. Hence the quantum variance paves the way to the measurement of macroscopic quantum coherence and quantum correlations in most complex quantum systems.
Quantum systems as classical systems
Cassa, Antonio
2001-01-01
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several values with only a predictable probability. However, even in the classical case, when an observer is intrinsically unable to distinguish between some distinct states he can convince himself that the measure of its ''observables'' can have several values in ...
Quantum cloning attacks against PUF-based quantum authentication systems
Yao, Yao; Gao, Ming; Li, Mo; Zhang, Jian
2016-05-01
With the advent of physical unclonable functions (PUFs), PUF-based quantum authentication systems have been proposed for security purposes, and recently, proof-of-principle experiment has been demonstrated. As a further step toward completing the security analysis, we investigate quantum cloning attacks against PUF-based quantum authentication systems and prove that quantum cloning attacks outperform the so-called challenge-estimation attacks. We present the analytical expression of the false-accept probability by use of the corresponding optimal quantum cloning machines and extend the previous results in the literature. In light of these findings, an explicit comparison is made between PUF-based quantum authentication systems and quantum key distribution protocols in the context of cloning attacks. Moreover, from an experimental perspective, a trade-off between the average photon number and the detection efficiency is discussed in detail.
Quantum cloning attacks against PUF-based quantum authentication systems
Yao, Yao; Gao, Ming; Li, Mo; Zhang, Jian
2016-08-01
With the advent of physical unclonable functions (PUFs), PUF-based quantum authentication systems have been proposed for security purposes, and recently, proof-of-principle experiment has been demonstrated. As a further step toward completing the security analysis, we investigate quantum cloning attacks against PUF-based quantum authentication systems and prove that quantum cloning attacks outperform the so-called challenge-estimation attacks. We present the analytical expression of the false-accept probability by use of the corresponding optimal quantum cloning machines and extend the previous results in the literature. In light of these findings, an explicit comparison is made between PUF-based quantum authentication systems and quantum key distribution protocols in the context of cloning attacks. Moreover, from an experimental perspective, a trade-off between the average photon number and the detection efficiency is discussed in detail.
The quantum Hall effect in quantum dot systems
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
Entanglement within the Quantum Trajectory Description of Open Quantum Systems
Nha, Hyunchul; Carmichael, H J
2004-01-01
The degree of entanglement in an open quantum system varies according to how information in the environment is read. A measure of this contextual entanglement is introduced based on quantum trajectory unravelings of the open system dynamics. It is used to characterize the entanglement in a driven quantum system of dimension $2\\times\\infty$ where the entanglement is induced by the environmental interaction. A detailed mechanism for the environment-induced entanglement is given.
Dynamics of complex quantum systems
Akulin, Vladimir M
2014-01-01
This book gathers together a range of similar problems that can be encountered in different fields of modern quantum physics and that have common features with regard to multilevel quantum systems. The main motivation was to examine from a uniform standpoint various models and approaches that have been developed in atomic, molecular, condensed matter, chemical, laser and nuclear physics in various contexts. The book should help senior-level undergraduate, graduate students and researchers putting particular problems in these fields into a broader scientific context and thereby taking advantage of well-established techniques used in adjacent fields. This second edition has been expanded to include substantial new material (e.g. new sections on Dynamic Localization and on Euclidean Random Matrices and new chapters on Entanglement, Open Quantum Systems, and Coherence Protection). It is based on the author’s lectures at the Moscow Institute of Physics and Technology, at the CNRS Aimé Cotton Laboratory, and on ...
Entangled systems. New directions in quantum physics
Entangled Systems is an introductory textbook for advanced students of physics, chemistry and computer science which covers an area of physics that has lately witnessed rapid expansion. The topics treated here include foundations of quantum theory, quantum information, quantum communication, quantum computing, quantum teleportation and hidden variables, thus providing not only a solid basis for the study of quantum theory as such, but also a profound foundation of knowledge from which readers can follow the rapid development of the topic or start out into a more specialized branch of research. Commented recommendations for further reading as well as end-of-chapter problems help the reader to access quickly the basic theoretical concepts of future key technologies. Only a basic prior knowledge of quantum theory and the necessary mathematical foundations is assumed, as introductory chapters are provided to present these to the readers. Thus, 'Entangled Systems' can be used both as a course book and for self-study purposes. From the contents: - The Mathematical Framework - Basic Concepts of Quantum Theory - The Simplest Quantum Systems: Qubits - Mixed State and Density Operator - Shannon's Entropy and Classical Information - The von Neumann Entropy and Quantum Information - Composite Systems - Entanglement - Correlations and Non-Local Measurements - There is no (Local-Realistic) Alternative to the Quantum Theory - Working with Entanglement - The Quantum Computer - General Measurements, POVM - The General Evolution of an Open Quantum System and Special Quantum Channels - Decoherence and Approaches to the Description of the Quantum Measurement Process - Two Implementations of Quantum Operations. (orig.)
Perturbative approach to Markovian open quantum systems
Li, Andy C. Y.; F. Petruccione; Jens Koch
2013-01-01
Perturbation theory (PT) is a powerful and commonly used tool in the investigation of closed quantum systems. In the context of open quantum systems, PT based on the Markovian quantum master equation is much less developed. The investigation of open systems mostly relies on exact diagonalization of the Liouville superoperator or quantum trajectories. In this approach, the system size is rather limited by current computational capabilities. Analogous to closed-system PT, we develop a PT suitab...
Quantum Indeterminacy of Cosmic Systems
Hogan, Craig J. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
2013-12-30
It is shown that quantum uncertainty of motion in systems controlled mainly by gravity generally grows with orbital timescale $H^{-1}$, and dominates classical motion for trajectories separated by distances less than $\\approx H^{-3/5}$ in Planck units. For example, the cosmological metric today becomes indeterminate at macroscopic separations, $H_0^{-3/5}\\approx 60$ meters. Estimates suggest that entangled non-localized quantum states of geometry and matter may significantly affect fluctuations during inflation, and connect the scale of dark energy to that of strong interactions.
Polygamy of Entanglement in Multipartite Quantum Systems
Kim, Jeong San
2009-01-01
We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytic upper bound for the concurrence of assistance in bipartite quantum systems, and derive a polygamy inequality of multipartite entanglement in arbitrary dimensional quantum systems.
Overview of progress in quantum systems control
CONG Shuang; ZHENG Yisong; JI Beichen; DAI Yi
2007-01-01
The development of the theory on quantum systems control in the last 20 years is reviewed in detail.The research on the controllability of quantum systems is first introduced,then the study on the quantum open-loop control methods often used for controlling simple quantum systems is analyzed briefly.The learning control method and the feedback control method are mainly discussed for they are two important methods in quantum systems control and their advantages and disadvantages are presented.According to the trends in quantum systems control development,the paper predicts the future trends of its development and applications.A complete design procedure necessary for the quantum control system is presented.Finally,several vital problems hindering the advancement of quantum control are pointed out.
QUANTUM AND CLASSICAL CORRELATIONS IN GAUSSIAN OPEN QUANTUM SYSTEMS
Aurelian ISAR
2015-01-01
Full Text Available In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum correlations (quantum entanglement and quantum discord for a system consisting of two noninteracting bosonic modes embedded in a thermal environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement and discord in terms of the covariance matrix for Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial squeezed thermal state, entanglement suppression takes place for all temperatures of the environment, including zero temperature. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that it decays asymptotically in time under the effect of the thermal bath. This is in contrast with the sudden death of entanglement. Before the suppression of the entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also the time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of the quantum system.
Applications of Feedback Control in Quantum Systems
Jacobs, Kurt
2006-01-01
We give an introduction to feedback control in quantum systems, as well as an overview of the variety of applications which have been explored to date. This introductory review is aimed primarily at control theorists unfamiliar with quantum mechanics, but should also be useful to quantum physicists interested in applications of feedback control. We explain how feedback in quantum systems differs from that in traditional classical systems, and how in certain cases the results from modern optim...
Software-defined Quantum Communication Systems
Humble, Travis S.; Sadlier, Ronald J.
2014-01-01
Quantum communication systems harness modern physics through state-of-the-art optical engineering to provide revolutionary capabilities. An important concern for quantum communication engineering is designing and prototyping these systems to evaluate proposed capabilities. We apply the paradigm of software-defined communication for engineering quantum communication systems to facilitate rapid prototyping and prototype comparisons. We detail how to decompose quantum communication terminals int...
Eigenfunctions in chaotic quantum systems
Baecker, Arnd
2007-07-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Eigenfunctions in chaotic quantum systems
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Quantum Computing in Solid State Systems
Ruggiero, B; Granata, C
2006-01-01
The aim of Quantum Computation in Solid State Systems is to report on recent theoretical and experimental results on the macroscopic quantum coherence of mesoscopic systems, as well as on solid state realization of qubits and quantum gates. Particular attention has been given to coherence effects in Josephson devices. Other solid state systems, including quantum dots, optical, ion, and spin devices which exhibit macroscopic quantum coherence are also discussed. Quantum Computation in Solid State Systems discusses experimental implementation of quantum computing and information processing devices, and in particular observations of quantum behavior in several solid state systems. On the theoretical side, the complementary expertise of the contributors provides models of the various structures in connection with the problem of minimizing decoherence.
Quantum chaos in open systems: a quantum state diffusion analysis
Brun, Todd A.; Percival, Ian C.; Schack, Rüdiger
1995-01-01
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with the environment, and makes the quasiclassical limit of such systems both more realistic and simpler in many respects than the more familiar quasiclassical limit for closed systems. A linearized version of this theory leads to the correct classical dynamics in...
Logical entropy of quantum dynamical systems
Ebrahimzadeh Abolfazl
2016-01-01
Full Text Available This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.
Quantum systems, channels, information. A mathematical introduction
Holevo, Alexander S.
2012-07-01
The subject of this book is theory of quantum system presented from information science perspective. The central role is played by the concept of quantum channel and its entropic and information characteristics. Quantum information theory gives a key to understanding elusive phenomena of quantum world and provides a background for development of experimental techniques that enable measuring and manipulation of individual quantum systems. This is important for the new efficient applications such as quantum computing, communication and cryptography. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world. This book gives an accessible, albeit mathematically rigorous and self-contained introduction to quantum information theory, starting from primary structures and leading to fundamental results and to exiting open problems.
Note on entropies for quantum dynamical systems.
Watanabe, Noboru
2016-05-28
Quantum entropy and channel are fundamental concepts for quantum information theory progressed recently in various directions. We will review the fundamental aspects of mean entropy and mean mutual entropy and calculate them for open system dynamics. PMID:27091165
Optimal protocols for slowly driven quantum systems.
Zulkowski, Patrick R; DeWeese, Michael R
2015-09-01
The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing. PMID:26465432
Repeated interactions in open quantum systems
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium
Repeated interactions in open quantum systems
Bruneau, Laurent, E-mail: laurent.bruneau@u-cergy.fr [Laboratoire AGM, Université de Cergy-Pontoise, Site Saint-Martin, BP 222, 95302 Cergy-Pontoise (France); Joye, Alain, E-mail: Alain.Joye@ujf-grenoble.fr [Institut Fourier, UMR 5582, CNRS-Université Grenoble I, BP 74, 38402 Saint-Martin d’Hères (France); Merkli, Marco, E-mail: merkli@mun.ca [Department of Mathematics and Statistics Memorial University of Newfoundland, St. John' s, NL Canada A1C 5S7 (Canada)
2014-07-15
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium.
Quantum state engineering in hybrid open quantum systems
Joshi, Chaitanya; Larson, Jonas; Spiller, Timothy P.
2016-04-01
We investigate a possibility to generate nonclassical states in light-matter coupled noisy quantum systems, namely, the anisotropic Rabi and Dicke models. In these hybrid quantum systems, a competing influence of coherent internal dynamics and environment-induced dissipation drives the system into nonequilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi model, the steady state is given by an incoherent mixture of two states of opposite parities, but as each parity state displays light-matter entanglement, we also find that the full state is entangled. Furthermore, as a natural extension of the anisotropic Rabi model to an infinite spin subsystem, we next explored the NESS of the anisotropic Dicke model. The NESS of this linearized Dicke model is also an inseparable state of light and matter. With an aim to enrich the dynamics beyond the sustainable entanglement found for the NESS of these hybrid quantum systems, we also propose to combine an all-optical feedback strategy for quantum state protection and for establishing quantum control in these systems. Our present work further elucidates the relevance of such hybrid open quantum systems for potential applications in quantum architectures.
Optimal Lyapunov-based quantum control for quantum systems
Hou, S C; Dong, Daoyi; Petersen, Ian R; Yi, X X
2012-01-01
Quantum Lyapunov control was developed in order to transform a quantum system from arbitrary initial states to a target state. The idea is to find control fields that steer the Lyapunov function to zero as $t\\rightarrow \\infty$, meanwhile the quantum system is driven to the target state. In order to shorten the time required to reach the target state, we propose two designs to optimize Lyapunov control in this paper. The first design makes the Lyapunov function decrease as fast as possible with a constraint on the total power of control fields, and the second design has the same purpose but with a constraint on each control field. Examples of a three-level system demonstrate that the evolution time for Lyapunov control can be significantly shortened, especially when high control fidelity is required. Besides, this optimal Lyapunov-based quantum control is robust against uncertainties in the free Hamiltonian and decoherence in the system compared to conventional Lyapunov control.
Entangling transformations in composite finite quantum systems
Vourdas, A [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom)
2003-12-01
Phase space methods are applied in the context of finite quantum systems. 'Galois quantum systems' (with a dimension which is a power of a prime number) are considered, and symplectic Sp(2,Z(d)) transformations are studied. Composite systems comprising two finite quantum systems are also considered. Symplectic Sp(4,Z(d)) transformations are classified into local and entangling ones and the necessary matrices which perform such transformations are calculated numerically.
Quantum Simulation of Tunneling in Small Systems
Andrew T Sornborger
2012-01-01
A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator....
Quantum probabilities and entanglement for multimode quantum systems
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain measurements, and for entangled composite events. The role of the prospect and state entanglement is emphasized. Numerical modeling is presented for a two-mode Bose-condensed system of trapped atoms. The interference factor is calculated by invoking the channel-state duality.
Thermodynamics of Weakly Measured Quantum Systems
Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro
2016-02-01
We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.
Thermodynamics of Weakly Measured Quantum Systems.
Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro
2016-02-26
We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics. PMID:26967399
Quantum Heat Engine With Multi-Level Quantum Systems
Quan, H T; Sun, C P
2005-01-01
By reformulating the first law of thermodynamics in the fashion of quantum-mechanical operators on the parameter manifold, we propose a universal class of quantum heat engines (QHE) using the multi-level quantum system as the working substance. We obtain a general expression of work for the thermodynamic cycle with two thermodynamic adiabatic processes, which are microscopically quantum adiabatic processes. We also classify the conditions for a 3-level QHE to extract positive work from a heat bath. Our result is counter-intuitively different from that of a 2-level system. As a more realistic illustration, a 3-level atom system with dark state configuration manipulated by classical light is used to demonstrate our central idea.
Quantum mechanics in complex systems
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown
Quantum Open System Theory: Bipartite Aspects
Yu, Ting; Eberly, J. H.
2006-01-01
We demonstrate in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics. While additivity of decay rates is known to be generic for decoherence of a single system, we demonstrate that it breaks down for bipartite coherence of even the simplest composite systems.
Hybrid quantum systems of atoms and ions
In recent years, ultracold atoms have emerged as an exceptionally controllable experimental system to investigate fundamental physics, ranging from quantum information science to simulations of condensed matter models. Here we go one step further and explore how cold atoms can be combined with other quantum systems to create new quantum hybrids with tailored properties. Coupling atomic quantum many-body states to an independently controllable single-particle gives access to a wealth of novel physics and to completely new detection and manipulation techniques. We report on recent experiments in which we have for the first time deterministically placed a single ion into an atomic Bose Einstein condensate. A trapped ion, which currently constitutes the most pristine single particle quantum system, can be observed and manipulated at the single particle level. In this single-particle/many-body composite quantum system we show sympathetic cooling of the ion and observe chemical reactions of single particles in situ.
Macroscopic quantum systems and gravitational phenomena
Low-energy quantum systems are studied theoretically in light of possible experiments to test the interplay between quantum theory and general relativity. The research focus in this thesis is on quantum systems which can be controlled with very high precision and which allow for tests of quantum theory at novel scales in terms of mass and size. The pulsed regime of opto-mechanics is explored and it is shown how short optical pulses can be used to prepare and characterize quantum states of a massive mechanical resonator, and how some phenomenological models of quantum gravity can be probed. In addition, quantum interferometry with photons and matter-waves in the presence of gravitational time dilation is considered. It is shown that time dilation causes entanglement between internal states and the center-of-mass position and that it leads to decoherence of all composite quantum systems. The results of the thesis show that the interplay between quantum theory and general relativity affects even low-energy quantum systems and that it offers novel phenomena which can be probed in experiments. (author)
Controlling quantum critical dynamics of isolated systems
Del Campo, A.; K. Sengupta
2014-01-01
Controlling the non adiabatic dynamics of isolated quantum systems driven through a critical point is of interest in a variety of fields ranging from quantum simulation to finite-time thermodynamics. We briefly review the different methods for designing protocols which minimize excitation (defect) production in a closed quantum critical system driven out of equilibrium. We chart out the role of specific driving schemes for this procedure, point out their experimental relevance, and discuss th...
Robust observer for uncertain linear quantum systems
Yamamoto, Naoki
2006-01-01
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that th...
Tailoring superradiance to design artificial quantum systems
Longo, Paolo; Keitel, Christoph H.; Evers, Jörg
2016-03-01
Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This “reverse engineering” of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems.
Quantum mechanics of open systems
Melikidze, Akakii
In quantum mechanics, there is a set of problems where the system of interest interacts with another system, usually called "environment". This interaction leads to the exchange of energy and information and makes the dynamics of the system of interest essentially non-unitary. Such problems often appeared in condensed matter physics and attracted much attention after recent advances in nanotechnology. As broadly posed as they are, these problems require a variety of different approaches. This thesis is an attempt to examine several of these approaches in applications to different condensed matter problems. The first problem concerns the so-called "Master equation" approach which is very popular in quantum optics. I show that analytic properties of environmental correlators lead to strong restrictions on the applicability of the approach to the strong-coupling regime of interest in condensed matter physics. In the second problem, I use path integrals to treat the localization of particles on attractive short-range potentials when the environment produces an effective viscous friction force. I find that friction changes drastically the localization properties and leads to much stronger localization in comparison to the non-dissipative case. This has implications for the motion of heavy particles in fermionic liquids and, as will be argued below, is also relevant to the problem of high-temperature superconductivity. Finally, the third problem deals with the interplay of geometric phases and energy dissipation which occurs in the motion of vortices in superconductors. It is shown that this interplay leads to interesting predictions for vortex tunneling in high-temperature superconductors which have been partially confirmed by experiments.
Linear response theory for quantum open systems
J. H. Wei; Yan, YiJing
2011-01-01
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
Dynamical entropy for infinite quantum systems
We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)
Quantum information theory with Gaussian systems
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Quantum information theory with Gaussian systems
Krueger, O.
2006-04-06
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Measuring quantum systems with tunnel junctions
Full text: We present a formalism that allows to describe a quantum system modulating the transmission of a tunnel junction. The tunnel junction acts as an environment for the quantum system. Contrary to the conventional approach to open quantum systems we retain a degree of freedom of the environment, the charge passed through the junction, after averaging over the bath degrees of freedom, employing a projection operator technique. The resulting object characterizing the joint dynamics of the system and the charge is the charge specific density matrix. We derive a master equation describing the time evolution of the charge specific density matrix. We consider two examples of quantum systems coupled to the junction: a spin and a harmonic oscillator. In the spin case we are able to analyze a quantum measurement process in detail. For the oscillator we investigate the noise in the tunnel junction induced by the coupling. (author)
Logic of infinite quantum systems
Mundici, Daniele
1993-10-01
Limits of sequences of finite-dimensional (AF) C *-algebras, such as the CAR algebra for the ideal Fermi gas, are a standard mathematical tool to describe quantum statistical systems arising as thermodynamic limits of finite spin systems. Only in the infinite-volume limit one can, for instance, describe phase transitions as singularities in the thermodynamic potentials, and handle the proliferation of physically inequivalent Hilbert space representations of a system with infinitely many degrees of freedom. As is well known, commutative AF C *-algebras correspond to countable Boolean algebras, i.e., algebras of propositions in the classical two-valued calculus. We investigate the noncommutative logic properties of general AF C *-algebras, and their corresponding systems. We stress the interplay between Gödel incompleteness and quotient structures in the light of the “nature does not have ideals” program, stating that there are no quotient structures in physics. We interpret AF C *-algebras as algebras of the infinite-valued calculus of Lukasiewicz, i.e., algebras of propositions in Ulam's “ twenty questions” game with lies.
Slightly anharmonic systems in quantum optics
Klimov, Andrey B.; Chumakov, Sergey M.
1995-01-01
We consider an arbitrary atomic system (n-level atom or many such atoms) interacting with a strong resonant quantum field. The approximate evolution operator for a quantum field case can be produced from the atomic evolution operator in an external classical field by a 'quantization prescription', passing the operator arguments to Wigner D-functions. Many important phenomena arising from the quantum nature of the field can be described by such a way.
Interaction between classical and quantum systems
An unconventional approach to the measurement problem in quantum mechanics is considered--the apparatus is treated as a classical system, belonging to the macro-world. In order to have a measurement the apparatus must interact with the quantum system. As a first step, the classical apparatus is embedded into a large quantum mechanical structure, making use of a superselection principle. The apparatus and system are coupled such that the apparatus remains classical (principle of integrity), and unambiguous information of the values of a quantum observable are transferred to the variables of the apparatus. Further measurement of the classical apparatus can be done, causing no problems of principle. Thus interactions causing pointers to move (which are not treated) can be added. The restrictions placed by the principle of integrity on the form of the interaction between classical and quantum systems are examined and illustration is given by means of a simple example in which one sees the principle of integrity at work
Mixing and entropy increase in quantum systems
This paper attempts to explain the key feature of deterministic chaotic classical systems and how they can be translated to quantum systems. To do so we develop the appropriate algebraic language for the non-specialist. 22 refs. (Author)
Quantum entanglement in photoactive prebiotic systems
Tamulis, Arvydas; Grigalavicius, Mantas
2014-01-01
This paper contains the review of quantum entanglement investigations in living systems, and in the quantum mechanically modelled photoactive prebiotic kernel systems. We define our modelled self-assembled supramolecular photoactive centres, composed of one or more sensitizer molecules, precursors of fatty acids and a number of water molecules, as a photoactive prebiotic kernel systems. We propose that life first emerged in the form of such minimal photoactive prebiotic kernel systems and lat...
Local Unitary Invariants for Multipartite Quantum Systems
Wang, Jing; Li, Ming; Fei, Shao-Ming; Li-Jost, Xianqing
2014-01-01
We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples are given to compute such invariant in detail. It is shown that these invariants can be used to detect the local unitary equivalence of degenerated quantum states.
Limit cycles in quantum systems
Niemann, Patrick
2015-04-27
In this thesis we investigate Limit Cycles in Quantum Systems. Limit cycles are a renormalization group (RG) topology. When degrees of freedom are integrated out, the coupling constants flow periodically in a closed curve. The presence of limit cycles is restricted by the necessary condition of discrete scale invariance. A signature of discrete scale invariance and limit cycles is log-periodic behavior. The first part of this thesis is concerned with the study of limit cycles with the similarity renormalization group (SRG). Limit cycles are mainly investigated within conventional renormalization group frameworks, where degrees of freedom, which are larger than a given cutoff, are integrated out. In contrast, in the SRG potentials are unitarily transformed and thereby obtain a band-diagonal structure. The width of the band structure can be regarded as an effective cutoff. We investigate the appearance of limit cycles in the SRG evolution. Our aim is to extract signatures as well as the scaling factor of the limit cycle. We consider the 1/R{sup 2}-potential in a two-body system and a three-body system with large scattering lengths. Both systems display a limit cycle. Besides the frequently used kinetic energy generator we apply the exponential and the inverse generator. In the second part of this thesis, Limit Cycles at Finite Density, we examine the pole structure of the scattering amplitude for distinguishable fermions at zero temperature in the medium. Unequal masses and a filled Fermi sphere for each fermion species are considered. We focus on negative scattering lengths and the unitary limit. The properties of the three-body spectrum in the medium and implications for the phase structure of ultracold Fermi gases are discussed.
Limit cycles in quantum systems
In this thesis we investigate Limit Cycles in Quantum Systems. Limit cycles are a renormalization group (RG) topology. When degrees of freedom are integrated out, the coupling constants flow periodically in a closed curve. The presence of limit cycles is restricted by the necessary condition of discrete scale invariance. A signature of discrete scale invariance and limit cycles is log-periodic behavior. The first part of this thesis is concerned with the study of limit cycles with the similarity renormalization group (SRG). Limit cycles are mainly investigated within conventional renormalization group frameworks, where degrees of freedom, which are larger than a given cutoff, are integrated out. In contrast, in the SRG potentials are unitarily transformed and thereby obtain a band-diagonal structure. The width of the band structure can be regarded as an effective cutoff. We investigate the appearance of limit cycles in the SRG evolution. Our aim is to extract signatures as well as the scaling factor of the limit cycle. We consider the 1/R2-potential in a two-body system and a three-body system with large scattering lengths. Both systems display a limit cycle. Besides the frequently used kinetic energy generator we apply the exponential and the inverse generator. In the second part of this thesis, Limit Cycles at Finite Density, we examine the pole structure of the scattering amplitude for distinguishable fermions at zero temperature in the medium. Unequal masses and a filled Fermi sphere for each fermion species are considered. We focus on negative scattering lengths and the unitary limit. The properties of the three-body spectrum in the medium and implications for the phase structure of ultracold Fermi gases are discussed.
Nonclassical light from an incoherently pumped quantum dot in a microcavity
Teuber, L.; Grünwald, P.; Vogel, W.
2015-11-01
Semiconductor microcavities with artificial single-photon emitters have become one of the backbones of semiconductor quantum optics. In many cases, however, technical and physical issues limit the study of optical fields to incoherently excited systems. We analyze the model of an incoherently driven two-level system in a single-mode cavity. The specific structure of the applied master equation yields a recurrence relation for the steady-state values of correlations of the intracavity field and the emitter. We provide boundary conditions that permit a systematic solution which is numerically less demanding than standard methods. The method allows us to directly infer reasonable cutoff conditions from the system parameters. Different cavity systems from previous experiments are analyzed in terms of field correlation functions which can be measured via homodyne correlation measurements. We find that nonclassical correlations occur in systems of moderate quantum-dot-cavity coupling rather than strong coupling. Our boundary conditions also allow us to derive analytical results for the overall quantum state and its higher-order moments. We obtain very good approximations for the full quantum state of the field in terms of the characteristic functions. It turns out that for every physically reasonable set of system parameters, the state of the intracavity field is nonclassical.
Avoiding irreversible dynamics in quantum systems
Karasik, Raisa Iosifovna
2009-10-01
Devices that exploit laws of quantum physics offer revolutionary advances in computation and communication. However, building such devices presents an enormous challenge, since it would require technologies that go far beyond current capabilities. One of the main obstacles to building a quantum computer and devices needed for quantum communication is decoherence or noise that originates from the interaction between a quantum system and its environment, and which leads to the destruction of the fragile quantum information. Encoding into decoherence-free subspaces (DFS) provides an important strategy for combating decoherence effects in quantum systems and constitutes the focus of my dissertation. The theory of DFS relies on the existence of certain symmetries in the decoherence process, which allow some states of a quantum system to be completely decoupled from the environment and thus to experience no decoherence. In this thesis I describe various approaches to DFS that are developed in the current literature. Although the general idea behind various approaches to DFS is the same, I show that different mathematical definitions of DFS actually have different physical meaning. I provide a rigorous definition of DFS for every approach, explaining its physical meaning and relation to other definitions. I also examine the theory of DFS for Markovian systems. These are systems for which the environment has no memory, i.e., any change in the environment affects the quantum system instantaneously. Examples of such systems include many systems in quantum optics that have been proposed for implementation of a quantum computer, such as atomic and molecular gases, trapped ions, and quantum dots. Here I develop a rigorous theory that provides necessary and sufficient conditions for the existence of DFS. This theory allows us to identify a special new class of DFS that was not known before. Under particular circumstances, dynamics of a quantum system can connive together with
Level shift operators for open quantum systems
Merkli, Marco
2006-01-01
Level shift operators describe the second order displacement of eigenvalues under perturbation. They play a central role in resonance theory and ergodic theory of open quantum systems at positive temperatures. We exhibit intrinsic properties of level shift operators, properties which stem from the structure of open quantum systems at positive temperatures and which are common to all such systems. They determine the geometry of resonances bifurcating from eigenvalues of positive temperature Ha...
Optimal control of open quantum systems
The present work deals with the application of Optimal Control Theory (OCT) to open quantum systems with a particular focus on solid-state quantum information processing devices. The latter are typically nanoscale structures that have to be manufactured, prepared, controlled and measured with an extraordinary degree of precision so that their quantum properties can be harnessed. Because array scalability is one of the main advantages of solid-state qubit realizations, they distinguish themselves as promising candidates for the implementation of efficient quantum information processors. However, these devices usually interact with a solid-state environment that may lead to adverse effects regarding their performance. Therefore, isolation of the nanostructure from its environment poses an important problem. This corresponds to a somewhat contradictory requirement since unwanted interactions can affect the quantum system by the same channels that are used to control the qubit. Closing these channels would lead to a reduction in the sensitivity with respect to environmental interacti
Chapter 2 A Single Quantum System
Toschek, Peter E.
The evolution of quantum mechanics has followed the critical analysis of "gedanken" experiments. Many of these concrete speculations can become implemented today in the laboratory--thanks to now available techniques. A key experiment is concerned with the time evolution of a quantum system under repeated or continuing observation. Here, three problems overlap: (1) The microphysical measurement by a macroscopic device, (2) the system's temporal evolution, and (3) the emergence of macroscopic reality out of the microcosmos. A well-known calculation shows the evolution of a quantum system being slowed down, or even obstructed, when the system is merely observed. An experiment designed to demonstrate this "quantum Zeno effect" and performed in the late eighties on an ensemble of identical atomic ions confirmed its quantum description, but turned out inconclusive with respect to the very origin of the impediment of evolution. During the past years, experiments on individual electrodynamically stored and laser-cooled ions have been performed that unequivocally demonstrate the observed system's quantum evolution being impeded. Strategy and results exclude any physical reaction on the measured object, but reveal the effect of the gain of information as put forward by the particular correlation of the ion state with the detected signal. They shed light on the process of measurement as well as on the quantum evolution and allow an epistemological interpretation.
Quantum Implemention of an LTI System with the minimal number of additional quantum noise inputs
Vuglar, Shanon L.; Petersen, Ian R.
2013-01-01
Physical Realizability addresses the question of whether it is possible to implement a given LTI system as a quantum system. It is in general not true that a given synthesized quantum controller described by a set of stochastic differential equations is equivalent to some physically meaningful quantum system. However, if additional quantum noises are permitted in the implementation it is always possible to implement an arbitrary LTI system as a quantum system. In this paper we give an express...
Quantum entanglement in condensed matter systems
Laflorencie, Nicolas
2016-08-01
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial information can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Rényi entropies are now well recognized to contain key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in detail. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.
Quantum dynamics of complex molecular systems
Miller, William H.
2005-01-01
This Perspective presents a broad overview of the present status of theoretical capabilities for describing quantum dynamics in molecular systems with many degrees of freedom, e.g., chemical reactions in solution, clusters, solids, or biomolecular environments.
Teleportation in an indivisible quantum system
Kiktenko E.O.; Fedorov A.K.; Man’ko V.I.
2016-01-01
Teleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding o...
Combinatorial Approach to Modeling Quantum Systems
Kornyak, Vladimir V.
2016-02-01
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers and unitarity in the formalism of the quantum mechanics. In our approach, the quantum behavior can be explained by the fundamental impossibility to trace the identity of the indistinguishable objects in their evolution. Any observation only provides information about the invariant relations between such objects. The trajectory of a quantum system is a sequence of unitary evolutions interspersed with observations—non-unitary projections. We suggest a scheme to construct combinatorial models of quantum evolution. The principle of selection of the most likely trajectories in such models via the large numbers approximation leads in the continuum limit to the principle of least action with the appropriate Lagrangians and deterministic evolution equations
Spectrum analysis with quantum dynamical systems
Ng, Shilin; Ang, Shan Zheng; Wheatley, Trevor A.; Yonezawa, Hidehiro; Furusawa, Akira; Huntington, Elanor H.; Tsang, Mankei
2016-04-01
Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future technology, especially in optomechanics for temperature, stochastic gravitational wave, and decoherence measurements. Motivated by this concern, here we prove a measurement-independent quantum limit to the accuracy of estimating the spectrum parameters of a classical stochastic process coupled to a quantum dynamical system. We demonstrate our results by analyzing the data from a continuous-optical-phase-estimation experiment and showing that the experimental performance with homodyne detection is close to the quantum limit. We further propose a spectral photon-counting method that can attain quantum-optimal performance for weak modulation and a coherent-state input, with an error scaling superior to that of homodyne detection at low signal-to-noise ratios.
Quantum electro-mechanical system (QEMS)
Full text: Recent development in Nano Electro-Mechanical Systems (NEMS) has yield oscillators with resonant frequencies above Giga Hertz with quality factors above 100,000. At this scale a NEMS oscillator becomes a quantum device capable of operating at the atomic level with extraordinary sensitivity to small forces or molecular masses. With this motivation, we study the phonon-electron interaction in several quantum electromechanical systems (QEMS). First, a system comprising a single quantum dot harmonically bound between two electrodes which facilitates a tunneling current between them and secondly the electron shuttle system firstly introduced by Gorelik. We describe the system via quantum master equation for the density operator of the electronic and vibrational degrees of freedom and thus incorporates the dynamics of both diagonal (population) and off diagonal (coherence) terms. We derive coupled equations of motion for the electron occupation number of the dot and the vibrational degrees of freedom, including damping of the vibration and thermo-mechanical noise. This dynamical description is related to observable features of the system including the stationary current as a function of bias voltage. A number of possible applications are explored for feasibility including molecular QEMS devices as quantum limited nanoscale detectors and as elements in quantum computer architectures. Copyright (2005) Australian Institute of Physics
Measurement, Filtering and Control in Quantum Open Dynamical Systems
Belavkin, V. P.
2002-01-01
A Markovian model for a quantum automata, i.e. an open quantum dynamical discrete-time system with input and output channels and a feedback, is described. A dynamical theory of quantum discrete-time adaptive measurements and multi-stage quantum statistical decisions is developed and applied to the optimal feedback control problem for the quantum dynamical objects. Quantum analogies of Stratonovich non-stationary filtering, and Bellman quantum dynamical programming in the discrete time are der...
CIME School on Quantum Many Body Systems
Rivasseau, Vincent; Solovej, Jan Philip; Spencer, Thomas
2012-01-01
The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.
Noise in quantum systems: facts and fantasies
Full text: We present a critical review of recent developments on quantum noise in a variety of mesoscopic conductors including ballistic, diffusive and tunnelling systems. We begin with a microscopic approach that describes quantum transport and fluctuations for correlated electrons at high external field taking the system beyond the linear response regime. We discuss two commonly believed results that (a) shot noise in diffusive systems is suppressed by '1/3' universally and (b) there is a 'crossover' of shot noise to thermal noise at finite temperature and applied field. Our analysis reveals contradictions based on fundamental physics and its logical implications. We examine another issue of measuring fractional charges in fractional quantum Hall effect (FQHE) experiments. It is believed that shot noise spectral density reveals the charge quantum of the current carriers as a Schottky phenomenon. Here again we analyse a number of unverified assumptions beyond the myth
Robust observer for uncertain linear quantum systems
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although in the linear case much of classical control theory can be applied to quantum systems, the quantum robust observer obtained in this paper does not have a classical analog due to the system's specific structure with respect to the uncertainties. Moreover, by considering a typical quantum control problem, we show that the proposed robust observer is fairly robust against a parametric uncertainty of the system even when the other estimators--the optimal Kalman filter and risk-sensitive observer--fail in the estimation
Exotic Quantum Order in Low-Dimensional Systems
Girvin, Steven M.
1997-01-01
Strongly correlated quantum systems in low dimensions often exhibit novel quantum ordering. This ordering is sometimes hidden and can be revealed only by examining new `dual' types of correlations. Such ordering leads to novel collective modes and fractional quantum numbers. Examples will be presented from quantum spin chains and the quantum Hall effect.
T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras
Tomoki Nakanishi; Junji Suzuki; Atsuo Kuniba
2009-01-01
The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a wide class of quantum Kac-Moody algebras by Hernandez. In this note we introduce the corresponding Y-systems and establish a relation between T and Y-systems. We also introduce the T and Y-systems associated with a class of cluster algebras, which include the former T and Y-systems of simply laced ...
Quantum optical properties in plasmonic systems
Ooi, C. H. Raymond [Department of Physics, University of Malaya, 50603, Kuala Lumpur (Malaysia)
2015-04-24
Plasmonic metallic particle (MP) can affect the optical properties of a quantum system (QS) in a remarkable way. We develop a general quantum nonlinear formalism with exact vectorial description for the scattered photons by the QS. The formalism enables us to study the variations of the dielectric function and photon spectrum of the QS with the particle distance between QS and MP, exciting laser direction, polarization and phase in the presence of surface plasmon resonance (SPR) in the MP. The quantum formalism also serves as a powerful tool for studying the effects of these parameters on the nonclassical properties of the scattered photons. The plasmonic effect of nanoparticles has promising possibilities as it provides a new way for manipulating quantum optical properties of light in nanophotonic systems.
Random Control over Quantum Open Systems
Jing, Jun; Bishop, C. Allen; Wu, Lian-Ao
2014-01-01
Parametric fluctuations or stochastic signals are introduced into the control pulse sequence to investigate the feasibility of random control over quantum open systems. In a large parameter error region, the out-of-order control pulses work as well as the regular pulses for dynamical decoupling and dissipation suppression. Calculations and analysis are based on a non-perturbative control approach allowed by an exact quantum-state-diffusion equation. When the average frequency and duration of ...
Note on quantum groups and integrable systems
Popolitov, A.
2016-01-01
The free-field formalism for quantum groups [preprint ITEP-M3/94, CRM-2202 hep-th/9409093] provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system [arXiv:1207.1869] is especially simple. This choice also fits into general framework of cluster varieties [math.AG/0311245]—natural changes in coordinates are cluster mutations.
The Moyal equation for open quantum systems
We generalize the Moyal equation, which describes the dynamics of quantum observables in phase space, to quantum systems coupled to a reservoir. It is shown that phase space observables become functionals of fluctuating noise forces introduced by the coupling to the reservoir. For Markovian reservoirs, the Moyal equation turns into a functional differential equation in which the reservoir’s effect can be described by a single parameter. (paper)
Quartz-superconductor quantum electromechanical system
Woolley, M. J.; Emzir, M. F.; Milburn, G. J.; Jerger, M.; Goryachev, M.; Tobar, M. E.; Fedorov, A.
2016-01-01
We propose and analyse a quantum electromechanical system composed of a monolithic quartz bulk acoustic wave (BAW) oscillator coupled to a superconducting transmon qubit via an intermediate LC electrical circuit. Monolithic quartz oscillators offer unprecedentedly high effective masses and quality factors for the investigation of mechanical oscillators in the quantum regime. Ground-state cooling of such mechanical modes via resonant piezoelectric coupling to an LC circuit, which is itself sid...
Guaranteed Cost LQG Control of Uncertain Linear Quantum Stochastic Systems
A. J. SHAIJU; Petersen, I. R.; James, M R
2008-01-01
In this paper, we formulate and solve a guaranteed cost control problem for a class of uncertain linear stochastic quantum systems. For these quantum systems, a connection with an associated classical (non-quantum) system is first established. Using this connection, the desired guaranteed cost results are established. The theory presented is illustrated using an example from quantum optics.
Symmetric and asymmetric quantum channels in quantum communication systems
Symmetric and asymmetric quantum channels which act on bipartite bosonic states are considered. The linear dissipative channel and the quantum teleportation channel are applied. The influences of the symmetric and asymmetric quantum channels on bipartite Gaussian states are investigated by means of the inseparability condition. Furthermore, quantum teleportation and quantum dense coding of continuous variables performed by means of two-mode squeezed-vacuum states under the influence of the noisy quantum channels are discussed
Cluster formation in quantum critical systems
The presence of magnetic clusters has been verified in both antiferromagnetic and ferromagnetic quantum critical systems. We review some of the strongest evidence for strongly doped quantum critical systems (Ce(Ru0.24Fe0.76)2Ge2) and we discuss the implications for the response of the system when cluster formation is combined with finite size effects. In particular, we discuss the change of universality class that is observed close to the order-disorder transition. We detail the conditions under which clustering effects will play a significant role also in the response of stoichiometric systems and their experimental signature.
Open quantum systems far from equilibrium
Schaller, Gernot
2014-01-01
This monograph provides graduate students and also professional researchers aiming to understand the dynamics of open quantum systems with a valuable and self-contained toolbox. Special focus is laid on the link between microscopic models and the resulting open-system dynamics. This includes how to derive the celebrated Lindblad master equation without applying the rotating wave approximation. As typical representatives for non-equilibrium configurations it treats systems coupled to multiple reservoirs (including the description of quantum transport), driven systems, and feedback-controlled quantum systems. Each method is illustrated with easy-to-follow examples from recent research. Exercises and short summaries at the end of every chapter enable the reader to approach the frontiers of current research quickly and make the book useful for quick reference.
PSPACE has 2-round quantum interactive proof systems
Watrous, John
1999-01-01
In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a quantum interactive proof system that requires only two rounds of communication between the prover and verifier, while having exponentially small (one-sided) probability of error. It follows that quantum interactive proof systems are strictly more powerful t...
Incoherent control of locally controllable quantum systems
An incoherent control scheme for state control of locally controllable quantum systems is proposed. This scheme includes three steps: (1) amplitude amplification of the initial state by a suitable unitary transformation, (2) projective measurement of the amplified state, and (3) final optimization by a unitary controlled transformation. The first step increases the amplitudes of some desired eigenstates and the corresponding probability of observing these eigenstates, the second step projects, with high probability, the amplified state into a desired eigenstate, and the last step steers this eigenstate into the target state. Within this scheme, two control algorithms are presented for two classes of quantum systems. As an example, the incoherent control scheme is applied to the control of a hydrogen atom by an external field. The results support the suggestion that projective measurements can serve as an effective control and local controllability information can be used to design control laws for quantum systems. Thus, this scheme establishes a subtle connection between control design and controllability analysis of quantum systems and provides an effective engineering approach in controlling quantum systems with partial controllability information.
Quantum Dynamics of Nonlinear Cavity Systems
Nation, Paul D
2010-01-01
We investigate the quantum dynamics of three different configurations of nonlinear cavity systems. To begin, we carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprised of a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing a flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal and noise response where it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state. Next, we make use of a superconducting transmission line formed from an array of dc-SQUIDs for investigating analogue Hawking radiation. Biasing the array with a space-time varying flux modifies the propagation velocity of the transmission line, leading to an effective metric with a horizon. This setup allows for quan...
Computational quantum-classical boundary of complex and noisy quantum systems
Fujii, Keisuke; Tamate, Shuhei
2014-01-01
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on...
Scattering theory for open quantum systems
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator AD in a Hilbert space H is used to describe an open quantum system. In this case the minimal self-adjoint dilation K of AD can be regarded as the Hamiltonian of a closed system which contains the open system {AD,h}, but since K is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {A(μ)} of maximal dissipative operators depending on energy μ, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schroedinger-Poisson systems. (orig.)
Quantum Systems and Alternative Unitary Descriptions
Marmo, G; Ventriglia, F
2003-01-01
Motivated by the existence of bi-Hamiltonian classical systems and the correspondence principle, in this paper we analyze the problem of finding Hermitian scalar products which turn a given flow on a Hilbert space into a unitary one. We show how different invariant Hermitian scalar products give rise to different descriptions of a quantum system in the Ehrenfest and Heisenberg picture.
Recent advances in quantum integrable systems
Amico, L.; Belavin, A.; Buffenoir, E.; Castro Alvaredo, A.; Caudrelier, V.; Chakrabarti, A.; Corrig, E.; Crampe, N.; Deguchi, T.; Dobrev, V.K.; Doikou, A.; Doyon, B.; Feher, L.; Fioravanti, D.; Gohmann, F.; Hallnas, M.; Jimbo, M.; Konno, N.C.H.; Korchemsky, G.; Kulish, P.; Lassalle, M.; Maillet, J.M.; McCoy, B.; Mintchev, M.; Pakuliak, S.; Quano, F.Y.Z.; Ragnisco, R.; Ravanini, F.; Rittenberg, V.; Rivasseau, V.; Rossi, M.; Satta, G.; Sedrakyan, T.; Shiraishi, J.; Suzuki, N.C.J.; Yamada, Y.; Zamolodchikov, A.; Ishimoto, Y.; Nagy, Z.; Posta, S.; Sedra, M.B.; Zuevskiy, A.; Gohmann, F
2005-07-01
This meeting was dedicated to different aspects of the theory of quantum integrable systems. The organizers have intended to concentrate on topics related to the study of correlation functions, to systems with boundaries and to models at roots of unity. This document gathers the abstracts of 32 contributions, most of the contributions are accompanied by the set of transparencies.
Recent advances in quantum integrable systems
This meeting was dedicated to different aspects of the theory of quantum integrable systems. The organizers have intended to concentrate on topics related to the study of correlation functions, to systems with boundaries and to models at roots of unity. This document gathers the abstracts of 32 contributions, most of the contributions are accompanied by the set of transparencies
Coherent polulation trapping in quantum systems
A coherent popualation trapping is a recently developed tool for high resolution spectroscopy. This method if based on a linear coherent interaction betwen the atomic system and the electromagnetic radiaiton falling upon and a registration of medium responses for a subsequent analysis of their fine structure which contains information about spectral characteristics of a quantum system
Quantum games in open systems using biophysical Hamiltonians
We analyze the necessary physical conditions to model an open quantum system as a quantum game. By applying the formalism of quantum operations on a particular system, we use Kraus operators as quantum strategies. The physical interpretation is a conflict among different configurations of the environment. The resolution of the conflict displays regimes of minimum loss of information
Quantum games in open systems using biophysical Hamiltonians
Faber, Jean [National Laboratory of Scientific Computing (LNCC), Av. Getulio Vargas 333, Quitandinha 25651-075, Petropolis, RJ (Brazil)]. E-mail: faber@lncc.br; Portugal, Renato [National Laboratory of Scientific Computing (LNCC), Av. Getulio Vargas 333, Quitandinha 25651-075, Petropolis, RJ (Brazil)]. E-mail: portugal@lncc.br; Rosa, Luiz Pinguelli [Federal University of Rio de Janeiro, COPPE-UFRJ, RJ (Brazil)]. E-mail: lpr@adc.coppe.ufrj.br
2006-09-25
We analyze the necessary physical conditions to model an open quantum system as a quantum game. By applying the formalism of quantum operations on a particular system, we use Kraus operators as quantum strategies. The physical interpretation is a conflict among different configurations of the environment. The resolution of the conflict displays regimes of minimum loss of information.
Quantum Algorithm for the Toeplitz Systems
Wan, Lin-Chun; Pan, Shi-Jie; Gao, Fei; Wen, Qiao-Yan
2016-01-01
Solving the Toeplitz systems, which is to find the vector $x$ such that $T_nx = b$ given a $n\\times n$ Toeplitz matrix $T_n$ and a vector $b$, has a variety of applications in mathematics and engineering. In this paper, we present a quantum algorithm for solving the Toeplitz systems, in which a quantum state encoding the solution with error $\\epsilon$ is generated. It is shown that our algorithm's complexity is nearly linear in the condition number, and polylog in the dimensions $n$ and in the inverse error $\\epsilon^{-1}$. This implies our algorithm is exponentially faster than the best classical algorithm for the same problem if the condition number of $T_n$ is $O(\\textrm{poly}(\\textrm{log}\\,n))$. Since no assumption on the sparseness of $T_n$ is demanded in our algorithm, the algorithm can serve as an example of quantum algorithms for solving non-sparse linear systems.
Current in open quantum systems.
Gebauer, Ralph; Car, Roberto
2004-10-15
We show that a dissipative current component is present in the dynamics generated by a Liouville-master equation, in addition to the usual component associated with Hamiltonian evolution. The dissipative component originates from coarse graining in time, implicit in a master equation, and needs to be included to preserve current continuity. We derive an explicit expression for the dissipative current in the context of the Markov approximation. Finally, we illustrate our approach with a simple numerical example, in which a quantum particle is coupled to a harmonic phonon bath and dissipation is described by the Pauli master equation. PMID:15524960
Heisenberg picture approach to the stability of quantum Markov systems
Pan, Yu, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Miao, Zibo, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au [Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia); Amini, Hadis, E-mail: nhamini@stanford.edu [Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305 (United States); Gough, John, E-mail: jug@aber.ac.uk [Institute of Mathematics and Physics, Aberystwyth University, SY23 3BZ Wales (United Kingdom); Ugrinovskii, Valery, E-mail: v.ugrinovskii@gmail.com [School of Engineering and Information Technology, University of New South Wales at ADFA, Canberra, ACT 2600 (Australia); James, Matthew R., E-mail: matthew.james@anu.edu.au [ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia)
2014-06-15
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
Heisenberg picture approach to the stability of quantum Markov systems
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks
Teleportation in an indivisible quantum system
Kiktenko E.O.
2016-01-01
Full Text Available Teleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding operations and discuss an alternative way of implementation of similar tasks.
Tunneling with dissipation in open quantum systems
Based on the general form of the master equation for open quantum systems the tunneling is considered. Using the path integral technique a simple closed form expression for the tunneling rate through a parabolic barrier is obtained. The tunneling in the open quantum systems strongly depends on the coupling with environment. We found the cases when the dissipation prohibits tunneling through the barrier but decreases the crossing of the barrier for the energies above the barrier. As a particular application, the case of decay from the metastable state is considered
Quantum GIS (QGIS) Geographic Information System Tutorial
Urrutia Fernández, M. Àngels
2014-01-01
The goal of the present Master’s Thesis is to develop a learning tutorial for Lisboa Quantum GIS v.1.8.0 Geographic Information System. The resulting document is intended as a learning tool. This document should be useful to those people who wish to acquire basic skills in the use of Quantum GIS and, at the same time, should provide the user with a picture of what Geographic Information Systems (GIS) are. The skills that this tutorial aims to teach are how to locate and down...
Quantum Hall effect in semiconductor systems with quantum dots and antidots
The integer quantum Hall effect in systems of semiconductor quantum dots and antidots is studied theoretically as a factor of temperature. It is established that the conditions for carrier localization in quantum-dot systems favor the observation of the quantum Hall effect at higher temperatures than in quantum-well systems. The obtained numerical results show that the fundamental plateau corresponding to the transition between the ground and first excited Landau levels can be retained up to a temperature of T ∼ 50 K, which is an order of magnitude higher than in the case of quantum wells. Implementation of the quantum Hall effect at such temperatures requires quantum-dot systems with controllable characteristics, including the optimal size and concentration and moderate geometrical and composition fluctuations. In addition, ordered arrangement is desirable, hence quantum antidots are preferable
Nonequilibrium quantum dynamics in optomechanical systems
Patil, Yogesh Sharad; Cheung, Hil F. H.; Shaffer, Airlia; Wang, Ke; Vengalattore, Mukund
2016-05-01
The thermalization dynamics of isolated quantum systems has so far been explored in the context of cold atomic systems containing a large number of particles and modes. Quantum optomechanical systems offer prospects of studying such dynamics in a qualitatively different regime - with few individually addressable modes amenable to continuous quantum measurement and thermalization times that vastly exceed those observed in cold atomic systems. We have experimentally realized a dynamical continuous phase transition in a quantum compatible nondegenerate mechanical parametric oscillator. This system is formally equivalent to the optical parametric amplifiers whose dynamics have been a subject of intense theoretical study. We experimentally verify its phase diagram and observe nonequilibrium behavior that was only theorized, but never directly observed, in the context of optical parametric amplifiers. We discuss prospects of using nonequilibrium protocols such as quenches in optomechanical systems to amplify weak nonclassical correlations and to realize macroscopic nonclassical states. This work was supported by the DARPA QuASAR program through a Grant from the ARO and the ARO MURI on non-equilibrium manybody dynamics.
Enhancing the capability of controlling quantum systems via ancillary systems
Zhang Ming; Gao Da-Yuan; Dai Hong-Yi; Xie Hong-Wei; Hu De-Wen
2007-01-01
This paper explores the potential of controlling quantum systems by introducing ancillary systems and then performing unitary operation on the resulting composite systems. It generalizes the concept of pure state controllability for quantum systems and establishes the link between the operator controllability of the composite system and the generalized pure state controllability of its subsystem. It is constructively demonstrated that if a composite quantum system can be transferred between any pair of orthonormal pure vectors, then its subsystem is generalized pure-state controllable. Furthermore, the unitary operation and the coherent control can be concretely given to transfer the system from an initial state to the target state. Therefore, these properties may be potentially applied in quantum information,such as manipulating multiple quantum bits and creating entangled pure states. A concrete example has been given to illustrate that a maximally entangled pure state of a quantum system can be generated by introducing an ancillary system and performing open-loop coherent control on the resulting composite system.
Quantum statistical ensemble for emissive correlated systems
Shakirov, Alexey M.; Shchadilova, Yulia E.; Rubtsov, Alexey N.
2016-06-01
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the canonical ensemble which assumes the probability distribution for energy to be of the Boltzmann form. The emergence of this probability distribution is ensured by the detailed balance of the transitions induced by the interaction with the environment. Here we consider relaxation of an open correlated quantum system brought into contact with a reservoir in the vacuum state. We refer to such a system as emissive since particles irreversibly evaporate into the vacuum. The steady state of the system is a statistical mixture of the stable eigenstates. We found that, despite the absence of the detailed balance, the stationary probability distribution over these eigenstates is of the Boltzmann form in each N -particle sector. A quantum statistical ensemble corresponding to the steady state is characterized by different temperatures in the different sectors, in contrast to the Gibbs ensemble. We investigate the transition rates between the eigenstates to understand the emergence of the Boltzmann distribution and find their exponential dependence on the transition energy. We argue that this property of transition rates is generic for a wide class of emissive quantum many-body systems.
An exactly solvable system from quantum optics
Maciejewski, Andrzej J., E-mail: maciejka@astro.ia.uz.zgora.pl [J. Kepler Institute of Astronomy, University of Zielona Góra, Licealna 9, PL-65-417 Zielona Góra (Poland); Przybylska, Maria, E-mail: M.Przybylska@if.uz.zgora.pl [Institute of Physics, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra (Poland); Stachowiak, Tomasz, E-mail: stachowiak@cft.edu.pl [Center for Theoretical Physics PAS, Al. Lotników 32/46, 02-668 Warsaw (Poland)
2015-07-31
We investigate a generalisation of the Rabi system in the Bargmann–Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable. The system has only one irregular singular point at infinity. We show how the quantisation of the model is related to asymptotic behaviour of solutions in a vicinity of this point. The explicit formulae for the spectrum and eigenfunctions of the model follow from an analysis of the Stokes phenomenon. An interpretation of the obtained results in terms of differential Galois group of the system is also given. - Highlights: • New exactly solvable system from quantum optics is found. • Normalisation condition for system in Bargmann representation is used. • Formulae for spectrum and eigenfunctions from analysis of Stokes phenomenon are given.
Exact and non-smooth control of quantum spin systems
Ciaramella, Gabriele
2015-01-01
An efficient and accurate computational framework for solving control problems governed by quantum spin systems is presented. Spin systems are extremely important in modern quantum technologies such as nuclear magnetic resonance spectroscopy, quantum imaging and quantum computing. In these applications, two classes of quantum control problems arise: optimal control problems and exact-controllability problems, with a bilinear con- trol structure. These models correspond to the Schrödinger-Paul...
Strongly Interacting Quantum Systems out of Equilibrium
Kasztelan, Christian
2010-01-01
The main topic of this thesis is the study of many-body effects in strongly correlated one- or quasi one-dimensional condensed matter systems. These systems are characterized by strong quantum and thermal fluctuations, which make mean-field methods fail and demand for a fully numerical approach. Fortunately, a numerical method exist, which allows to treat unusually large one -dimensional system at very high precision. This method is the density-matrix renormalization group method (DMRG), in...
EDITORIAL: CAMOP: Quantum Non-Stationary Systems CAMOP: Quantum Non-Stationary Systems
Dodonov, Victor V.; Man'ko, Margarita A.
2010-09-01
Although time-dependent quantum systems have been studied since the very beginning of quantum mechanics, they continue to attract the attention of many researchers, and almost every decade new important discoveries or new fields of application are made. Among the impressive results or by-products of these studies, one should note the discovery of the path integral method in the 1940s, coherent and squeezed states in the 1960-70s, quantum tunneling in Josephson contacts and SQUIDs in the 1960s, the theory of time-dependent quantum invariants in the 1960-70s, different forms of quantum master equations in the 1960-70s, the Zeno effect in the 1970s, the concept of geometric phase in the 1980s, decoherence of macroscopic superpositions in the 1980s, quantum non-demolition measurements in the 1980s, dynamics of particles in quantum traps and cavity QED in the 1980-90s, and time-dependent processes in mesoscopic quantum devices in the 1990s. All these topics continue to be the subject of many publications. Now we are witnessing a new wave of interest in quantum non-stationary systems in different areas, from cosmology (the very first moments of the Universe) and quantum field theory (particle pair creation in ultra-strong fields) to elementary particle physics (neutrino oscillations). A rapid increase in the number of theoretical and experimental works on time-dependent phenomena is also observed in quantum optics, quantum information theory and condensed matter physics. Time-dependent tunneling and time-dependent transport in nano-structures are examples of such phenomena. Another emerging direction of study, stimulated by impressive progress in experimental techniques, is related to attempts to observe the quantum behavior of macroscopic objects, such as mirrors interacting with quantum fields in nano-resonators. Quantum effects manifest themselves in the dynamics of nano-electromechanical systems; they are dominant in the quite new and very promising field of circuit
Wigner quantum systems (Lie superalgebraic approach)
Palev, T. D.; Stoilova, N. I.
2001-01-01
We present three groups of examples of Wigner Quantum Systems related to the Lie superalgebras $osp(1/6n)$, $sl(1/3n)$ and $sl(n/3)$ and discuss shortly their physical features. In the case of $sl(1/3n)$ we indicate that the underlying geometry is noncommutative.
Quantum chromatic numbers via operator systems
Paulsen, Vern I.; Todorov, Ivan G.
2013-01-01
We define several new types of quantum chromatic numbers of a graph and characterise them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the literature and exhibit a link between them and non-signalling correlation boxes.
Quantum mechanics of a system with confinement
A study is made of the quantum mechanical model of confinement. The spectrum of a system with permanently confined channel is investiogated. A closed analytical expression is obtained for the S-matrix describing the scattering on N levels in the confined channel. The influence of the confined channel on the resonant and Coulomb states in the scattering channel is considered
Nonseparability and noncommutativity in quantum systems
de La Torre, A. C.; Catuogno, P.; Ferrando, S.
1991-02-01
The quantum covariance function is calculated in some EPR-like systems for commuting observables in order to illustrate the nonseparability contribution to the incompatibility between commuting operators. It is shown that an attempt to eliminate the noncommutativity contribution to incompatibility fails in finite-dimensional cases and would require a nonseparable Hilbert space (nonseparable in the mathematical sense).
Lithography system using quantum entangled photons
Williams, Colin (Inventor); Dowling, Jonathan (Inventor); della Rossa, Giovanni (Inventor)
2002-01-01
A system of etching using quantum entangled particles to get shorter interference fringes. An interferometer is used to obtain an interference fringe. N entangled photons are input to the interferometer. This reduces the distance between interference fringes by n, where again n is the number of entangled photons.
Local thermoelectric probes of nonequilibrium quantum systems
Stafford, Charles
A theory of local temperature and voltage measurement in an interacting quantum system far from equilibrium is developed. We prove that a steady-state measurement by a floating thermoelectric probe is unique if it exists. Furthermore, we show that a solution exists provided there is no net local population inversion. In the case of population inversion, the system may be assigned a (unique) negative temperature. An expression for the local entropy of a nonequilibrium quantum system is introduced that, together with the local temperature and voltage, allows for a complete analysis of the local thermodynamics of the thermoelectric processes in the system. The Clausius form of the second law and the third law are shown to hold exactly locally, while the zeroth and first laws are shown to be valid to leading order in the Sommerfeld expansion. The local quantum thermodynamics underlying the enhancement of thermoelectricity by quantum interference is discussed. Work supported by the U.S. Department of Energy, Office of Science, Award No. DE-SC0006699.
System and method for making quantum dots
Bakr, Osman M.
2015-05-28
Embodiments of the present disclosure provide for methods of making quantum dots (QDs) (passivated or unpassivated) using a continuous flow process, systems for making QDs using a continuous flow process, and the like. In one or more embodiments, the QDs produced using embodiments of the present disclosure can be used in solar photovoltaic cells, bio-imaging, IR emitters, or LEDs.
Quantum field theory and multiparticle systems
The use of quantum field theory methods for the investigation of the physical characteristics of the MANY-BODY SYSTEMS is discussed. Mainly discussed is the method of second quantization and the method of the Green functions. Briefly discussed is the method of calculating the Green functions at finite temperatures. (Z.J.)
Quantum mechanics classical results, modern systems, and visualized examples
Robinett, Richard W
2006-01-01
`Quantum Mechanics'' is a comprehensive introduction to quantum mechanics for advanced undergraduate students in physics. It provides the reader with a strong conceptual background in the subject, extensive experience with the necessary mathematical background, as well as numerous visualizations of quantum concepts and phenomena. - ;Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples is a comprehensive introduction to non-relativistic quantum mechanics for advanced undergraduate students in physics and related fields. It provides students with a strong conceptual background in the most important theoretical aspects of quantum mechanics, extensive experience with the mathematical tools required to solve problems, the opportunity to use quantum ideas to confront modern experimental. realizations of quantum systems, and numerous visualizations of quantum concepts and phenomena. Changes from the First Edition include many new discussions of modern quantum systems (such as Bose-Einstein c...
Cui, Ping
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO
Symmetry and stability of open quantum systems
The presentation of the thesis involves an introduction and six chapters. Chapter 1 presents notions and results used in the other chpaters. Chapters 2-6 present our results which are focused on two notions: generalized observable and dynamic semigroup. These notions characterize a specific research domain (set up during the last 10 years) which is currently called quantum mechanics of open systems. The two notions (generalized observable and dynamic semigroup) are mathematically correlated. They belong to the set of completely positive linear applications among observable algebras. This fact, associated with that formulation of quantum mechanics according to which it is a special case of quantum mechanics namely, that for which the observable algebra is commutative, help to understand the similar essence of the results presented in chapter 2-6. Thus, the natural mathematical background has been achieved for our results; it is represented by that category whose objects are the observable algebras and whose morphisms are completely positive linear contractions generating unity within unity. These ideas are extensively presented in the introduction. The fact that the relations between classical mechanics and quantum mechanics can be rigorously treated as positive linear applications between classical observable algebras commutative and quantum observable algebras non-commutative, which are automatically fully positive, has been initially shown in our paper. (author)
Ion-cavity system for quantum networks
Full text: A single atom interacting with a single mode of a cavity allows us to probe the quantum interaction between light and matter. In the context of quantum networks, such a system can provide an interface between stationary and flying qubits, making it possible for single photons to transport quantum information between the network nodes. We study a single 40Ca+ ion trapped inside a high-finesse optical resonator. First, we demonstrate and characterize a single-photon source, in which a vacuum-stimulated Raman process transfers atomic population between two Zeeman states of the ion, creating a single photon in the cavity. We evaluate the photon statistics by measuring the second-order correlation function. Moreover, we obtain the photon temporal profile and investigate the dynamics of the process. Secondly, we perform Raman spectroscopy using the cavity. Residual motion of the ion introduces motional sidebands in the Raman spectrum and thus offers prospects for cavity-assisted cooling. (author)
Quantum-mechanical aspects of classically chaotic driven systems
This paper treats atoms and molecules in laser fields as periodically driven quantum systems. The paper concludes by determining that stochastic excitation is possible in quantum systems with quasiperiodic driving. 17 refs
A Direct Coupling Coherent Quantum Observer for a Single Qubit Finite Level Quantum System
Petersen, Ian R.
2014-01-01
This paper considers the problem of constructing a direct coupling quantum observer for a single qubit finite level quantum system plant. The proposed observer is a single mode linear quantum system which is shown to be able to estimate one of the plant variables in a time averaged sense. A numerical example and simulations are included to illustrate the properties of the observer.
Periodic thermodynamics of open quantum systems
Brandner, Kay; Seifert, Udo
2016-06-01
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
Quantum-cryptography key distribution (QCKD) experiments have been recently reported using polarization-entangled photons. However, in any practical realization, quantum systems suffer from either unwanted or induced interactions with the environment and the quantum measurement system, showing up as quantum and, ultimately, statistical noise. In this paper, we investigate how an ideal polarization entanglement in spontaneous parametric down-conversion (SPDC) suffers quantum noise in its practical implementation as a secure quantum system, yielding errors in the transmitted bit sequence. Since all SPDC-based QCKD schemes rely on the measurement of coincidence to assert the bit transmission between the two parties, we bundle up the overall quantum and statistical noise in an exhaustive model to calculate the accidental coincidences. This model predicts the quantum-bit error rate and the sifted key and allows comparisons between different security criteria of the hitherto proposed QCKD protocols, resulting in an objective assessment of performances and advantages of different systems
An impurity-induced gap system as a quantum data bus for quantum state transfer
Chen, Bing, E-mail: chenbingphys@gmail.com [Department of Applied Physics, College of Electronics, Communication and Physics, Shandong University of Science and Technology, Qingdao 266590 (China); Li, Yong [Beijing Computational Science Research Center, Beijing 100084 (China); Song, Z. [School of Physics, Nankai University, Tianjin 300071 (China); Sun, C.-P. [Beijing Computational Science Research Center, Beijing 100084 (China)
2014-09-15
We introduce a tight-binding chain with a single impurity to act as a quantum data bus for perfect quantum state transfer. Our proposal is based on the weak coupling limit of the two outermost quantum dots to the data bus, which is a gapped system induced by the impurity. By connecting two quantum dots to two sites of the data bus, the system can accomplish a high-fidelity and long-distance quantum state transfer. Numerical simulations for finite system show that the numerical and analytical results of the effective coupling strength agree well with each other. Moreover, we study the robustness of this quantum communication protocol in the presence of disorder in the couplings between the nearest-neighbor quantum dots. We find that the gap of the system plays an important role in robust quantum state transfer.
From classical to quantum theory of open systems
The paper presents a short survey of some results concerning the physical interpretation of the basic equations for quantum open systems. The concept of continuous medium for quantum systems is introduced. From this point of view, the question of completeness of a description and hidden parameters (scale) for quantum open systems are considered. The Heisenberg uncertainty principle in the physics of open quantum systems is represented
Security of practical quantum key distribution systems
Jain, Nitin
2015-02-24
This thesis deals with practical security aspects of quantum key distribution (QKD) systems. At the heart of the theoretical model of any QKD system lies a quantum-mechanical security proof that guarantees perfect secrecy of messages - based on certain assumptions. However, in practice, deviations between the theoretical model and the physical implementation could be exploited by an attacker to break the security of the system. These deviations may arise from technical limitations and operational imperfections in the physical implementation and/or unrealistic assumptions and insufficient constraints in the theoretical model. In this thesis, we experimentally investigate in depth several such deviations. We demonstrate the resultant vulnerabilities via proof-of-principle attacks on a commercial QKD system from ID Quantique. We also propose countermeasures against the investigated loopholes to secure both existing and future QKD implementations.
Security of practical quantum key distribution systems
This thesis deals with practical security aspects of quantum key distribution (QKD) systems. At the heart of the theoretical model of any QKD system lies a quantum-mechanical security proof that guarantees perfect secrecy of messages - based on certain assumptions. However, in practice, deviations between the theoretical model and the physical implementation could be exploited by an attacker to break the security of the system. These deviations may arise from technical limitations and operational imperfections in the physical implementation and/or unrealistic assumptions and insufficient constraints in the theoretical model. In this thesis, we experimentally investigate in depth several such deviations. We demonstrate the resultant vulnerabilities via proof-of-principle attacks on a commercial QKD system from ID Quantique. We also propose countermeasures against the investigated loopholes to secure both existing and future QKD implementations.
Kinetic and thermodynamic temperatures in quantum systems
Gagliardi, Alessio; Pecchia, Alessandro; Di Carlo, Aldo
2013-01-01
In this work we present a formalism to describe non equilibrium conditions in systems with a discretized energy spectrum, such as quantum systems. We develop a formalism based on a combination of Gibbs-Shannon entropy and information thermodynamics that arrives to a generalization of the De-Brujin identity applicable to discrete and non-symmetric distributions. This allows to define the concept of a thermodynamic temperature with a different, albeit complementary meaning to the equilibrium ki...
Chiral quantum mechanics (CQM) for antihydrogen systems
Van hooydonk, G.
2005-01-01
A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a permutation of reference frames. With chiral quantum mechanics (CQM), the theoretical ban on natural antiH must be lifted as soon as possible.
Simulating open quantum systems by applying SU(4) to quantum master equations
Xu, Minghui; Tieri, D. A.; Holland, M J
2013-01-01
We show that open quantum systems of two-level atoms symmetrically coupled to a single-mode photon field can be efficiently simulated by applying a SU(4) group theory to quantum master equations. This is important since many foundational examples in quantum optics fall into this class. We demonstrate the method by finding exact solutions for many-atom open quantum systems such as lasing and steady state superradiance.
Compact quantum systems and the Pauli data problem
Bracken, A.J. (Univ. of Queensland, Brisbane (Australia)); Fawcett, R.J.B. (Queensland Univ. of Technology, Brisbane (Australia))
1993-02-01
Compact quantum systems have underlying compact kinematical Lie algebras, in contrast to familiar noncompact quantum systems built on the Weyl-Heisenberg algebra. Pauli asked in the latter case: to what extent does knowledge of the probability distributions in coordinate and momentum space determine the state vector The analogous questions for compact quantum system is raised, and some preliminary results are obtained.
Quantum mechanics in general quantum systems (II): Perturbation theory
Wang, A M
2006-01-01
We propose an improved scheme of perturbation theory based on our exact solution [See: An Min Wang, quant-ph/0611217] in general quantum systems independent of time. Our elementary start-point is to introduce the perturbing parameter as late as possible. Our main skills are Hamiltonian redivision so as to overcome a flaw of the usual perturbation theory, and the perturbing Hamiltonian matrix product decomposition in order to separate the contraction and anti-contraction terms. Our calculational technology is the limit process for eliminating apparent divergences. Our central idea is ``dynamical rearrangement and summation" for the sake of the partial contributions from the high order even all order approximations absorbed in our perturbed solution. Consequently, we obtain the improved forms of the zeroth, first, second and third order perturbed solutions absorbing the partial contributions from the high order even all order approximations of perturbation. Then we deduce the improved transition probability. In...
Topological Excitations in Double-Layer Quantum Hall systems
Moon, Kyungsun
1996-01-01
Double-layer quantum Hall systems with spontaneous broken symmetry can exhibit a novel manybody quantum Hall effect due to the strong interlayer coherence. When the layer separation becomes close to the critical value, quantum fluctuations can destroy the interlayer coherence and the quantum Hall effect will disappear. We calculate the renormalized isospin stiffness $\\rho_s$ due to quantum fluctuations within the Hartree-Fock-RPA formalism. The activation energy of the topological excitations...
Mathematical Structure in Quantum Systems and applications
This volume contains most of the contributions presented at the Conference 'Mathematical Structures in Quantum Systems and applications', held at the Centro de Ciencias de Benasque 'Pedro Pascual', Benasque (Spain) from 8-14 July 2012. The aim of the Conference was to bring together physicists working on different applications of mathematical methods to quantum systems in order to enable the different communities to become acquainted with other approaches and techniques that could be used in their own fields of expertise. We concentrated on three main subjects: – the geometrical description of Quantum Mechanics; – the Casimir effect and its mathematical implications; – the Quantum Zeno Effect and Open system dynamics. Each of these topics had a set of general lectures, aimed at presenting a global view on the subject, and other more technical seminars. We would like to thank all participants for their contribution to creating a wonderful scientific atmosphere during the Conference. We would especially like to thank the speakers and the authors of the papers contained in this volume, the members of the Scientific Committee for their guidance and support and, of course, the referees for their generous work. Special thanks are also due to the staff of the Centro de Ciencias de Benasque 'Pedro Pascual' who made this successful meeting possible. On behalf of the organising committee and the authors we would also like to acknowledge the partial support provided by the ESF-CASIMIR network ('New Trends and Applications of the Casimir Effect'), the QUITEMAD research Project (“Quantum technologies at Madrid”, Ref. Comunidad de Madrid P2009/ESP-1594), the MICINN Project (MTM2011-16027-E) and the Government from Arag´on (DGA) (DGA, Department of Industry and Innovation and the European Social Fund, DGA-Grant 24/1) who made the Conference and this Proceedings volume possible.
Quantum Transport in Strongly Correlated Systems
Bohr, Dan
2007-01-01
In the past decade there has been a trend towards studying ever smaller devices. Improved experimental techniques have made new experiments possible, one class of which is electron transport through molecules and artificially manufactured structures like quantum dots. In this type of systems...... screening plays a much less significant role than in bulk systems due to the reduced size of the objects, therefore making it necessary to consider the importance of correlations between electrons. The work presented in this thesis deals with quantum transport through strongly correlated systems using the...... describes the leads in momentum-space. We benchmark each of these schemes against exact Greens function results for the conductance in the non-interacting limit, thus demonstrating the accuracy of the lead descriptions. We first use the DMRG implementations to calculate the conductance of an interacting...
Focus on coherent control of complex quantum systems
Whaley, Birgitta; Milburn, Gerard
2015-10-01
The rapid growth of quantum information sciences over the past few decades has fueled a corresponding rise in high profile applications in fields such as metrology, sensors, spintronics, and attosecond dynamics, in addition to quantum information processing. Realizing this potential of today’s quantum science and the novel technologies based on this requires a high degree of coherent control of quantum systems. While early efforts in systematizing methods for high fidelity quantum control focused on isolated or closed quantum systems, recent advances in experimental design, measurement and monitoring, have stimulated both need and interest in the control of complex or large scale quantum systems that may also be coupled to an interactive environment or reservoir. This focus issue brings together new theoretical and experimental work addressing the formulation and implementation of quantum control for a broad range of applications in quantum science and technology today.
Quantum decoherence in the theory of open systems
Isar, A.
2007-01-01
In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We calculate also the decoherence time scale and analyze the transition from quantum to classical behaviour of the considered system.
General System theory, Like-Quantum Semantics and Fuzzy Sets
Licata, Ignazio
2007-01-01
It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for systemics . In conclusion we...
Quantum Annealing and Quantum Fluctuation Effect in Frustrated Ising Systems
Tanaka, Shu; Tamura, Ryo
2012-01-01
Quantum annealing method has been widely attracted attention in statistical physics and information science since it is expected to be a powerful method to obtain the best solution of optimization problem as well as simulated annealing. The quantum annealing method was incubated in quantum statistical physics. This is an alternative method of the simulated annealing which is well-adopted for many optimization problems. In the simulated annealing, we obtain a solution of optimization problem b...
Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow
Sapin, O; Weigert, S
2005-01-01
We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperbolicity properties of almost-periodic quantum parametric oscillators and we show that their upper Lyapunov exponents are positive and equal to the Lyapunov exponent of the corresponding classical parametric oscillators. As second example, we show that the configurational quantum cat system satisfies quantum Anosov properties.
Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations
Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu
2013-01-01
In this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.
Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2014-01-01
In this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.
Quantum response of dephasing open systems
We develop a theory of adiabatic response for open systems governed by Lindblad evolutions. The theory determines the dependence of the response coefficients on the dephasing rates and allows for residual dissipation even when the ground state is protected by a spectral gap. We give the quantum response a geometric interpretation in terms of Hilbert space projections: for a two-level system and, more generally, for systems with a suitable functional form of the dephasing, the dissipative and non-dissipative parts of the response are linked to a metric and to a symplectic form. The metric is the Fubini-Study metric and the symplectic form is the adiabatic curvature. When the metric and symplectic structures are compatible, the non-dissipative part of the inverse matrix of response coefficients turns out to be immune to dephasing. We give three examples of physical systems whose quantum states induce compatible metric and symplectic structures on control space: qubit, coherent states and a model of the integer quantum Hall effect.
Nonequilibrium representative ensembles for isolated quantum systems
An isolated quantum system is considered, prepared in a nonequilibrium initial state. In order to uniquely define the system dynamics, one has to construct a representative statistical ensemble. From the principle of least action it follows that the role of the evolution generator is played by a grand Hamiltonian, but not merely by its energy part. A theorem is proved expressing the commutators of field operators with operator products through variational derivatives of these products. A consequence of this theorem is the equivalence of the variational equations for field operators with the Heisenberg equations for the latter. A finite quantum system cannot equilibrate in the strict sense. But it can tend to a quasi-stationary state characterized by ergodic averages and the appropriate representative ensemble depending on initial conditions. Microcanonical ensemble, arising in the eigenstate thermalization, is just a particular case of representative ensembles. Quasi-stationary representative ensembles are defined by the principle of minimal information. The latter also implies the minimization of an effective thermodynamic potential. -- Highlights: → The evolution of a nonequilibrium isolated quantum system is considered. → The grand Hamiltonian is shown to be the evolution generator. → A theorem is proved connecting operator commutators with variational derivatives. → Quasi-stationary states are described by representative ensembles. → These ensembles, generally, depend on initial conditions.
Multimode optomechanical system in the quantum regime
Nielsen, William H P; Møller, Christoffer B; Polzik, Eugene S; Schliesser, Albert
2016-01-01
We realise a simple and robust optomechanical system with a multitude of long-lived ($Q>10^7$) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate ($96~\\mathrm{kHz}$) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures ($10\\,\\mathrm{K}$). Reaching this quantum regime entails, i.~a., quantum measurement backaction exceeding thermal forces, and thus detectable optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths $\\lesssim 90\\,\\mathrm{ kHz}$. The multi-mode nature of the employed membrane and Fabry-Perot resonators lends itself to hybrid entanglement schemes involving multiple electromagnetic, mechanical, and spin degrees of freedom.
Quantum phases and dynamics of geometric phase in a quantum spin chain system under linear quench
Sarkar, Sujit
2011-01-01
We study the quantum phases of anisotropic XY spin chain system in presence and absence of adiabatic quench. A connection between geometric phase and criticality is established from the dynamical behaviour of the geometric phase for a quench induced quantum phase transition in a quantum spin chain. We predict XX criticality associated with a sequence of non-contractible geometric phases.
Formulation and Application of Quantum Monte Carlo Method to Fractional Quantum Hall Systems
Suzuki, Sei; Nakajima, Tatsuya
2003-01-01
Quantum Monte Carlo method is applied to fractional quantum Hall systems. The use of the linear programming method enables us to avoid the negative-sign problem in the Quantum Monte Carlo calculations. The formulation of this method and the technique for avoiding the sign problem are described. Some numerical results on static physical quantities are also reported.
One-Way Quantum Deficit for 2 ⊗ d Systems
Ye, Biao-Liang; Fei, Shao-Ming
2016-08-01
We investigate one-way quantum deficit for 2 ⊗ d systems. Analytical expressions of one-way quantum deficit under both von Neumann measurement and weak measurement are presented. As an illustration, qubit-qutrit systems are studied in detail. It is shown that there exists non-zero one-way quantum deficit even quantum entanglement vanishes. Moreover, one-way quantum deficit via weak measurement turns out to be weaker than that via von Neumann measurement. The dynamics of entanglement and one-way quantum deficit under dephasing channels is also investigated.
The Quantum as an Emergent System
Groessing, Gerhard; Pascasio, Johannes Mesa; Schwabl, Herbert; 10.1088/1742-6596/361/1/012008
2012-01-01
Double slit interference is explained with the aid of what we call "21stcentury classical physics". We model a particle as an oscillator ("bouncer") in a thermal context, which is given by some assumed "zero-point" field of the vacuum. In this way, the quantum is understood as an emergent system, i.e., a steady-state system maintained by a constant throughput of (vacuum) energy. To account for the particle's thermal environment, we introduce a "path excitation field", which derives from the thermodynamics of the zero-point vacuum and which represents all possible paths a particle can take via thermal path fluctuations. The intensity distribution on a screen behind a double slit is calculated, as well as the corresponding trajectories and the probability density current. Further, particular features of the relative phase are shown to be responsible for nonlocal effects not only in ordinary quantum theory, but also in our classical approach.
Bilayer Quantum Hall Systems: Spin-Pseudospin Symmetry Breaking and Quantum Phase Transitions
Sarma, Sankar Das; Demler, Eugene
2000-01-01
We discuss and review recent advances in our understaning of quantum Hall systems where additional quantum numbers associated with spin and/or layer (pseudospin) indices play crucial roles in creating exotic quantum phases. Among the novel quantum phases we discuss are the recently discovered canted antiferromagnetic phase, the spontaneous interlayer coherent phase, and various spin Bose glass phases. We describe the theoretical models used in studying these novel phases and the various exper...
General Properties of Overlap Operators in Disordered Quantum Spin Systems
Itoi, C.
2016-04-01
We study short-range quantum spin systems with Gaussian disorder. We obtain quantum mechanical extensions of the Ghirlanda-Guerra identities. We discuss properties of overlap spin operators with these identities.
Li, Jun; Lu, Dawei; Luo, Zhihuang; Laflamme, Raymond; Peng, Xinhua; Du, Jiangfeng
2016-07-01
Precisely characterizing and controlling realistic quantum systems under noises is a challenging frontier in quantum sciences and technologies. In developing reliable controls for open quantum systems, one is often confronted with the problem of the lack of knowledge on the system controllability. The purpose of this paper is to give a numerical approach to this problem, that is, to approximately compute the reachable set of states for coherently controlled quantum Markovian systems. The approximation consists of setting both upper and lower bounds for system's reachable region of states. Furthermore, we apply our reachability analysis to the control of the relaxation dynamics of a two-qubit nuclear magnetic resonance spin system. We implement some experimental tasks of quantum state engineering in this open system at a near optimal performance in view of purity: e.g., increasing polarization and preparing pseudopure states. These results demonstrate the usefulness of our theory and show interesting and promising applications of environment-assisted quantum dynamics.
Open quantum systems and random matrix theory
A simple model for open quantum systems is analyzed with RMT. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the level spacing, width distribution and Δ3(L) statistic are examined as a function of the strength of this coupling. The usual super-radiant state is observed, and it is seen that as it is formed, the level spacing and Δ3(L) statistic exhibit the signatures of missed levels
Open quantum systems and Random Matrix Theory
Mulhall, Declan
2014-01-01
A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the $\\Delta_3(L)$ statistic, width distribution and level spacing are examined as a function of the strength of this coupling. A super-radiant transition is observed, and it is seen that as it is formed, the level spacing and $\\Delta_3(L)$ statistic exhibit the signat...
Ji Ying-Hua; Hu Ju-Ju; Hu Yan
2012-01-01
We investigate the influence of environmental decoherence on the dynamics of a coupled qubit system and quantum correlation.We analyse the relationship between concurrence and the degree of initial entanglement or the purity of initial quantum state,and also their relationship with quantum discord.The results show that the decrease of the purity of an initial quantum state can induce the attenuation of concurrence or quantum discord,but the attenuation of quantum discord is obviously slower than the concurrence's,correspondingly the survival time of quantum discord is longer.Further investigation reveals that the robustness of quantum discord and concurrence relies on the entanglement degree of the initial quantum state.The higher the degree of entanglement,the more robust the quantum discord is than concurrence.And the reverse is equally true.Birth and death happen to quantum discord periodically and a newborn quantum discord comes into being under a certain condition,so does the concurrence.
Experimental quantum teleportation of a two-qubit composite system
无
2006-01-01
@@ Quantum teleportation, a way to state transfer the of a quantum system from one location to another, is central to quantum communication and plays an important role in a number of quantum computation protocols.Although significant experimental advances have been made in teleportation of single qubits (photons and ions), large scale applications require the transfer of composite systems containing two or more qubits, which has remained a real experimental challenge.
Quantum phase transition and entanglement in Li atom system
2008-01-01
By use of the exact diagonalization method, the quantum phase transition and en- tanglement in a 6-Li atom system are studied. It is found that entanglement appears before the quantum phase transition and disappears after it in this exactly solvable quantum system. The present results show that the von Neumann entropy, as a measure of entanglement, may reveal the quantum phase transition in this model.
Huge Quantum Gravity Effects in the Solar System
Page, Don N.
2010-01-01
Normally one thinks of the motion of the planets around the Sun as a highly classical phenomenon, so that one can neglect quantum gravity in the Solar System. However, classical chaos in the planetary motion amplifies quantum uncertainties so that they become very large, giving huge quantum gravity effects. For example, evidence suggests that Uranus may eventually be ejected from the Solar System, but quantum uncertainties would make the direction at which it leaves almost entirely uncertain,...
Quantum Information Biology: From Theory of Open Quantum Systems to Adaptive Dynamics
Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro
This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB re ects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.
Quartz-superconductor quantum electromechanical system
Woolley, Matt; Emzir, Muhammad; Milburn, Gerard; Jerger, Markus; Goryachev, Maxim; Tobar, Mike; Fedorov, Arkady
Quartz bulk acoustic wave oscillators support mechanical modes with very high resonance frequencies and extremely high quality factors. As such, they provide an appealing platform for quantum optics experiments with phonons, gravitational wave detection, and tests of quantum mechanics. We propose to cool and measure the motion of a quartz oscillator using a transmon, with the coupling mediated by a tuneable superconducting LC circuit. The mechanical motion (~250MHz) is resonantly coupled to the LC circuit (~250MHz) by a piezoelectric interaction, the LC circuit is coupled to the transmon (~8GHz) via sideband transitions, and there is a smaller direct coupling between the quartz oscillator and the transmon. By driving the transmon on its red sideband, the mechanical and electrical oscillators may be cooled close to their quantum ground state. By observing the fluorescence of the qubit, the occupations of the oscillators may be determined via the motional sidebands they induce. A minimal model of this system consists of a qubit coupled to two oscillators, which are themselves mutually coupled. The steady-state of the system and the qubit fluorescence spectrum are evaluated analytically using a perturbative projection operator technique, and verified numerically.
Colloquium: Non-Markovian dynamics in open quantum systems
Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano
2016-04-01
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of
Quantum statistical gravity: time dilation due to local information in many-body quantum systems
Sels, Dries; Wouters, Michiel
2016-01-01
We propose a generic mechanism for the emergence of a gravitational potential that acts on all classical objects in a quantum system. Our conjecture is based on the analysis of mutual information in many-body quantum systems. Since measurements in quantum systems affect the surroundings through entanglement, a measurement at one position reduces the entropy in its neighbourhood. This reduction in entropy can be described by a local temperature, that is directly related to the gravitational po...
A kicked quantum system including the continuum
The behaviour of a quantum particle in a separable one-term potential with three-dimensional form factor is investigated under the influence of an external force which alters the potential strength periodically or quasiperiodically. The unperturbed system possesses one bound state and a continuum of scattering states which has treated almost analytically. First numerical results, fully including the emission channel, indicate, for certain parameter combinations with commensurate or incommensurate frequency ratios, either a regular or an irregular dynamical behaviour of the system. 17 refs.; 3 figs
Many-body Wigner quantum systems
We present examples of many-body Wigner quantum systems. The position and the momentum operators RA and PA, A = 1, ..., n + 1, of the particles are noncanonical and are chosen so that Heisenberg and the Hamiltonian equations are identical. The spectrum of the energy with respect to the centre of mass is equidistant and has finite number of energy levels. The composite system is spread in a small volume around the centre of mass and within it the geometry is noncommutative. The underlying statistics is an exclusion statistics. (author). 23 refs
Parallel decoherence in composite quantum systems
M Dugići; J Jeknić-Dugić
2012-08-01
For the standard quantum Brownian motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard Brownian particle, we show that there is at least another system undergoing the dynamics described by the QBM model. We do this by selecting the two mutually irreducible, global structures (decompositions into subsystems) of the composite system of the QBM model. The generalization of this observation is a new, challenging task in the foundations of the decoherence theory. We do not place our findings in any interpretational context.
Effective operator formalism for open quantum systems
Reiter, Florentin; Sørensen, Anders Søndberg
2012-01-01
We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution...... involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method...
Constructing quantum games from a system of Bell's inequalities
Iqbal, Azhar
2009-01-01
We report constructing quantum games directly from a system of Bell's inequalities using Arthur Fine's analysis published in early 1980s. This analysis showed that such a system of inequalities forms a set of both necessary and sufficient conditions required to find a joint distribution function compatible with a given set of joint probabilities, in terms of which the system of Bell's inequalities is usually expressed. Using the setting of a quantum correlation experiment for playing a quantum game, and considering the examples of Prisoners' Dilemma and Matching Pennies, we argue that this approach towards constructing quantum games addresses well known criticism of quantum games.
Quantum Rotational Effects in Nanomagnetic Systems
O'Keeffe, Michael F.
Quantum tunneling of the magnetic moment in a nanomagnet must conserve the total angular momentum. For a nanomagnet embedded in a rigid body, reversal of the magnetic moment will cause the body to rotate as a whole. When embedded in an elastic environment, tunneling of the magnetic moment will cause local elastic twists of the crystal structure. In this thesis, I will present a theoretical study of the interplay between magnetization and rotations in a variety of nanomagnetic systems which have some degree of rotational freedom. We investigate the effect of rotational freedom on the tunnel splitting of a nanomagnet which is free to rotate about its easy axis. Calculating the exact instanton of the coupled equations of motion shows that mechanical freedom of the particle renormalizes the easy axis anisotropy, increasing the tunnel splitting. To understand magnetization dynamics in free particles, we study a quantum mechanical model of a tunneling spin embedded in a rigid rotor. The exact energy levels for a symmetric rotor exhibit first and second order quantum phase transitions between states with different values the magnetic moment. A quantum phase diagram is obtained in which the magnetic moment depends strongly on the moments of inertia. An intrinsic contribution to decoherence of current oscillations of a flux qubit must come from the angular momentum it transfers to the surrounding body. Within exactly solvable models of a qubit embedded in a rigid body and an elastic medium, we show that slow decoherence is permitted if the solid is macroscopically large. The spin-boson model is one of the simplest representations of a two-level system interacting with a quantum harmonic oscillator, yet has eluded a closed-form solution. I investigate some possible approaches to understanding its spectrum. The Landau-Zener dynamics of a tunneling spin coupled to a torsional resonator show that for certain parameter ranges the system exhibits multiple Landau-Zener transitions
Integrable quantum Stäckel systems
The Stäckel separability of a Hamiltonian system is well known to ensure existence of a complete set of Poisson commuting integrals of motion quadratic in the momenta. We consider a class of Stäckel separable systems where the entries of the Stäckel matrix are monomials in the separation variables. We show that the only systems in this class for which the integrals of motion arising from the Stäckel construction keep commuting after quantization are, up to natural equivalence transformations, the so-called Benenti systems. Moreover, it turns out that the latter are the only quantum separable systems in the class under study.
Integrable quantum Stäckel systems
Błaszak, Maciej, E-mail: blaszakm@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland); Domański, Ziemowit, E-mail: ziemowit@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland); Sergyeyev, Artur, E-mail: Artur.Sergyeyev@math.slu.cz [Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava (Czech Republic); Szablikowski, Błażej M., E-mail: bszablik@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland)
2013-11-15
The Stäckel separability of a Hamiltonian system is well known to ensure existence of a complete set of Poisson commuting integrals of motion quadratic in the momenta. We consider a class of Stäckel separable systems where the entries of the Stäckel matrix are monomials in the separation variables. We show that the only systems in this class for which the integrals of motion arising from the Stäckel construction keep commuting after quantization are, up to natural equivalence transformations, the so-called Benenti systems. Moreover, it turns out that the latter are the only quantum separable systems in the class under study.
Topological entanglement entropy in bilayer quantum Hall systems
Chung, Myung-Hoon
2013-01-01
We calculate the topological entanglement entropy in bilayer quantum Hall systems, dividing the set of quantum numbers into four parts. This topological entanglement entropy allows us to draw a phase diagram in the parameter space of layer separation and tunneling amplitude. We perform the finite size scaling analysis of the topological entanglement entropy in order to see the quantum phase transition clearly.
A toy model of a macroscopic quantum coherent system
This paper deals with macroscopic quantum coherence while using only basic quantum mechanics. A square double well is used to illustrate Leggett–Caldeira oscillations. The effect of thermal radiation on two-level systems is discussed. The concept of decoherence is introduced at an elementary level. Reference values are deduced for the energy, temperature and time scales involved in macroscopic quantum coherence. (paper)
Comparison of quantum discord and relative entropy in some bipartite quantum systems
Mahdian, M.; Arjmandi, M. B.
2016-04-01
The study of quantum correlations in high-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the quantum state to the closest classical-classical state. In particular, we establish relations between relative entropy and quantum discord quantifiers obtained by means of orthogonal projection measurements. We show that for symmetrical X-states density matrices the quantum discord is equal to relative entropy. At the end of paper, various examples of X-states such as two-qubit and qubit-qutrit have been demonstrated.
Characterizing and Quantifying Frustration in Quantum Many-Body Systems
Giampaolo, S. M.; Gualdi, G.; A. Monras; Illuminati, F.
2011-01-01
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical...
The transition to chaos conservative classical systems and quantum manifestations
Reichl, Linda E
2004-01-01
This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes Specific discussions include • Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior • Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems • Random matrix theory and supersymmetry The book is divided into several parts Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapt...
Complex flows in granular and quantum systems
Herrera, Mark Richard
In this thesis we investigate three problems involving complex flows in granular and quantum systems. (a) We first study the dynamics of granular particles in a split-bottom shear cell experiment. We utilize network theory to quantify the dynamics of the granular system at the mesoscopic scale. We find an apparent phase transition in the formation of a giant component of broken links as a function of applied shear. These results are compared to a numerical model where breakages are based on the amount of local stretching in the granular pile. (b) Moving to quantum mechanical systems, we study revival and echo phenomena in systems of anharmonically confined atoms, and find a novel phenomena we call the "pre-revival echo". We study the effect of size and symmetry of the perturbations on the various echoes and revivals, and form a perturbative model to describe the phenomena. We then model the effect of interactions using the Gross-Pitaevskii Equation and study interactions' effect on the revivals. (c) Lastly, we continue to study the effect of interactions on particles in weakly anharmonic traps. We numerically observe a "dynamical localization" phenomena in the presence of both anharmonicity and interactions. States may remain localized or become spread out in the potential depending on the strength and sign of the anharmonicity and interactions. We formulate a model for this phenomena in terms of a classical phase space.
We present the experimental observation of the effects of macroscopic quantum tunnelling in a SQUID device, consisting of a rf SQUID coupled to a readout system based on a dc SQUID sensor. Data on the decay rate from the metastable flux states of a rf SQUID are reported, both in the classical and quantum regimes. The low dissipation level and the good insulation of the probe from external noise are encouraging in view of building a macroscopic quantum coherent system
Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow
Sapin, O.; Jauslin, H. R.; Weigert, S.
2005-01-01
We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperbolicity properties of almost-periodic quantum parametric oscillators and we show that their upper Lyapu...
Some aspects of quantum entanglement for CAR systems
Moriya, Hajime
2001-01-01
We study quantum entanglement for CAR systems. Since the subsystems of disjoint regions are not independent for CAR systems, there are some distinct features of quantum entanglement which cannot be observed in tensor product systems. We show the failure of triangle inequality of von Neumann and the possible increase of entanglement degree under operations done in a local region for a bipartite CAR system.
Quantum MIMO n-Systems and Conditions for Stability
Mansourbeigi, Seyed M H
2009-01-01
In this paper we present some conditions for the (strong) stabilizability of an n-D Quantum MIMO system P(X). It contains two parts. The first part is to introduce the n-D Quantum MIMO systems where the coefficients vary in the algebra of Q-meromorphic functions. Then we introduce some conditions for the stabilizability of these systems. The second part is to show that this Quantum system has the n-D system as its quantum limit and the results for the SISO,SIMO,MISO,MIMO are obtained again as special cases.
Superconducting system for adiabatic quantum computing
We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose a scheme and the first realization of an experimental device suitable for verifying the theoretical results
The Dalton quantum chemistry program system
Aidas, Kestutis; Angeli, Celestino; Bak, Keld Lars;
2014-01-01
Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self-consistent-field, Møller–Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide vari......-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms....
Scattering properties of an open quantum system
We study the scattering properties of an open quantum system, in terms of the complex poles of the analytically continued energy Green's function. We use a model for which many dynamical properties can be expressed analytically. We first study particle wave scattering and compute the Wigner delay times. Then, using perturbation theory, we compute the photodetachment rate due to a weak time-periodic electric field. In addition, we show that the model we use qualitatively reproduces several features of the experimentally obtained photodetachment cross section of H- ions and gives interesting insight into the mechanism underlying the photodetachment of H- ions. (c) 2000 The American Physical Society
Optimal dynamics for quantum-state and entanglement transfer through homogeneous quantum systems
The capability of faithfully transmit quantum states and entanglement through quantum channels is one of the key requirements for the development of quantum devices. Different solutions have been proposed to accomplish such a challenging task, which, however, require either an ad hoc engineering of the internal interactions of the physical system acting as the channel or specific initialization procedures. Here we show that optimal dynamics for efficient quantum-state and entanglement transfer can be attained in generic quantum systems with homogeneous interactions by tuning the coupling between the system and the two attached qubits. We devise a general procedure to determine the optimal coupling, and we explicitly implement it in the case of a channel consisting of a spin-(1/2)XY chain. The quality of quantum-state and entanglement transfer is found to be very good and, remarkably, almost independent of the channel length.
Measuring entanglement entropy in a quantum many-body system.
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems. PMID:26632587
Quantum Integrable Systems from Conformal Blocks
Chen, Heng-Yu
2016-01-01
In this note, we extend the striking connections between quantum integrable systems and conformal blocks recently found in http://arxiv.org/abs/1602.01858 in several directions. First, we explicitly demonstrate that the action of quartic conformal Casimir operator on general d-dimensional scalar conformal blocks, can be expressed in terms of certain combinations of commuting integrals of motions of the two particle hyperbolic BC2 Calogero-Sutherland system. The permutation and reflection properties of the underlying Dunkl operators play crucial roles in establishing such a connection. Next, we show that the scalar superconformal blocks in SCFTs with four and eight supercharges and suitable chirality constraints can also be identified with the eigenfunctions of the same Calogero-Sutherland system, this demonstrates the universality of such a connection. Finally, we observe that the so-called "seed" conformal blocks for constructing four point functions for operators with arbitrary space-time spins in four dime...
Asymptotically open quantum systems; Asymptotisch offene Quantensysteme
Westrich, M.
2008-04-15
In the present thesis we investigate the structure of time-dependent equations of motion in quantum mechanics.We start from two coupled systems with an autonomous equation of motion. A limit, in which the dynamics of one of the two systems has a decoupled evolution and imposes a non-autonomous evolution for the second system is identified. A result due to K. Hepp that provides a classical limit for dynamics turns out to be part and parcel for this limit and is generalized in our work. The method introduced by J.S. Howland for the solution of the time-dependent Schroedinger equation is interpreted as such a limit. Moreover, we associate our limit with the modern theory of quantization. (orig.)
Level statistics for quantum Hall systems
Level statistics for two classes of disordered systems at criticality are analyzed in terms of different realizations of the Chalker-Coddington network model. These include: 1) Re-examination of the standard U(1) model describing dynamics of electrons on the lowest Landau level in the quantum Hall effect, where it is shown that after proper local unfolding the nearest-neighbor spacing distribution (NNSD) at the critical energy follows the Wigner surmise for Gaussian unitary ensembles (GUE). 2) Quasi-particles in disordered superconductors with broken time reversal and spin rotation invariance (in the language of random matrix theory this system is a representative of symmetry class D in the classification scheme of Altland and Zirnbauer). Here again the NNSD obeys the Wigner surmise for GUE, reflecting therefore only 'basic' discrete symmetries of the system (time reversal violation) and ignoring particle-hole symmetries and other finer details (criticality). In the localized regime level repulsion is suppressed
On synthesis of linear quantum stochastic systems by pure cascading
Nurdin, Hendra I
2010-01-01
Recently, it has been demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simple one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, realizations by pure cascading, without a direct interaction Hamiltonian, would be much simpler to implement and this raises the natural question of what class of linear quantum stochastic systems are realizable by cascading alone. This paper gives a precise characterization of this class of linear quantum stochastic systems and then it is proved that, in the weaker sense of transfer function realizability, all passive linear quantum stochastic systems belong to this class. A constructive example is given to show the transfer function realization of a two degrees of freedom passive linear quantum stochastic system by pure cascading.
Characterizing and quantifying frustration in quantum many-body systems.
Giampaolo, S M; Gualdi, G; Monras, A; Illuminati, F
2011-12-23
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration. PMID:22243147
Probability representation of kinetic equation for open quantum system
Man'ko, V I; Shchukin, E V
2003-01-01
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
Quantum systems related to root systems and radial parts of Laplace operators
Olshanetsky, M. A.; Perelomov, A.M.
2002-01-01
The relation between quantum systems associated to root systems and radial parts of Laplace operators on symmetric spaces is established. From this it follows the complete integrability of some quantum systems.
Correlations, quantum entanglement and interference in nanoscopic systems
Several of the most interesting quantum effects can or could be observed in nanoscopic systems. For example, the effect of strong correlations between electrons and of quantum interference can be measured in transport experiments through quantum dots, wires, individual molecules and rings formed by large molecules or arrays of quantum dots. In addition, quantum coherence and entanglement can be clearly observed in quantum corrals. In this paper we present calculations of transport properties through Aharonov–Bohm strongly correlated rings where the characteristic phenomenon of charge–spin separation is clearly observed. Additionally quantum interference effects show up in transport through π-conjugated annulene molecules producing important effects on the conductance for different source–drain configurations, leading to the possibility of an interesting switching effect. Finally, elliptic quantum corrals offer an ideal system to study quantum entanglement due to their focalizing properties. Because of an enhanced interaction between impurities localized at the foci, these systems also show interesting quantum dynamical behaviour and offer a challenging scenario for quantum information experiments
Quantum and statistical mechanics in open systems: theory and examples
Zueco, David
2009-01-01
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum master equations, phase space and numerical methods and Linear and non Linear Response Theory. Applications are the transport in periodic potentials and the dynamics of spins.
Stationary states of two-level open quantum systems
A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two-level open quantum systems under certain conditions applied on both the qubit and the surrounding.
Stationary states of two-level open quantum systems
Gardas, Bartlomiej; Puchala, Zbigniew
2010-01-01
A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two--level open quantum systems under certain conditions applied both on the qubit and the surrounding.
Everitt, M. J.; Henshaw, Michael J de C; Dwyer, Vincent M
2016-01-01
The exciting possibilities in the field of new quantum technologies extend far beyond the well-reported application of quantum computing. Precision timing, gravity sensors and imagers, cryptography, navigation, metrology, energy harvesting and recovery, biomedical sensors and imagers, and real-time optimisers all indicate the potential for quantum technologies to provide the basis of a technological revolution. From the field of Systems Engineering emerges a focused strategy for the developme...
Spin systems and long-range interactions for quantum memories and quantum computing
Pedrocchi, Fabio Luigi
2013-01-01
Since the seminal work by Shor who proposed a quantum algorithm factorizing integers into prime factors, it has become manifest that the laws of quantum mechanics provide resources for computation that overpower classical physics. The computational advantages that quantum physics offers have stimulated a tremendous amount of theoretical and experimental research. In this context, spin systems have played a major role, given that the spin degree of freedom -- with the paradigmatic case of the ...
Work exchange between quantum systems: the spin-oscillator model
Schröder, Heiko
2009-01-01
With the development of quantum thermodynamics it has been shown that relaxation to thermal equilibrium and with it the concept of heat flux may emerge directly from quantum mechanics. This happens for a large class of quantum systems if embedded into another quantum environment. In this paper, we discuss the complementary question of the emergence of work flux from quantum mechanics. We introduce and discuss two different methods to assess the work source quality of a system, one based on the generalized factorization approximation, the other based on generalized definitions of work and heat. By means of those methods, we show that small quantum systems can, indeed, act as work reservoirs. We illustrate this behavior for a simple system consisting of a spin coupled to an oscillator and investigate the effects of two different interactions on the work source quality. One case will be shown to allow for a work source functionality of arbitrarily high quality.
Holonomic Quantum Control with Continuous Variable Systems
Albert, Victor V.; Shu, Chi; Krastanov, Stefan; Shen, Chao; Liu, Ren-Bao; Yang, Zhen-Biao; Schoelkopf, Robert J.; Mirrahimi, Mazyar; Devoret, Michel H.; Jiang, Liang
2016-04-01
Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems that support tunable nonlinearities, such as trapped ions and circuit QED.
On the kinetic theory of quantum systems
The contents of this thesis which deals with transport phenomena of specific gases, plasmas and fluids, can be separated into two distinct parts. In the first part a statistical way is suggested to estimate the neutrino mass. Herefore use is made of the fact that massive neutrinos possess a non-zero volume viscosity in contrast with massless neutrinos. The second part deals with kinetic theory of strongly condensed quantum systems of which examples in nature are: liquid Helium, heavy nuclei, electrons in a metal and the interior of stars. In degenerate systems fermions in general interact strongly so that ordinary kinetic theory is not directly applicable. For such cases Landau-Fermi-liquid theory, in which the strongly interacting particles are replaced by much weaker interacting quasiparticles, proved to be very useful. A method is developed in this theory to calculate transport coefficients. Applications of this method on liquid 3Helium yield surprisingly good agreement with experimental results for thermal conductivities. (Auth.)
Uncertainty relations, quantum and thermal fluctuations in Lindblad theory of open quantum systems
In the framework of the Lindblad theory for open quantum systems we derive closed analytical expressions of the uncertainty relation for a particle moving in a harmonic oscillator potential. The particle is in arbitrarily squeezed initial state and interacts with an environment at finite temperature. We examine how the quantum and thermal fluctuations of the environment contribute to the uncertainty in the canonical variables of the systems and study their relative importance in the evolution of the system towards equilibrium with be aim of clarifying the meaning of quantum, classical and thermal dissipation of energy. We show that upon contact with the bath the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is of the same order as the decoherence time calculated before in similar models in the context of a transition from quantum mechanics to classical mechanics. (authors)
Constructing quantum games from a system of Bell's inequalities
We report constructing quantum games directly from a system of Bell's inequalities using Arthur Fine's analysis published in early 1980s. This analysis showed that such a system of inequalities forms a set of both necessary and sufficient conditions required to find a joint distribution function compatible with a given set of joint probabilities, in terms of which the system of Bell's inequalities is usually expressed. Using the setting of a quantum correlation experiment for playing a quantum game, and considering the examples of Prisoners' Dilemma and Matching Pennies, we argue that this approach towards constructing quantum games addresses some of their well-known criticisms.
Concepts and methods in the theory of open quantum systems
Breuer, Heinz-Peter; Petruccione, Francesco
2003-01-01
The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches. Starting from the appropriate characterization of the quantum statistical ensembles naturally arising in the description of open quantum systems, the corresponding dynamical evolution equations are derived for the Markovian as well as for the non-Markovian case.
Quantum Correlations Reduce Classical Correlations with Ancillary Systems
LUO Shun-Long; LI Nan
2010-01-01
@@ We illustrate the dichotomy of classical/quantum correlations by virtue of monogamy.More precisely,we show that correlations in a bipartite state are classical if and only if each party of the state can be perfectly correlated with other ancillary systems.In particular,this means that if there are quantum correlations between two parties,then the classical(as well as quantum)correlating capabilities of the two parties with other systems have to be strictly reduced.
Coherent and Collective Quantum Optical Effects in Mesoscopic Systems
Brandes, Tobias
2004-01-01
A review of coherent and collective quantum optical effects like superradiance and coherent population trapping in mesoscopic systems is presented. Various new physical realizations of these phenomena are discussed, with a focus on their role for electronic transport and quantum dissipation in coupled nano-scale systems like quantum dots. A number of theoretical tools such as Master equations, polaron transformations, correlation functions, or level statistics are used to describe recent work...
Computable measure of total quantum correlations of multipartite systems
Behdani, Javad; Akhtarshenas, Seyed Javad; Sarbishaei, Mohsen
2016-04-01
Quantum discord as a measure of the quantum correlations cannot be easily computed for most of density operators. In this paper, we present a measure of the total quantum correlations that is operationally simple and can be computed effectively for an arbitrary mixed state of a multipartite system. The measure is based on the coherence vector of the party whose quantumness is investigated as well as the correlation matrix of this part with the remainder of the system. Being able to detect the quantumness of multipartite systems, such as detecting the quantum critical points in spin chains, alongside with the computability characteristic of the measure, makes it a useful indicator to be exploited in the cases which are out of the scope of the other known measures.
Hybrid quantum systems with ultracold spins and optomechanics
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Date, Aditya; Schwab, Keith; Meystre, Pierre; Vengalattore, Mukund
2016-05-01
Linear cavity optomechanics has enabled radiation pressure cooling and sensing of mechanical resonators at the quantum limits. However, exciting and unrealized avenues such as generating massive macroscopic nonclassical states, quantum signal transduction, and phonon-based manybody physics each require strong, nonlinear interactions. In our group, we are exploring three approaches to realizing strong optomechanical nonlinearities - i. using atomically thin graphene membranes, ii. coupling optomechanical systems with ultracold atomic spins, and iii. using microtoroidal optomechanical resonators strongly coupled to atoms trapped in their evanescent fields. We describe our progress in each of these efforts and discuss ongoing studies on various aspects of quantum enhanced metrology, nonequilibrium dynamics of open quantum systems and quantum transduction using these novel hybrid quantum systems. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Shrinked systems. Quantum physics on new paths
This introducing textbook for students of higher semesters of physics, chemistry, and informatics treats a in latest time dynamically expanding field of physics. This book deals among others with the themes quantum information theory, quantum communications, quantum computing, teleportation, hidden parameters, which-way-marking, quantum measuring process, POVM, quantum channels and mediates by this not only a deepened understanding of quantum theory but also basic science, in order to follow the fast development of the field respectively to enter a special field of research. Commented recommendations for further literature as well as exercise problems help the reader to find quickly a founded approach to the theoretical foundations of future key technologies. The book can be made to a base of courses and seminars. Because the required basic knowledge in mathematics and quantum theory is presented in introductory chapters, the book is also suited for the self-study
Correlation Functions in Open Quantum-Classical Systems
Chang-Yu Hsieh
2013-12-01
Full Text Available Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.
Maps for general open quantum systems and a theory of linear quantum error correction
We show that quantum subdynamics of an open quantum system can always be described by a linear, Hermitian map irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the assumption of completely positive (CP) maps, we present a generalized theory of linear quantum error correction, which applies to any linear map describing the open system evolution. In the physically relevant setting of Hermitian maps, we show that the CP-map-based version of quantum error correction theory applies without modifications. However, we show that a more general scenario is also possible, where the recovery map is Hermitian but not CP. Since non-CP maps have nonpositive matrices in their range, we provide a geometric characterization of the positivity domain of general linear maps. In particular, we show that this domain is convex and that this implies a simple algorithm for finding its boundary.
Towards the experimental realization of hybrid quantum systems
One of the main interests of quantum physics in this new millennium is the exploitation of quantum mechanical principles in technical applications. One approach here is to use entanglement and superpositions of states to realize powerful algorithms capable of solving challenging computational tasks on a much faster time scale than a classical computer ever could. To find the quantum analogue of a classical bit one needs a quantum mechanical two level system that can be used to store and process quantum information. Most of the current approaches to find such a 'qubit' have the intention to find a single system that is able to fulfill all desirable tasks. But actually most quantum systems are only favorable for very specific tasks (e.g storage, processing, data exchange,..), similar as it is in classical computing. For some qubits the main disadvantages is that their quantum state is very fragile. Those systems loose their 'quantum information' (that is the possibility to store superpositions of their states coherently) easily. They 'decohere' on a timescale that is much shorter then any more involving algorithm. Other systems can keep those superposition states for quite a while, but are so difficult to address that the number of operations that can be made is very limited. The task of a so called hybrid quantum system is now to combine the strengths of these different systems, using e.g. one for manipulation and an other system for storage. Similar to a processor/memory architecture in conventional computers these systems could use a kind of bus system to couple between them. The main task of this thesis was to make steps towards the realization of such a system using two different combinations of quantum systems. Both are planned to use superconducting qubits (transmons) as processor qubit and either atoms (ultra cold rubidium 87 ensembles) or solid state spin systems (Nitrogen Vacancies in diamonds - NV centers) as memory. (author)
Generation and confirmation of a (100 × 100)-dimensional entangled quantum system
Krenn, Mario; Huber, Marcus; Fickler, Robert; Lapkiewicz, Radek; Ramelow, Sven; Zeilinger, Anton
2014-01-01
Quantum entanglement is one of the key features of quantum mechanics. Quantum systems are the basis of new paradigms in quantum computation, quantum cryptography, or quantum teleportation. By increasing the size of the entangled quantum system, a wider variety of fundamental tests as well as more realistic applications can be performed. The size of the entangled quantum state can increase with the number of particles or, as in the present paper, with the number of involved dimensions. We expl...
Automated drawing system of quantum energy levels
The purpose of this work is to derive an automated system that provides advantageous drawings of energy spectra for quantum systems (nuclei, atoms, molecules, etc.) required in various physical sciences. The automation involves the development of appropriate computational code and graphical imaging system based on raw data insertion, theoretical calculations and experimental or bibliographic data insertion. The system determines the appropriate scale to depict graphically with the best possible way in the available space. The presently developed code operates locally and the results are displayed on the screen and can be exported to a PostScript file. We note its main features to arrange and visualize in the available space the energy levels with their identity, taking care the existence in the final diagram the least auxiliary deviations. Future improvements can be the use of Java and the availability on the Internet. The work involves the automated plotting of energy levels in molecules, atoms, nuclei and other types of quantized energy spectra. The automation involves the development of an appropriate computational code and graphical imaging system
Orbits of hybrid systems as qualitative indicators of quantum dynamics
Burić, N., E-mail: buric@ipb.ac.rs; Popović, D.B.; Radonjić, M.; Prvanović, S.
2014-03-01
Hamiltonian theory of hybrid quantum–classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem clearly indicate if the quantum subsystem does or does not have additional conserved observables.
Schmidt information and entanglement in quantum systems
Bogdanov, A Y; Valiev, K A; Bogdanov, Yu.I.
2005-01-01
The purpose of this paper is to study entanglement of quantum states by means of Schmidt decomposition. The notion of Schmidt information which characterizes the non-randomness of correlations between two observers that conduct measurements of EPR-states is proposed. In two important particular cases - a finite number of Schmidt modes with equal probabilities and Gaussian correlations- Schmidt information is equal to Shannon information. A universal measure of a dependence of two variables is proposed. It is based on Schmidt number and it generalizes the classical Pearson correlation coefficient. It is demonstrated that the analytical model obtained can be applied to testing the numerical algorithm of Schmidt modes extraction. A thermodynamic interpretation of Schmidt information is given. It describes the level of entanglement and correlations of micro-system with its environment
Quantum integrable systems. Quantitative methods in biology
Feverati, Giovanni
2011-01-01
Quantum integrable systems have very strong mathematical properties that allow an exact description of their energetic spectrum. From the Bethe equations, I formulate the Baxter "T-Q" relation, that is the starting point of two complementary approaches based on nonlinear integral equations. The first one is known as thermodynamic Bethe ansatz, the second one as Kl\\"umper-Batchelor-Pearce-Destri- de Vega. I show the steps toward the derivation of the equations for some of the models concerned. I study the infrared and ultraviolet limits and discuss the numerical approach. Higher rank integrals of motion can be obtained, so gaining some control on the eigenvectors. After, I discuss the Hubbard model in relation to the N = 4 supersymmetric gauge theory. The Hubbard model describes hopping electrons on a lattice. In the second part, I present an evolutionary model based on Turing machines. The goal is to describe aspects of the real biological evolution, or Darwinism, by letting evolve populations of algorithms. ...
Thermalization and pseudolocality in extended quantum systems
Doyon, Benjamin
2015-01-01
Recently, it was understood that extended concepts of locality played important roles in the study of extended quantum systems out of equilibrium, in particular in so-called generalized Gibbs ensembles. In this paper, we rigorously study pseudolocal charges and their involvement in time evolutions and in the thermalization process of arbitrary states with strong enough clustering properties. We show that the densities of pseudolocal charges form a Hilbert space, with inner product determined by response functions. Using this, we define the family of pseudolocal states: clustering states connected to the infinite-temperature state by paths whose tangents are actions of pseudolocal charges. This family includes thermal Gibbs states, as well as (a precise definition of) generalized Gibbs ensembles. We prove that the family of pseudolocal states is preserved by finite time evolution, and that, under certain conditions, the stationary state emerging at infinite time is a generalized Gibbs ensemble with respect to ...
Slow scrambling in disordered quantum systems
Swingle, Brian
2016-01-01
Recent work has studied the growth of commutators as a probe of chaos and information scrambling in quantum many-body systems. In this work we study the effect of static disorder on the growth of commutators in a variety of contexts. We find generically that disorder slows the onset of scrambling, and, in the case of a many-body localized state, partially halts it. We access the many-body localized state using a standard fixed point Hamiltonian, and we show that operators exhibit slow logarithmic growth under time evolution. We compare the result with the expected growth of commutators in both localized and delocalized non-interacting disordered models. Finally, based on a scaling argument, we state a conjecture about the effect of weak interactions on the growth of commutators in an interacting diffusive metal.
Anions, quantum particles in planar systems
Our purpose here is to present a general review of the non-relativistic quantum-mechanical description of excitations that do not obey neither the Fermi-Dirac nor the Bose-Einstein statistics; they rather fulfill an intermediate statistics, the we called 'any-statistics'. As we shall see, this is a peculiarity of (1+1) and (1+2) dimensions, due to the fact that, in two space dimensions, the spin is not quantised, once the rotation group is Abelian. The relevance of studying theories in (1+2) dimensions is justified by the evidence that, in condensed matter physics, there are examples of planar systems, for which everything goes as if the third spatial dimension is frozen. (author)
Measures of quantum synchronization in continuous variable systems.
Mari, A; Farace, A; Didier, N; Giovannetti, V; Fazio, R
2013-09-01
We introduce and characterize two different measures which quantify the level of synchronization of coupled continuous variable quantum systems. The two measures allow us to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is, in principle, unbounded; however, in the absence of quantum resources (e.g., squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum optomechanical systems. PMID:25166668
Measures of Quantum Synchronization in Continuous Variable Systems
Mari, A.; Farace, A.; Didier, N.; Giovannetti, V.; Fazio, R.
2013-09-01
We introduce and characterize two different measures which quantify the level of synchronization of coupled continuous variable quantum systems. The two measures allow us to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is, in principle, unbounded; however, in the absence of quantum resources (e.g., squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum optomechanical systems.
Optimal signal detection in entanglement-assisted quantum communication systems
Minimization of error probability is considered in entanglement-assisted quantum communication systems. It is shown that although quantum state signals being sent are not symmetric at a sender side, the square root measurement becomes optimum when they are made symmetric at the receiver side. For communication systems of coherent signals, where a two-mode squeezed-vacuum state is used as an entanglement resource, the quantum entanglement greatly reduces the average probability of error. The relation to the quantum dense coding of continuous variables is also discussed
Quantum-classical correspondence in steady states of nonadiabatic systems
We first present nonadiabatic path integral which is exact formulation of quantum dynamics in nonadiabatic systems. Then, by applying the stationary phase approximations to the nonadiabatic path integral, a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems is presented as a nonadiabatic trace formula. The present quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow degree of freedom, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels
Process tomography via sequential measurements on a single quantum system
Bassa, Humairah; Goyal, Sandeep K.; Choudhary, Sujit K.; Uys, Hermann; Diósi, Lajos; Konrad, Thomas
2015-09-01
We utilize a discrete (sequential) measurement protocol to investigate quantum process tomography of a single two-level quantum system, with an unknown initial state, undergoing Rabi oscillations. The ignorance of the dynamical parameters is encoded into a continuous-variable classical system which is coupled to the two-level quantum system via a generalized Hamiltonian. This combined estimate of the quantum state and dynamical parameters is updated by using the information obtained from sequential measurements on the quantum system and, after a sufficient waiting period, faithful state monitoring and parameter determination is obtained. Numerical evidence is used to demonstrate the convergence of the state estimate to the true state of the hybrid system.
A Popov Stability Condition for Uncertain Linear Quantum Systems
James, Matthew R.; Petersen, Ian R.; Ugrinovskii, Valery
2013-01-01
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general class of perturbations to the system Hamiltonian. Then, the special case of a nominal linear quantum system is considered with quadratic perturbations to the system Hamiltonian. In this case, a robust stability condition is given in terms of a frequency domain ...
Fate of classical solitons in one-dimensional quantum systems.
Pustilnik, M.; Matveev, K. A.
2015-11-23
We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, and argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.
Hacking commercial quantum cryptography systems by tailored bright illumination
Lydersen, Lars; Wittmann, Christoffer; Elser, Dominique; Skaar, Johannes; Makarov, Vadim; 10.1038/NPHOTON.2010.214
2010-01-01
The peculiar properties of quantum mechanics allow two remote parties to grow a private, secret key, even if the eavesdropper can do anything permitted by the laws of nature. In quantum key distribution (QKD) the parties exchange non-orthogonal or entangled quantum states to generate quantum correlated classical data. Consequently, QKD implementations always rely on detectors to measure the relevant quantum property of the signal states. However, practical detectors are not only sensitive to quantum states. Here we show how an eavesdropper can exploit such deviations from the ideal behaviour: We demonstrate experimentally how the detectors in two commercially available QKD systems can be fully remote controlled using specially tailored bright illumination. This makes it possible to acquire the full secret key without leaving any trace; we propose an eavesdropping apparatus built of off-the-shelf components. The loophole is likely to be present in most QKD systems using avalanche photo diodes (APDs) to detect ...
Quantum interference in an electron-hole graphene ring system
Smirnov, D.; Schmidt, H.; Haug, R. J. [Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstr. 2 30167 Hannover (Germany)
2013-12-04
Quantum interference is observed in a graphene ring system via the Aharonov Bohm effect. As graphene is a gapless semiconductor, this geometry allows to study the unique situation of quantum interference between electrons and holes in addition to the unipolar quantum interference. The period and amplitude of the observed Aharonov-Bohm oscillations are independent of the sign of the applied gate voltage showing the equivalence between unipolar and dipolar interference.
Controlling open quantum systems: Tools, achievements, and limitations
Koch, Christiane P.
2016-01-01
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge to preserve the relevant nonclassical features at the level of device operation. A major obstacle is decoherence which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence...
Pole placement design for quantum systems via coherent observers
Miao, Zibo; James, Matthew R.; Ugrinovskii, Valery A.
2015-01-01
We previously extended Luenberger's approach for observer design to the quantum case, and developed a class of coherent observers which tracks linear quantum stochastic systems in the sense of mean values. In light of the fact that the Luenberger observer is commonly and successfully applied in classical control, it is interesting to investigate the role of coherent observers in quantum feedback. As the first step in exploring observer-based coherent control, in this paper we study pole-place...
Quantum Hysteresis in Coupled Light-Matter Systems
Gómez-Ruiz, F. J.; Acevedo, O. L.; Quiroga, L.; Rodríguez, F. J.; Johnson, N. F.
2016-01-01
We investigate the non-equilibrium quantum dynamics of a canonical light-matter system, namely the Dicke model, when the light-matter interaction is ramped up and down through a cycle across the quantum phase transition. Our calculations reveal a rich set of dynamical behaviors determined by the cycle times, ranging from the slow, near adiabatic regime through to the fast, sudden quench regime. As the cycle time decreases, we uncover a crossover from an oscillatory exchange of quantum informa...
Measures of quantum synchronization in continuous variable systems
Mari, A.; Farace, A.; Didier, N.; Giovannetti, V.; Fazio, R.
2013-01-01
We introduce and characterize two different measures which quantify the level of synchronization of interacting continuous variable quantum systems. The two measures allow to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is in principle unbounded, however in the absence of quantum resources (e.g. squeezing) the synchronization level is bounded bel...
The Geometric Phase in Quantum Systems
The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke 'after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is
Theory of quantum control of spin-photon dynamics and spin decoherence in semiconductors
Yao, Wang
Single electron spin in a semiconductor quantum dot (QD) and single photon wavepacket propagating in an optical waveguide are investigated as carriers of quantum bit (qubit) for information processing. Cavity quantum electrodynamics of the coupled system composed of charged QD, microcavity and waveguide provides a quantum interface for the interplay of stationary spin qubits and flying photon qubits via cavity assisted optical control. This interface forms the basis for a wide range of essential functions of a quantum network, including transferring, swapping, and entangling qubits at distributed quantum nodes as well as a deterministic source and an efficient detector of a single photon wavepacket with arbitrarily specified shape. The cavity assisted optical process also made possible ultrafast initialization and QND readout of the spin qubit in QD. In addition, the strong optical nonlinearity of dot-cavity-waveguide coupled system enables phase gate and entanglement operation for flying single photon qubits in waveguides. The coherence of the electron spin is the wellspring of these quantum applications being investigated. At low temperature and strong magnetic field, the dominant cause of electron spin decoherence is the coupling with the interacting lattice nuclear spins. We present a quantum solution to the coupled dynamics of the electron with the nuclear spin bath. The decoherence is treated in terms of quantum entanglement of the electron with the nuclear pair-flip excitations driven by the various nuclear interactions. A novel nuclear interaction, mediated by virtue spin-flips of the single electron, plays an important role in single spin free-induction decay (FID). The spin echo not only refocuses the dephasing by inhomogeneous broadening in ensemble dynamics but also eliminates the decoherence by electron-mediated nuclear interaction. Thus, the decoherence times for single spin FID and ensemble spin echo are significantly different. The quantum theory of
Quantum-based electronic devices and systems selected topics in electronics and systems, v.14
Dutta, Mitra
1998-01-01
This volume includes highlights of the theories and experimental findings that underlie essential phenomena occurring in quantum-based devices and systems as well as the principles of operation of selected novel quantum-based electronic devices and systems. A number of the emerging approaches to creating new types of quantum-based electronic devices and systems are also discussed.
Classical and quantum simulations of many-body systems
This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new ''analog'' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)
Trojan Horse attacks on Quantum Key Distribution systems
Gisin, Nicolas; Fasel, Sylvain; Kraus, Barbara; Zbinden, Hugo; Ribordy, Grégoire
2005-01-01
General Trojan-horse attacks on quantum-key-distribution systems, i.e., attacks on Alice or Bob’s system via the quantum channel, are analyzed. We illustrate the power of such attacks with today’s technology and conclude that all systems must implement active counter measures. In particular, all systems must include an auxiliary detector that monitors any incoming light. We show that such counter measures can be efficient, provided that enough additional privacy amplification is applied to th...
Quantum narrowing effect in a spin-Peierls system with quantum lattice fluctuation
We investigate a one-dimensional S=1/2 antiferromagnetic Heisenberg model coupled to quantum lattice vibration using a quantum Monte Carlo method. We study the ground-state lattice fluctuation where the system shows a characteristic structure factor. We also study the mass dependence of magnetic properties such as the magnetic susceptibility and the magnetic excitation spectrum. For heavy mass, the system shows the same behavior as the case of classical lattice vibration. On the other hand, for light mass, magnetic properties coincide with those of the static uniform chain. We investigate the physical mechanism of this behavior and propose the picture of quantum narrowing. (author)
Quantum correlations in B and K meson systems
Banerjee, Subhashish; MacKenzie, Richard
2014-01-01
We study quantum correlations in meson-antimeson systems, as provided for example in meson factories used mainly to probe physics beyond the Standard Model of particle physics. We use a semigroup formalism to compute a trace-preserving density matrix for these systems, in spite of the fact that the particles are unstable. This is used to compute the time evolution of several measures of quantum correlations for three meson systems (KKbar, BdBdbar and BsBsbar). We find that the quantum correlations for these systems can be non-trivially different from their stable counterparts.
Alternative Hamiltonian description for quantum systems
The existence of time-invariant Kahler structures is analyzed in both Classical and Quantum Mechanics. In Quantum Mechanics, a family of such Kahler structures is found, in the finite-dimensional case it is proven that this family is complete
Thermal and quantum noise in active systems
Courty, Jean-Michel; Grassia, Francesca; Reynaud, Serge
2001-01-01
We present a quantum network approach to the treatment of thermal and quantum fluctuations in measurement devices. The measurement is described as a scattering process of input fluctuations towards output ones. We present the results obtained with this method for the treatment of a cold damped capacitive accelerometer.
Quasiclassical dynamics in a closed quantum system
Kent, A
1995-01-01
We give a simple argument to show that, in Gell-Mann and Hartle's consistent histories formulation of quantum cosmology, if one assumes that an observed quasiclassical structure will continue to be quasiclassical, one cannot infer that it will obey the predictions of classical or Copenhagen quantum mechanics.
Inequalities detecting quantum entanglement for 2 x d systems
We present a set of inequalities for detecting quantum entanglement of 2 x d quantum states. For 2 x 2 and 2 x 3 systems, the inequalities give rise to sufficient and necessary separability conditions for both pure and mixed states. For the case of d>3, these inequalities are necessary conditions for separability, which detect all entangled states that are not positive under partial transposition and even some entangled states with positive partial transposition. These inequalities are given by mean values of local observables and present an experimental way of detecting the quantum entanglement of 2 x d quantum states and even multiqubit pure states.
Anonymous voting for multi-dimensional CV quantum system
Rong-Hua, Shi; Yi, Xiao; Jin-Jing, Shi; Ying, Guo; Moon-Ho, Lee
2016-06-01
We investigate the design of anonymous voting protocols, CV-based binary-valued ballot and CV-based multi-valued ballot with continuous variables (CV) in a multi-dimensional quantum cryptosystem to ensure the security of voting procedure and data privacy. The quantum entangled states are employed in the continuous variable quantum system to carry the voting information and assist information transmission, which takes the advantage of the GHZ-like states in terms of improving the utilization of quantum states by decreasing the number of required quantum states. It provides a potential approach to achieve the efficient quantum anonymous voting with high transmission security, especially in large-scale votes. Project supported by the National Natural Science Foundation of China (Grant Nos. 61272495, 61379153, and 61401519), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130162110012), and the MEST-NRF of Korea (Grant No. 2012-002521).
Quantum correlations in B and K meson systems
Banerjee, Subhashish; Alok, Ashutosh Kumar; MacKenzie, Richard
2016-05-01
The interplay between the various measures of quantum correlations is well known in stable optical and electronic systems. Here we study such foundational issues in unstable quantum systems. Specifically we study meson-antimeson systems ( Kbar{K}, Bd bar{B}d and Bsbar{B}s, which are produced copiously in meson factories. In particular, the nonclassicality of quantum correlations which can be characterized in terms of nonlocality (which is the strongest condition), entanglement, teleportation fidelity or weaker nonclassicality measures like quantum discord are analyzed. We also study the impact of decoherence on these measures of quantum correlations, using the semigroup formalism. A comparison of these measures brings out the fact that the relations between them can be nontrivially different from those of their stable counterparts such as neutrinos.
Optimal control of population transfer in Markovian open quantum systems
Cuia, Wei; Pan, Yu
2010-01-01
There has long been interest to control the transfer of population between specified quantum states. Recent work has optimized the control law for closed system population transfer by using a gradient ascent pulse engineer- ing algorithm [1]. Here, a spin-boson model consisting of two-level atoms which interact with the dissipative environment, is investigated. With opti- mal control, the quantum system can invert the populations of the quantum logic states. The temperature plays an important role in controlling popula- tion transfer. At low temperatures the control has active performance, while at high temperatures it has less erect. We also analyze the decoherence be- havior of open quantum systems with optimal population transfer control, and we find that these controls can prolong the coherence time. We hope that active optimal control can help quantum solid-state-based engineering.
Entanglement in the interaction between two quantum oscillator systems
Kim, I L; Kim, ILki; Iafrate, Gerald J.
2004-01-01
The fundamental quantum dynamics of two interacting oscillator systems are studied in two different scenarios. In one case, both oscillators are assumed to be linear, whereas in the second case, one oscillator is linear and the other is a non-linear, angular-momentum oscillator; the second case is, of course, more complex in terms of energy transfer and dynamics. These two scenarios have been the subject of much interest over the years, especially in developing an understanding of modern concepts in quantum optics and quantum electronics. In this work, however, these two scenarios are utilized to consider and discuss the salient features of quantum behaviors resulting from the interactive nature of the two oscillators, i.e., coherence, entanglement, spontaneous emission, etc., and to apply a measure of entanglement in analyzing the nature of the interacting systems. ... For the coupled linear and angular-momentum oscillator system in the fully quantum-mechanical description, we consider special examples of tw...
Chebyshev Expansion Applied to Dissipative Quantum Systems.
Popescu, Bogdan; Rahman, Hasan; Kleinekathöfer, Ulrich
2016-05-19
To determine the dynamics of a molecular aggregate under the influence of a strongly time-dependent perturbation within a dissipative environment is still, in general, a challenge. The time-dependent perturbation might be, for example, due to external fields or explicitly treated fluctuations within the environment. Methods to calculate the dynamics in these cases do exist though some of these approaches assume that the corresponding correlation functions can be written as a weighted sum of exponentials. One such theory is the hierarchical equations of motion approach. If the environment, however, is described by a complex spectral density or if its temperature is low, these approaches become very inefficient. Therefore, we propose a scheme based on a Chebyshev decomposition of the bath correlation functions and detail the respective quantum master equations within second-order perturbation theory in the environmental coupling. Similar approaches have recently been proposed for systems coupled to Fermionic reservoirs. The proposed scheme is tested for a simple two-level system and compared to existing results. Furthermore, the advantages and disadvantages of the present Chebyshev approach are discussed. PMID:26845380
Random matrix description of decaying quantum systems
This paper describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitly into account. The resulting expressions for the partial decay amplitudes and the corresponding cross sections may be considered a many-channel many-resonance generalization of Fano's original work on resonance lineshapes (Fano 1961 Phys. Rev. 124 1866). A statistical (random matrix) model is then introduced. It allows to describe chaotic scattering systems with tunable couplings to the decay channels. We focus on the autocorrelation function of the total (photo) cross section, and we find that it depends on the same combination of parameters, as the Fano-parameter distribution. These combinations are statistical variants of the one-channel Fano parameter. It is thus possible to study the Fano interference (i.e. the interference between direct and indirect decay paths) on the basis of the autocorrelation function, and thereby in the regime of overlapping resonances. It allows us to study the Fano interference in the limit of strongly overlapping resonances, where we find a persisting effect on the level of the weak localization correction
Attosecond neutron scattering from open quantum systems
Dreismann, C.; Aris, C. [Institute of Chemistry, Technical University of Berlin (Germany)
2010-07-01
Neutron Compton scattering (NCS) from single nuclei of atoms in molecules, e.g. H{sub 2} (and/or single atoms, e.g. He) is effectuated in the attosecond timescale. The related scattering time is considered in detail, in relation with the Uncertainty Relations. It is shown that the entity scattering time gives a statistical measure of the length of the time interval during which an elementary neutron-nucleus collision may occur, in the same way that the spatial extent of a particle wavefunction (or wavepacket) gives a statistical measure of the extent of the region in which the particle may be found. Consequently, the elementary neutron-nucleus scattering process represents a time-interference phenomenon over the sub-femtosecond ''scattering time'' window. Moreover, the very short-range strong interaction of the neutron-nucleus collision implies that the scattering system (e.g. a proton partically dressed'' with electrons) must be considered as an open quantum system. Experimental results from H{sub 2}, D{sub 2} and HD are mentioned and their anomalous scattering property in the attosecond timescale is qualitatively discussed, also in connection with the Schulman-Gaveau effect.
Alternative Algebraic Structures from Bi-Hamiltonian Quantum Systems
Marmo, G; Simoni, A; Ventriglia, F
2005-01-01
We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg picture in terms of deformations of the associative product on the space of observables.
Classical and thermodynamic limits for generalised quantum spin systems
Duffield, N. G.
1990-01-01
We prove that the rescaled upper and lower symbols for arbitrary generalised quantum spin systems converge in the classical limit. For a large class of models this enables us to derive the asyptotics of quantum free energies in the classical and in the thermodynamic limit.
Quantum-Classical Connection for Hydrogen Atom-Like Systems
Syam, Debapriyo; Roy, Arup
2011-01-01
The Bohr-Sommerfeld quantum theory specifies the rules of quantization for circular and elliptical orbits for a one-electron hydrogen atom-like system. This article illustrates how a formula connecting the principal quantum number "n" and the length of the major axis of an elliptical orbit may be arrived at starting from the quantum…
Quantum entanglement of unitary operators on bi-partite systems
Wang, X.; Zanardi, P.
2002-01-01
We study the entanglement of unitary operators on $d_1\\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified by the concept of concurrence.
Quantum Markov processes and applications in many-body systems
This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but
Model-Checking Linear-Time Properties of Quantum Systems
Ying, Mingsheng; Yu, Nengkun; Feng, Yuan
2011-01-01
We define a formal framework for reasoning about linear-time properties of quantum systems in which quantum automata are employed in the modeling of systems and certain closed subspaces of state (Hilbert) spaces are used as the atomic propositions about the behavior of systems. We provide an algorithm for verifying invariants of quantum automata. Then automata-based model-checking technique is generalized for the verification of safety properties recognizable by reversible automata and omega-properties recognizable by reversible Buechi automata.
Decoherence as irreversible dynamical process in open quantum systems
Full text: A framework for a general discussion in Heisenberg's representation of environmentally induced decoherence will be proposed. Example showing that classical properties do not have to be postulated as an independent ingredient will be given. It will be also shown that infinite open quantum systems in some case after decoherence behave like - simple classical dynamical systems; simples quantum mechanical systems representing one particle. (author)
Quantum Measurement Problem and Systems Selfdescription in Operators Algebras Formalism
Mayburov, S.
2002-01-01
Quantum Measurement problem studied in Information Theory approach of systems selfdescription which exploits the information acquisition incompleteness for the arbitrary information system. The studied model of measuring system (MS) consist of measured state S environment E and observer $O$ processing input S signal. $O$ considered as the quantum object which interaction with S,E obeys to Schrodinger equation (SE). MS incomplete or restricted states for $O$ derived by the algebraic QM formali...
The Power of Quantum Systems on a Line
Aharonov, Dorit; Gottesman, Daniel; Irani, Sandy; Kempe, Julia
2009-04-01
We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with 9 states per particle). This might have practical implications for experimentalists interested in constructing an adiabatic quantum computer. Building on the same construction, but with some additional technical effort and 12 states per particle, we show that the problem of approximating the ground state energy of a system composed of a line of quantum particles is QMA-complete; QMA is a quantum analogue of NP. This is in striking contrast to the fact that the analogous classical problem, namely, one-dimensional MAX-2-SAT with nearest neighbor constraints, is in P. The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Not all illegal configurations can be ruled out by local checks, so instead we rule out such illegal configurations because they would, in the future, evolve into a state which can be seen locally to be illegal. Our construction implies (assuming the quantum Church-Turing thesis and that quantum computers cannot efficiently solve QMA-complete problems) that there are one-dimensional systems which take an exponential time to relax to their ground states at any temperature, making them candidates for being one-dimensional spin glasses.
Detecting quantum speedup in closed and open systems
Xu, Zhen-Yu
2016-07-01
We construct a general measure for detecting the quantum speedup in both closed and open systems. The speed measure is based on the changing rate of the position of quantum states on a manifold with appropriate monotone Riemannian metrics. Any increase in speed is a clear signature of dynamical speedup. To clarify the mechanisms for quantum speedup, we first introduce the concept of longitudinal and transverse types of speedup: the former stems from the time evolution process itself with fixed initial conditions, while the latter is a result of adjusting initial conditions. We then apply the proposed measure to several typical closed and open quantum systems, illustrating that quantum coherence (or entanglement) and the memory effect of the environment together can become resources for longitudinally or transversely accelerating dynamical evolution under specific conditions and assumptions.
Open quantum spin systems in semiconductor quantum dots and atoms in optical lattices
In this Thesis, we study open quantum spin systems from different perspectives. The first part is motivated by technological challenges of quantum computation. An important building block for quantum computation and quantum communication networks is an interface between material qubits for storage and data processing and travelling photonic qubits for communication. We propose the realisation of a quantum interface between a travelling-wave light field and the nuclear spins in a quantum dot strongly coupled to a cavity. Our scheme is robust against cavity decay as it uses the decay of the cavity to achieve the coupling between nuclear spins and the travelling-wave light fields. A prerequiste for such a quantum interface is a highly polarized ensemble of nuclear spins. High polarization of the nuclear spin ensemble is moreover highly desirable as it protects the potential electron spin qubit from decoherence. Here we present the theoretical description of an experiment in which highly asymmetric dynamic nuclear spin pumping is observed in a single self-assembled InGaAs quantum dot. The second part of this Thesis is devoted to fundamental studies of dissipative spin systems. We study general one-dimensional spin chains under dissipation and propose a scheme to realize a quantum spin system using ultracold atoms in an optical lattice in which both coherent interaction and dissipation can be engineered and controlled. This system enables the study of non-equilibrium and steady state physics of open and driven spin systems. We find, that the steady state expectation values of different spin models exhibit discontinuous behaviour at degeneracy points of the Hamiltonian in the limit of weak dissipation. This effect can be used to dissipatively probe the spectrum of the Hamiltonian. We moreover study spin models under the aspect of state preparation and show that dissipation drives certain spin models into highly entangled state. Finally, we study a spin chain with
Open quantum spin systems in semiconductor quantum dots and atoms in optical lattices
Schwager, Heike
2012-07-04
In this Thesis, we study open quantum spin systems from different perspectives. The first part is motivated by technological challenges of quantum computation. An important building block for quantum computation and quantum communication networks is an interface between material qubits for storage and data processing and travelling photonic qubits for communication. We propose the realisation of a quantum interface between a travelling-wave light field and the nuclear spins in a quantum dot strongly coupled to a cavity. Our scheme is robust against cavity decay as it uses the decay of the cavity to achieve the coupling between nuclear spins and the travelling-wave light fields. A prerequiste for such a quantum interface is a highly polarized ensemble of nuclear spins. High polarization of the nuclear spin ensemble is moreover highly desirable as it protects the potential electron spin qubit from decoherence. Here we present the theoretical description of an experiment in which highly asymmetric dynamic nuclear spin pumping is observed in a single self-assembled InGaAs quantum dot. The second part of this Thesis is devoted to fundamental studies of dissipative spin systems. We study general one-dimensional spin chains under dissipation and propose a scheme to realize a quantum spin system using ultracold atoms in an optical lattice in which both coherent interaction and dissipation can be engineered and controlled. This system enables the study of non-equilibrium and steady state physics of open and driven spin systems. We find, that the steady state expectation values of different spin models exhibit discontinuous behaviour at degeneracy points of the Hamiltonian in the limit of weak dissipation. This effect can be used to dissipatively probe the spectrum of the Hamiltonian. We moreover study spin models under the aspect of state preparation and show that dissipation drives certain spin models into highly entangled state. Finally, we study a spin chain with
The Dalton quantum chemistry program system
Aidas, Kestutis; Angeli, Celestino; Bak, Keld L; Bakken, Vebjørn; Bast, Radovan; Boman, Linus; Christiansen, Ove; Cimiraglia, Renzo; Coriani, Sonia; Dahle, Pål; Dalskov, Erik K; Ekström, Ulf; Enevoldsen, Thomas; Eriksen, Janus J; Ettenhuber, Patrick; Fernández, Berta; Ferrighi, Lara; Fliegl, Heike; Frediani, Luca; Hald, Kasper; Halkier, Asger; Hättig, Christof; Heiberg, Hanne; Helgaker, Trygve; Hennum, Alf Christian; Hettema, Hinne; Hjertenæs, Eirik; Høst, Stinne; Høyvik, Ida-Marie; Iozzi, Maria Francesca; Jansík, Branislav; Jensen, Hans Jørgen Aa; Jonsson, Dan; Jørgensen, Poul; Kauczor, Joanna; Kirpekar, Sheela; Kjærgaard, Thomas; Klopper, Wim; Knecht, Stefan; Kobayashi, Rika; Koch, Henrik; Kongsted, Jacob; Krapp, Andreas; Kristensen, Kasper; Ligabue, Andrea; Lutnæs, Ola B; Melo, Juan I; Mikkelsen, Kurt V; Myhre, Rolf H; Neiss, Christian; Nielsen, Christian B; Norman, Patrick; Olsen, Jeppe; Olsen, Jógvan Magnus H; Osted, Anders; Packer, Martin J; Pawlowski, Filip; Pedersen, Thomas B; Provasi, Patricio F; Reine, Simen; Rinkevicius, Zilvinas; Ruden, Torgeir A; Ruud, Kenneth; Rybkin, Vladimir V; Sałek, Pawel; Samson, Claire C M; de Merás, Alfredo Sánchez; Saue, Trond; Sauer, Stephan P A; Schimmelpfennig, Bernd; Sneskov, Kristian; Steindal, Arnfinn H; Sylvester-Hvid, Kristian O; Taylor, Peter R; Teale, Andrew M; Tellgren, Erik I; Tew, David P; Thorvaldsen, Andreas J; Thøgersen, Lea; Vahtras, Olav; Watson, Mark A; Wilson, David J D; Ziolkowski, Marcin; Ågren, Hans
2014-01-01
Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self-consistent-field, Møller–Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms. PMID:25309629
Does an onlooker stop an evolving quantum system?
Toschek, P. E.
2007-10-01
The evolution of quantum mechanics has followed the critical analysis of "gedanken" experiments. Many of these concrete speculations can become implemented today in the laboratory - thanks to now available techniques. A key experiment is concerned with the time evolution of a quantum system under repeated or continuing observation. Here, three problems overlap: 1. The microphysical measurement by a macroscopic device, 2. the system's temporal evolution, and 3. the emergence of macroscopic reality out of the microcosmos. A well-known calculation shows the evolution of a quantum system being slowed down, or even obstructed, when the system is merely observed.An experiment designed to demonstrate this "quantum Zeno effect" and performed in the late eighties on an ensemble of identical atomic ions confirmed its quantum description, but turned out inconclusive with respect to the very origin of the impediment of evolution. During the past years, experiments on individualelectrodynamically stored and laser-cooled ions have been performed that unequivocally demonstrate the observed system's quantum evolution being impeded. Strategy and results exclude any physical reaction on the measured object, but reveal the effect of the gain of information as put forward by the particular correlation of the ion state with the detected signal. They shed light on the process of measurement as well as on the quantum evolution and allow an epistemological interpretation.
Does an onlooker stop an evolving quantum system?
The evolution of quantum mechanics has followed the critical analysis of 'gedanken' experiments. Many of these concrete speculations can become implemented today in the laboratory - thanks to now available techniques. A key experiment is concerned with the time evolution of a quantum system under repeated or continuing observation. Here, three problems overlap: 1. The microphysical measurement by a macroscopic device, 2. the system's temporal evolution, and 3. the emergence of macroscopic reality out of the microcosmos. A well-known calculation shows the evolution of a quantum system being slowed down, or even obstructed, when the system is merely observed.An experiment designed to demonstrate this 'quantum Zeno effect' and performed in the late eighties on an ensemble of identical atomic ions confirmed its quantum description, but turned out inconclusive with respect to the very origin of the impediment of evolution. During the past years, experiments on individualelectrodynamically stored and laser-cooled ions have been performed that unequivocally demonstrate the observed system's quantum evolution being impeded. Strategy and results exclude any physical reaction on the measured object, but reveal the effect of the gain of information as put forward by the particular correlation of the ion state with the detected signal. They shed light on the process of measurement as well as on the quantum evolution and allow an epistemological interpretation
Quantum dot systems: artificial atoms with tunable properties
Full text: Quantum dots - also called zero-dimensional electron systems or artificial atoms - are physical objects where the constituent electrons are confined in a small spatial region, leading to discrete eigenvalues for the energies of the confined electrons. Large quantum dots offer a dense energy spectrum comparable to that of metallic grains, whereas small quantum dots more closely resemble atoms in their electronic properties. Quantum dots can be linked to leads by tunnel barriers, hence permitting electrical transport measurements: Coulomb blockade and single-electron charging effects are observed due to the repulsive electron electron interaction on the quantum dot site. Usually fabricated by conventional semiconductor growth and processing technology, the advantage is that both simple and also more complex quantum dot systems can be designed to purpose, acting as model systems with in-situ tunable parameters such as the number of confined electrons in the quantum dot and the strength of the tunnel coupling to the leads, electrostatically controlled by the applied voltages to gate electrodes. With increasing the tunnel coupling to the leads, the virtual occupation of the quantum dot from the leads becomes more and more important -- the simple description of electrical transport by single-electron tunneling events breaks down. The basic physics is described by the Kondo physics based on the Anderson impurity model. A system consisting of strongly electrostatically coupled quantum dots with separate leads to each quantum dot represent another realization of the Anderson impurity model. Experiments to verify the analogy are presented. The experimental data embedded within this tutorial have been obtained with Alexander Huebel, Matthias Keller, Joerg Schmid, David Quirion, Armin Welker, Ulf Wilhelm, and Klaus von Klitzing. (author)
Quantum systems that follow classical dynamics
Manfredi, G; Feix, M R
1993-01-01
For a special class of potentials, the dynamical evolution of any quantum wavepacket is entirely determined by the laws of classical mechanics. Here, the properties of this class are investigated both from the viewpoint of the Ehrenfest theorem (which provides the evolution of the average position and momentum), and the Wigner representation (which expresses quantum mechanics in a phase space formalism). Finally, these results are extended to the case of a charged particle in a uniform magnetic field. (author)
Dressed excitonic states and quantum interference in a three-level quantum dot ladder system
Gerardot, B D; Brunner, D; Dalgarno, P A; Warburton, R J [School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Karrai, K [Center for NanoScience and Department fuer Physik der LMU, Geschwister-Scholl-Platz 1, 80539 Munich (Germany); Badolato, A [Institute of Quantum Electronics, ETH Zurich, 8093 Zurich (Switzerland); Petroff, P M [Materials Department, University of California, Santa Barbara, CA 93106 (United States)], E-mail: b.d.gerardot@hw.ac.uk
2009-01-15
We observe dressed states and quantum interference effects in a strongly driven three-level quantum dot ladder system. The effect of a strong coupling field on one dipole transition is measured by a weak probe field on the second dipole transition using differential reflection. When the coupling energy is much larger than both the homogeneous and inhomogeneous linewidths an Autler-Townes splitting is observed. Significant differences are observed when the transitions resonant with the strong and weak fields are swapped, particularly when the coupling energy is nearly equal to the measured linewidth. This result is attributed to quantum interference: destructive or constructive interference with modest visibility is observed depending on the pump/probe geometry. The data demonstrate that coherence of both the bi-exciton and the exciton is maintained in this solid-state system, even under intense illumination, which is crucial for prospects in quantum information processing and nonlinear optical devices.
Entanglement Concentration for Higher-Dimensional Quantum Systems
姚春梅; 顾永建; 叶柳; 郭光灿
2002-01-01
Using local operations and classicalcommunication, we present two schemes for realizing entanglement concentration from pure entangled pairs of qutrits. These methods can be easily generalized to d-dimensional (d ＞ 3)quantum systems.
Cooperative phenomena in open quantum systems subject to external control
Schmidt, Rebecca
2014-01-01
Subject of this cumulative thesis is the optimal control of open quantum systems. The cooperative interplay between strong driving and a dissipative medium is investigated, resulting in cooling and entanglement generation.
Quantum teleportation of composite systems via mixed entangled states
We analyze quantum teleportation for composite systems, specifically for concatenated teleporation (decomposing a large composite state into smaller states of dimension commensurate with the channel) and partial teleportation (teleporting one component of a larger quantum state). We obtain an exact expression for teleportation fidelity that depends solely on the dimension and singlet fraction for the entanglement channel and entanglement (measures by I concurrence) for the state; in fact quantum teleportation for composite systems provides an operational interpretation for I concurrence. In addition we obtain tight bounds on teleportation fidelity and prove that the average fidelity approaches the lower bound of teleportation fidelity in the high-dimension limit
Wave-Packet Revivals for Quantum Systems with Nondegenerate Energies
Bluhm, R; Tudose, B; Bluhm, Robert; Kostelecky, Alan; Tudose, Bogdan
1996-01-01
The revival structure of wave packets is examined for quantum systems having energies that depend on two nondegenerate quantum numbers. For such systems, the evolution of the wave packet is controlled by two classical periods and three revival times. These wave packets exhibit quantum beats in the initial motion as well as new types of long-term revivals. The issue of whether fractional revivals can form is addressed. We present an analytical proof showing that at certain times equal to rational fractions of the revival times the wave packet can reform as a sum of subsidiary waves and that both conventional and new types of fractional revivals can occur.
Quantum speed limit in a qubit-spin-bath system
We investigate the behavior of quantum speed limit (QSL) time for a typical non-Markovian system, a central spin coupled to a spin star configuration. We connect the QSL time with an external control and show that the effectiveness of the external magnetic field, as well as the coupling strength, is related to the fundamental bounds that affect the maximum speed at which a quantum system can evolve in its state space. We also demonstrate that a spin bath with larger size may shorten the QSL time, while the upper state population plays an important role for the acceleration of quantum evolution in the memory surrounding. (paper)
Quantum beats in fluorescence for multi-level atomic system
For Λ-type three-level atomic systems we have clarified using diagram that (1) it is impossible to observe quantum beats due to the ground state sublevels by measuring the time dependence of the fluorescence intensity, and (2) why it is physically possible to observe and how we can observe quantum beats in the ground state sublevels by using fluorescence. Generalization of the results shows that we can determine from which state (the ground state or the excited state) the quantum beats are originated. Analytical result is shown for four-level atomic systems.
Equivalence relations between deterministic and quantum mechanical systems
Several quantum mechanical models are shown to be equivalent to certain deterministic systems because a basis can be found in terms of which the wave function does not spread. This suggests that apparently indeterministic behavior typical for a quantum mechanical world can be the result of locally deterministic laws of physics. We show how certain deterministic systems allow the construction of a Hilbert space and a Hamiltonian so that at long distance scales they may appear to behave as quantum field theories, including interactions but as yet no mass term. These observations are suggested to be useful for building theories at the Planck scale
Fidelity and entanglement fidelity for infinite-dimensional quantum systems
Instead of unitary freedom for finite-dimensional cases, bi-contractive freedom in the operator-sum representation for quantum channels of infinite-dimensional systems is established. Specifically, if the channel sends every pure state to a finite rank state, then the isometric freedom feature holds. Then, a method of computing entanglement fidelity and a relation between quantum fidelity and entanglement fidelity for infinite-dimensional systems are obtained. In addition, upper and lower bounds of the quantum fidelity, and their connection to the trace distance, are also provided. (paper)
Fractional quantum Hall states in charge-imbalanced bilayer systems
Thiebaut, N.; Regnault, N.; Goerbig, M. O.
2013-01-01
We study the fractional quantum Hall effect in a bilayer with charge-distribution imbalance induced, for instance, by a bias gate voltage. The bilayer can either be intrinsic or it can be formed spontaneously in wide quantum wells, due to the Coulomb repulsion between electrons. We focus on fractional quantum Hall effect in asymmetric bilayer systems at filling factor nu=4/11 and show that an asymmetric Halperin-like trial wavefunction gives a valid description of the ground state of the system.
Quantum Brayton cycle with coupled systems as working substance
Huang, X. L.; Wang, L. C.; Yi, X. X.
2013-01-01
We explore the quantum version of the Brayton cycle with a composite system as the working substance. The actual Brayton cycle consists of two adiabatic and two isobaric processes. Two pressures can be defined in our isobaric process; one corresponds to the external magnetic field (characterized by Fx) exerted on the system, while the other corresponds to the coupling constant between the subsystems (characterized by Fy). As a consequence, we can define two types of quantum Brayton cycle for the composite system. We find that the subsystem experiences a quantum Brayton cycle in one quantum Brayton cycle (characterized by Fx), whereas the subsystem's cycle is quantum Otto cycle in another Brayton cycle (characterized by Fy). The efficiency for the composite system equals to that for the subsystem in both cases, but the work done by the total system is usually larger than the sum of the work done by the two subsystems. The other interesting finding is that for the cycle characterized by Fy, the subsystem can be a refrigerator, while the total system is a heat engine. The result in this paper can be generalized to a quantum Brayton cycle with a general coupled system as the working substance.
On the quantum dynamics of non-commutative systems
Bemfica, F. S.; Girotti, H. O.
2007-01-01
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and quantum dynamics for the models under investigation. We then elaborate on recently reported results concerned with the sufficient conditions for the existence of the Born series and unitarity and turn, afterwards, into analyzing the functional quantization of no...
Information Systems Self-description and Quantum Measurement Problem
Mayburov, S.
2004-01-01
Information-Theoretical restrictions on the systems self-descriptions are applied to Quantum Measurements Theory. For the quantum object S measurement by information system O such restrictions are described by the restricted states formalism by Breuer. The analogous restrictions obtained in Algebraic QM from the analysis of Segal algebra U of O observables; O restricted states set is defined as U dual space. From Segal theorem for the associative subalgebra it's shown that such states describ...
Classical interventions in quantum systems; 1, The measuring process
Peres, A
2000-01-01
The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing decoherence, and then the deletion of a subsystem. No ancilla is needed. The final result is represented by a completely positive map of the quantum state $\\rho$ (possibly with a change of the dimensions of $\\rho$). A continuous limit of this process leads to the Lindblad equation.
The static hyperpolarizability of space-fractional quantum systems
Dawson, Nathan J
2016-01-01
The nonlinear response is investigated for a space-fractional quantum mechanical system subject to a static electric field. Expressions for the polarizability and hyperpolarizability are derived from the fractional Schrodinger equation in the particle-centric view under the three-level ansatz. Two types of asymmetric single-particle quantum systems are studied and both the linear and first nonlinear response to the perturbing field are analyzed with respect to the space-fractional parameter.
Relative state measures of correlations in bipartite quantum systems
Rudolfsson, Pierre; Sjöqvist, Erik
2011-01-01
Everett's concept of relative state can be viewed as a map that contains information about correlations between measurement outcomes on two quantum systems. We demonstrate how geometric properties of the relative state map can be used to develop operationally well-defined measures of the total correlation in bipartite quantum systems of arbitrary state space dimension. These measures are invariant under local unitary transformations and non-increasing under local operations. We show that some...
Energy gaps and interaction blockade in confined quantum systems
Capelle, K.; Borgh, M.; Kärkkäinen, K.; Reimann, S. M.
2007-01-01
Many-body effects in confined quantum systems pose a challenging problem due to the simultaneous presence of particle-particle interactions and spatial inhomogeneity. Here we investigate universal properties of strongly confined particles that turn out to be dramatically different from what is observed for electrons in atoms and molecules. We show that for a large class of harmonically confined systems, including small quantum dots and optically trapped atoms, many-body particle addition and ...
Theory and simulation of cavity quantum electro-dynamics in multi-partite quantum complex systems
The cavity quantum electrodynamics of various complex systems is here analyzed using a general versatile code developed in this research. Such quantum multi-partite systems normally consist of an arbitrary number of quantum dots in interaction with an arbitrary number of cavity modes. As an example, a nine-partition system is simulated under different coupling regimes, consisting of eight emitters interacting with one cavity mode. Two-level emitters (e.g. quantum dots) are assumed to have an arrangement in the form of a linear chain, defining the mutual dipole-dipole interactions. It was observed that plotting the system trajectory in the phase space reveals a chaotic behavior in the so-called ultrastrong-coupling regime. This result is mathematically confirmed by detailed calculation of the Kolmogorov entropy, as a measure of chaotic behavior. In order to study the computational complexity of our code, various multi-partite systems consisting of one to eight quantum dots in interaction with one cavity mode were solved individually. Computation run times and the allocated memory for each system were measured. (orig.)
Theory and simulation of cavity quantum electro-dynamics in multi-partite quantum complex systems
Alidoosty Shahraki, Moslem; Khorasani, Sina; Aram, Mohammad Hasan [Sharif University of Technology, School of Electrical Engineering, Tehran (Iran, Islamic Republic of)
2014-05-15
The cavity quantum electrodynamics of various complex systems is here analyzed using a general versatile code developed in this research. Such quantum multi-partite systems normally consist of an arbitrary number of quantum dots in interaction with an arbitrary number of cavity modes. As an example, a nine-partition system is simulated under different coupling regimes, consisting of eight emitters interacting with one cavity mode. Two-level emitters (e.g. quantum dots) are assumed to have an arrangement in the form of a linear chain, defining the mutual dipole-dipole interactions. It was observed that plotting the system trajectory in the phase space reveals a chaotic behavior in the so-called ultrastrong-coupling regime. This result is mathematically confirmed by detailed calculation of the Kolmogorov entropy, as a measure of chaotic behavior. In order to study the computational complexity of our code, various multi-partite systems consisting of one to eight quantum dots in interaction with one cavity mode were solved individually. Computation run times and the allocated memory for each system were measured. (orig.)
Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics
Auffèves, Alexia; Grangier, Philippe
2016-02-01
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.
The entropy power inequality for quantum systems
Koenig, Robert
2012-01-01
When two independent analog signals, X and Y are added together giving Z=X+Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the entropy power inequality (EPI), which states that exp [2H(Z)] \\geq exp[2H(X) + exp[2H(Y)], gives a very tight restriction on the entropy of Z. This inequality has found many applications in information theory and statistics. The quantum analogue of adding two random variables is the combination of two independent bosonic modes at a beam splitter. The purpose of this work is to give a detailed outline of the proof of two separate generalizations of the entropy power inequality to the quantum regime. Our proofs are similar in spirit to standard classical proofs of the EPI, but some new quantities and ideas are needed in the quantum setting. Specifically, we find a new quantum de Bruijin identity relating entropy production under diffusion to a divergence-based quantum Fisher i...
Scavenging quantum information: Multiple observations of quantum systems
Given an unknown state of a qudit that has already been measured optimally, can one still extract any information about the original unknown state? Clearly, after a maximally informative measurement, the state of the system collapses into a postmeasurement state from which the same observer cannot obtain further information about the original state of the system. However, the system still encodes a significant amount of information about the original preparation for a second observer who is unaware of the actions of the first one. We study how a series of independent observers can obtain, or can scavenge, information about the unknown state of a system (quantified by the fidelity) when they sequentially measure it. We give closed-form expressions for the estimation fidelity when one or several qudits are available to carry information about the single-qudit state, and we study the classical limit when an arbitrarily large number of observers can obtain (nearly) complete information on the system. In addition to the case where all observers perform most informative measurements, we study the scenario where a finite number of observers estimates the state with equal fidelity, regardless of their position in the measurement sequence and the scenario where all observers use identical measurement apparatuses (up to a mutually unknown orientation) chosen so that a particular observer's estimation fidelity is maximized.
Scavenging quantum information: Multiple observations of quantum systems
Rapcan, P. [Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia); Calsamiglia, J.; Munoz-Tapia, R. [Fisica Teorica: Informacio i Fenomens Quantics, Edifici Cn, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Barcelona) (Spain); Bagan, E. [Fisica Teorica: Informacio i Fenomens Quantics, Edifici Cn, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Barcelona) (Spain); Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10021 (United States); Physics Department, Brookhaven National Laboratory, Upton, New York 11973 (United States); Buzek, V. [Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia); Faculty of Informatics, Masaryk University, Botanicka 68a, CZ-602 00 Brno (Czech Republic)
2011-09-15
Given an unknown state of a qudit that has already been measured optimally, can one still extract any information about the original unknown state? Clearly, after a maximally informative measurement, the state of the system collapses into a postmeasurement state from which the same observer cannot obtain further information about the original state of the system. However, the system still encodes a significant amount of information about the original preparation for a second observer who is unaware of the actions of the first one. We study how a series of independent observers can obtain, or can scavenge, information about the unknown state of a system (quantified by the fidelity) when they sequentially measure it. We give closed-form expressions for the estimation fidelity when one or several qudits are available to carry information about the single-qudit state, and we study the classical limit when an arbitrarily large number of observers can obtain (nearly) complete information on the system. In addition to the case where all observers perform most informative measurements, we study the scenario where a finite number of observers estimates the state with equal fidelity, regardless of their position in the measurement sequence and the scenario where all observers use identical measurement apparatuses (up to a mutually unknown orientation) chosen so that a particular observer's estimation fidelity is maximized.
Quantum statistical gravity: time dilation due to local information in many-body quantum systems
Sels, Dries
2016-01-01
We propose a generic mechanism for the emergence of a gravitational potential that acts on all classical objects in a quantum system. Our conjecture is based on the analysis of mutual information in many-body quantum systems. Since measurements in quantum systems affect the surroundings through entanglement, a measurement at one position reduces the entropy in its neighbourhood. This reduction in entropy can be described by a local temperature, that is directly related to the gravitational potential. A crucial ingredient in our argument is that ideal classical mechanical motion occurs at constant probability. This definition is motivated by the analysis of entropic forces in classical systems, which can be formally rewritten in terms of a gravitational potential.
Quantum phase transitions and quantum communication in a spin star system
We consider a generalized spin star system which can be solved exactly, with the central spin-1/2 system embedded in a bath of N spin-1/2 particles. In this system, in addition to the central-outer couplings, each pair of nearest neighbours of the bath spins interacts within themselves. The general expressions of the eigenstates as well as the eigenvalues of the model are derived with the use of symmetries of the system. We then investigate the quantum phase transitions in some limiting cases and show that the occurrence of the quantum phase transitions can be obtained by varying the external control parameters. We further analyse the properties of quantum communication in this model. In the time evolution, some simple and interesting results are discovered concerning transfer fidelity, cloning fidelity, as well as entanglements created
Controllable multiple-quantum transitions in a T-shaped small quantum dot-ring system
Chen, Xiongwen; Chen, Baoju; Song, Kehui; Zhou, Guanghui
2016-05-01
Based on the tight-binding model and the slave boson mean field approximation, we investigate the electron transport properties in a small quantum dot (QD)-ring system. Namely, a strongly correlated QD not only attaches directly to two normal metallic electrodes, but also forms a magnetic control Aharonov-Bohm quantum ring with a few noninteracting QDs. We show that the parity effect, the Kondo effect, and the multiple Fano effects coexist in our system. Moreover, the parities, defined by the odd- and even-numbered energy levels in this system, can be switched by adjusting magnetic flux phase ϕ located at the center of the quantum ring, which induces multiple controllable Fano-interference energy pathways. Therefore, the constructive and destructive multi-Fano interference transition, the Kondo and Fano resonance transition at the Fermi level, the Fano resonance and ani-resonance transition are realized in the even parity system. They can also be observed in the odd parity system when one adjusts the phase ϕ and the gate voltage Vg applied to the noninteracting QDs. The multi-quantum transitions determine some interesting transport properties such as the current switch and its multi-flatsteps, the differential conductance switch at zero bias voltage and its oscillation or quantization at the low bias voltage. These results may be useful for the observation of multiple quantum effect interplays experimentally and the design of controllable QD-based device.
Nanoscale thermal imaging of dissipation in quantum systems
Halbertal, Dorri; Shalom, Moshe Ben; Embon, Lior; Shadmi, Nitzan; Anahory, Yonathan; Naren, HR; Sarkar, Jayanta; Uri, Aviram; Ronen, Yuval; Myasoedov, Yury; Levitov, Leonid; Joselevich, Ernesto; Geim, Andre Konstantin; Zeldov, Eli
2016-01-01
Energy dissipation is a fundamental process governing the dynamics of physical, chemical, and biological systems. It is also one of the main characteristics distinguishing quantum and classical phenomena. In condensed matter physics, in particular, scattering mechanisms, loss of quantum information, or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Despite its vital importance the microscopic behavior of a system is usually not formulated in terms of dissipation because the latter is not a readily measureable quantity on the microscale. Although nanoscale thermometry is gaining much recent interest, the existing thermal imaging methods lack the necessary sensitivity and are unsuitable for low temperature operation required for study of quantum systems. Here we report a superconducting quantum interference nano-thermometer device with sub 50 nm diameter that resides at the apex of a sharp pipette and provides scanning cryogenic thermal se...
Alekseev, K N; Perina, J; Alekseev, Kirill N.; Alekseeva, Natasha V.; Perina, Jan
1999-01-01
We develop a semiclassical method for the determination of the nonlinear dynamics of dissipative quantum optical systems in the limit of large number of photons N, based on the 1/N-expansion and the quantum-classical correspondence. The method has been used to tackle two problems: to study the dynamics of nonclassical state generation in higher-order anharmonic dissipative oscillators and to establish the difference between the quantum and classical dynamics of the second-harmonic generation in a self-pulsing regime. In addressing the first problem, we have obtained an explicit time dependence of the squeezing and the Fano factor for an arbitrary degree of anharmonism in the short-time approximation. For the second problem, we have established analytically a characteristic time scale when the quantum dynamics differs insignificantly from the classical one.
Tampering detection system using quantum-mechanical systems
Humble, Travis S. (Knoxville, TN); Bennink, Ryan S. (Knoxville, TN); Grice, Warren P. (Oak Ridge, TN)
2011-12-13
The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.
Tampering detection system using quantum-mechanical systems
Humble, Travis S.; Bennink, Ryan S.; Grice, Warren P.
2011-12-13
The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.
Approximate locality for quantum systems on graphs.
Osborne, Tobias J
2008-10-01
In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis [Theory Comput. 1, 47 (2005)]: we show that if U is a sparse unitary operator with a gap Delta in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Delta increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk. PMID:18851512
Coherently tracking the covariance matrix of an open quantum system
Miao, Zibo; Hush, Michael R.; James, Matthew R.
2015-07-01
Coherent feedback control of quantum systems has demonstrable advantages over measurement-based control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant and are designed such that some subset of the observer's and plant's expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic oscillators that only converged in mean position and momentum; here we develop a class of covariance matrix tracking (CMT) coherent observers that track both the mean and the covariance matrix of a quantum plant. We derive necessary and sufficient conditions for the existence of a CMT observer and find that there are more restrictions on a CMT observer than there are on a MT observer. We give examples where we demonstrate how to design a CMT observer and show that it can be used to track properties like the entanglement of a plant. As the CMT observer provides more quantum information than a MT observer, we expect it will have greater application in future coherent feedback schemes mediated by coherent observers. Investigation of coherent quantum estimators and observers is important in the ongoing discussion of quantum measurement because they provide an estimation of a system's quantum state without explicit use of the measurement postulate in their derivation.
De Roeck, W., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be; Maes, C., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be; Schütz, M., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be [Instituut voor Theoretische Fysica, KU Leuven, Leuven (Belgium); Netočný, K., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be [Institute of Physics AS CR, Prague (Czech Republic)
2015-02-15
We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand, we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measurement induced entanglement and still satisfying a large deviation principle.
We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand, we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measurement induced entanglement and still satisfying a large deviation principle
A LONE code for the sparse control of quantum systems
Ciaramella, G.; Borzì, A.
2016-03-01
In many applications with quantum spin systems, control functions with a sparse and pulse-shaped structure are often required. These controls can be obtained by solving quantum optimal control problems with L1-penalized cost functionals. In this paper, the MATLAB package LONE is presented aimed to solving L1-penalized optimal control problems governed by unitary-operator quantum spin models. This package implements a new strategy that includes a globalized semi-smooth Krylov-Newton scheme and a continuation procedure. Results of numerical experiments demonstrate the ability of the LONE code in computing accurate sparse optimal control solutions.
Quantum information transfer between topological and spin qubit systems
Leijnse, Martin; Flensberg, Karsten [Nano-Science Center and Niels Bohr Institute, University of Copenhagen (Denmark)
2012-07-01
In this talk I introduce a method to coherently transfer quantum information, and to create entanglement, between topological qubits and conventional spin qubits. The transfer method uses gated control to transfer an electron (spin qubit) between a quantum dot and edge Majorana modes in adjacent topological superconductors. Because of the spin polarization of the Majorana modes, the electron transfer translates spin superposition states into superposition states of the Majorana system, and vice versa. Furthermore, I discuss how a topological superconductor can be used to facilitate long-distance quantum information transfer and entanglement between spatially separated spin qubits.
Time-resolved electron transport in quantum-dot systems
In this thesis the time-resolved electron transport in quantum dot systems was studied. For this two different formalisms were presented: The nonequilibrium Green functions and the generalized quantum master equations. For both formalisms a propagation method for the numerical calculation of time-resolved expectation values, like the occupation and the electron current, was developed. For the demonstration of the propagation method two different question formulations were considered. On the one hand the stochastically driven resonant-level model was studied. On the other hand the pulse-induced transport through a double quantum dot was considered.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban
2016-03-01
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them.
Teleportation of general finite dimensional quantum systems
Albeverio, Sergio; Fei, Shao-Ming
2000-01-01
Teleportation of finite dimensional quantum states by a non-local entangled state is studied. For a generally given entangled state, an explicit equation that governs the teleportation is presented. Detailed examples and the roles played by the dimensions of the Hilbert spaces related to the sender, receiver and the auxiliary space are discussed.
Moving Quantum Systems: Particles Versus Vacuum
Kuckert, Bernd
2002-01-01
We give an overview on a couple of recent results concerning the KMS-condition and the characterization of thermodynamic equilibrium states from a moving observer's point of view. These results include a characterization of vacuum states in relativistic quantum field theory and a general derivation of the Unruh effect.
Photoluminescence of hybrid quantum dot systems
Král, Karel; Menšík, Miroslav
2015-01-01
Roč. 7, č. 4 (2015), 347-349. ISSN 2164-6627 R&D Projects: GA MŠk LH12236; GA MŠk LH12186 Institutional support: RVO:68378271 ; RVO:61389013 Keywords : quantum dots * energy transfer * electron-phonon interaction Subject RIV: BM - Solid Matter Physics ; Magnetism
Reversal of Thermal Rectification in Quantum Systems
Zhang, Lifa; Yan, Yonghong; Wu, Chang-Qin; Wang, Jian-Sheng; Li, Baowen
2009-01-01
We study thermal transport in anisotropic Heisenberg spin chains using the quantum master equation. It is found that thermal rectification changes sign when the external homogeneous magnetic field is varied. This reversal also occurs when the magnetic field becomes inhomogeneous. Moreover, we can tune the reversal of rectification by temperatures of the heat baths, the anisotropy and size of the spin chains.
Atomic quantum systems in optical micro-structures
Full text: We combine state-of-the-art technology in micro-optics with the quantum optical techniques of laser cooling, laser trapping, and quantum control to open a new gateway for quantum information processing and matter wave optics with atomic systems. We use micro-fabricated optical systems to create light fields that allow us to trap and guide neutral atoms as a result of the optical dipole force experienced by the atoms. The realization of arrays of laser traps that can serve as registers for atomic quantum bits and as integrated waveguide structures for atom optics and atom interferometry has been achieved. This approach opens the possibility to scale, parallelize, and miniaturize systems for quantum information processing and atom optics. Currently we investigate the production of quantum-degenerate systems in pure optical trapping geometries and the coherent manipulation (1-qubit rotations, Ramsey-oscillations, spin-echo experiments) of internal qubit states for atoms trapped in arrays of dipole traps (author)
Quantum phase transitions in Bose-Fermi systems
Research highlights: → We study quantum phase transitions in a system of N bosons and a single-j fermion. → Classical order parameters and correlation diagrams of quantum levels are determined. → The odd fermion strongly influences the location and nature of the phase transition. → Experimental evidence for the U(5)-SU(3) transition in odd-even nuclei is presented. - Abstract: Quantum phase transitions in a system of N bosons with angular momentum L = 0, 2 (s, d) and a single fermion with angular momentum j are investigated both classically and quantum mechanically. It is shown that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially the critical value of the control parameter at which the phase transition occurs. Experimental evidence for the U(5)-SU(3) (spherical to axially-deformed) transition in odd-even nuclei is presented.
Enhancing quantum effects via periodic modulations in optomechanical systems
Farace, Alessandro; Giovannetti, Vittorio
2012-07-01
Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the oscillator position (or momentum) and the enhancement of entanglement between mechanical and radiation modes. In this paper we further investigate this modulation regime, considering an optomechanical system with one or more parameters being modulated over time. We first apply a sinusoidal modulation of the mechanical frequency and characterize the optimal regime in which the visibility of purely quantum effects is maximal. We then introduce a second modulation on the input laser intensity and analyze the interplay between the two. We find that an interference pattern shows up, so that different choices of the relative phase between the two modulations can either enhance or cancel the desired quantum effects, opening new possibilities for optimal quantum control strategies.
Controlling open quantum systems: tools, achievements, and limitations.
Koch, Christiane P
2016-06-01
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge of preserving relevant nonclassical features at the level of device operation. A major obstacle is decoherence, which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. Here we review recent advances in optimal control methodology that allow typical tasks in device operation for open quantum systems to be tackled and discuss examples of relaxation-optimized dynamics. Optimal control theory is also a useful tool to exploit the environment for control. We discuss examples and point out possible future extensions. PMID:27143501
Controlling open quantum systems: tools, achievements, and limitations
Koch, Christiane P.
2016-06-01
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge of preserving relevant nonclassical features at the level of device operation. A major obstacle is decoherence, which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. Here we review recent advances in optimal control methodology that allow typical tasks in device operation for open quantum systems to be tackled and discuss examples of relaxation-optimized dynamics. Optimal control theory is also a useful tool to exploit the environment for control. We discuss examples and point out possible future extensions.
Microscopic Properties of Quantum Annealing -- Application to Fully Frustrated Ising Systems
Tanaka, Shu
2011-01-01
In this paper we show quantum fluctuation effect of fully frustrated Ising spin systems. Quantum annealing has been expected to be an efficient method to find ground state of optimization problems. However it is not clear when to use the quantum annealing. In order to clarify when the quantum annealing works well, we have to study microscopic properties of quantum annealing. In fully frustrated Ising spin systems, there are macroscopically degenerated ground states. When we apply quantum anne...
Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
Borgonovi, F.; Izrailev, F. M.; Santos, L. F.; Zelevinsky, V. G.
2016-01-01
This review is devoted to the problem of thermalization in a small isolated conglomerate of interacting constituents. A variety of physically important systems of intensive current interest belong to this category: complex atoms, molecules (including biological molecules), nuclei, small devices of condensed matter and quantum optics on nano- and micro-scale, cold atoms in optical lattices, ion traps. Physical implementations of quantum computers, where there are many interacting qubits, also ...
Conductance distributions in disordered quantum spin-Hall systems
Kobayashi, K; Ohtsuki, T.; Obuse, H.; Slevin, K.
2010-01-01
We study numerically the charge conductance distributions of disordered quantum spin-Hall (QSH) systems using a quantum network model. We have found that the conductance distribution at the metal-QSH insulator transition is clearly different from that at the metal-ordinary insulator transition. Thus the critical conductance distribution is sensitive not only to the boundary condition but also to the presence of edge states in the adjacent insulating phase. We have also calculated the point-co...
Hierarchy of stochastic pure states for open quantum system dynamics
Süß, D.; Eisfeld, A.; Strunz, W. T.
2014-01-01
We derive a hierarchy of stochastic evolution equations for pure states (quantum trajectories) to efficiently solve open quantum system dynamics with non-Markovian structured environments. From this hierarchy of pure states (HOPS) the exact reduced density operator is obtained as an ensemble average. We demonstrate the power of HOPS by applying it to the Spin-Boson model, the calculation of absorption spectra of molecular aggregates and energy transfer in a photosynthetic pigment-protein comp...
Coherently tracking the covariance matrix of an open quantum system
Miao, Zibo; Hush, Michael R.; James, Matthew
2015-01-01
Coherent feedback control of quantum systems has demonstrable advantages over measurement-based control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant, and are designed such that some subset of the observer and plant's expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic osc...
GRAVITATIONAL WAVES AND STATIONARY STATES OF QUANTUM AND CLASSICAL SYSTEMS
Trunev A. P.
2014-03-01
Full Text Available In this paper, we consider gravitation theory in multidimensional space. The model of the metric satisfying the basic requirements of quantum theory is proposed. It is shown that gravitational waves are described by the Liouville equation and the Schrodinger equation as well. The solutions of the Einstein equations describing the stationary states of arbitrary quantum and classical systems with central symmetry have been obtained. Thus, it is proved that atoms and atomic nuclei can be represented as standing gravitational waves
Quantum mechanics of rapidly and periodically driven systems
Malay Bandyopadhyay; Sushanta Dattagupta
2008-03-01
This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a `Kapitza Window' over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields.
Quantum computing with collective ensembles of multi-level systems
Brion, E.; Moelmer, K.; Saffman, M.
2007-01-01
We propose a new physical approach for encoding and processing of quantum information in ensembles of multi-level quantum systems, where the different bits are not carried by individual particles but associated with the collective population of different internal levels. One- and two-bit gates are implemented by collective internal state transitions taking place in the presence of an excitation blockade mechanism which restricts the population of each internal state to the values zero and uni...
A term-rewriting system for computer quantum algebra
J. J. Hudson
2008-01-01
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the invariant formalism of quantum mechanics. I first describe the essential mathematical features of the Hilbert-space invariant formalism. This is followed by a formal characterisation of all possible algebraic expressions in this formalism. This characterisat...
Nuclear magnetometry studies of spin dynamics in quantum Hall systems
Fauzi, M. H.; Watanabe, S.; Hirayama, Y.
2014-12-01
We performed a nuclear magnetometry study on quantum Hall ferromagnet with a bilayer total filling factor of νtot=2 . We found not only a rapid nuclear relaxation but also a sudden change in the nuclear-spin polarization distribution after a one-second interaction with a canted antiferromagnetic phase. We discuss the possibility of observing cooperative phenomena coming from nuclear-spin ensemble triggered by hyperfine interaction in quantum Hall system.
Far from equilibrium energy flow in quantum critical systems
Bhaseen, M J; Lucas, Andrew; Schalm, Koenraad
2013-01-01
We investigate far from equilibrium energy transport in strongly coupled quantum critical systems. Combining results from gauge-gravity duality, relativistic hydrodynamics, and quantum field theory, we argue that long-time energy transport occurs via a universal steady-state for any spatial dimensionality. This is described by a boosted thermal state. We determine the transport properties of this emergent steady state, including the average energy flow and its long-time fluctuations.
A short review on entanglement in quantum spin systems
Latorre, J. I.; Riera, A.
2009-01-01
We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical ev...
Quantum Hall effect in bilayer system with array of antidots
Pagnossin, I. R.; Gusev, G. M.; Sotomayor, N. M.; Seabra, A. C.; Quivy, A. A.; Lamas, T. E.; Portal, J. C.
2007-04-01
We have studied the Quantum Hall effect in a bilayer system modulated by gate-controlled antidot lattice potential. The Hall resistance shows plateaus which are quantized to anomalous multiplies of h/e2. We suggest that this complex behavior is due to the nature of the edge-states in double quantum well (DQW) structures coupled to an array of antidots: these plateaus may be originated from the coexistence of normal and counter-rotating edge-states in different layers.
Quantum information transfer between topological and spin qubit systems
Leijnse, Martin; Flensberg, Karsten
2011-01-01
We propose a method to coherently transfer quantum information, and to create entanglement, between topological qubits and conventional spin qubits. Our suggestion uses gated control to transfer an electron (spin qubit) between a quantum dot and edge Majorana modes in adjacent topological superconductors. Because of the spin polarization of the Majorana modes, the electron transfer translates spin superposition states into superposition states of the Majorana system, and vice versa. Furthermo...
Petersen, Ian R.
2015-01-01
This paper considers the problem of constructing a direct coupled quantum observer network for a single qubit quantum system. The proposed observer consists of a network of quantum harmonic oscillators and it is shown that the observer network output converges to a consensus in a time averaged sense in which each component of the observer estimates a specified output of the quantum plant. An example and simulations are included.
Method for adding nodes to a quantum key distribution system
Grice, Warren P
2015-02-24
An improved quantum key distribution (QKD) system and method are provided. The system and method introduce new clients at intermediate points along a quantum channel, where any two clients can establish a secret key without the need for a secret meeting between the clients. The new clients perform operations on photons as they pass through nodes in the quantum channel, and participate in a non-secret protocol that is amended to include the new clients. The system and method significantly increase the number of clients that can be supported by a conventional QKD system, with only a modest increase in cost. The system and method are compatible with a variety of QKD schemes, including polarization, time-bin, continuous variable and entanglement QKD.
Deconstructing non-Dirac-Hermitian supersymmetric quantum systems
Ghosh, Pijush K, E-mail: pijushkanti.ghosh@visva-bharati.ac.in [Department of Physics, Siksha-Bhavana, Visva-Bharati University, Santiniketan 731 235, West Bengal (India)
2011-05-27
A method to construct a non-Dirac-Hermitian supersymmetric quantum system that is isospectral with a Dirac-Hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving both bosonic and fermionic degrees of freedom in terms of non-Dirac-Hermitian operators which are Hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. A pseudo-Hermitian realization of the Clifford algebra for a pre-determined positive-definite metric is used to construct supersymmetric systems with one or many degrees of freedom. It is shown that exactly solvable non-Dirac-Hermitian supersymmetric quantum systems can be constructed corresponding to each exactly solvable Dirac-Hermitian system. Examples of non-Dirac-Hermitian (i) non-relativistic Pauli Hamiltonian, (ii) super-conformal quantum system, and (iii) supersymmetric Calogero-type models admitting entirely real spectra are presented.
Heat-exchange statistics in driven open quantum systems
As the dimensions of physical systems approach the nanoscale, the laws of thermodynamics must be reconsidered due to the increased importance of fluctuations and quantum effects. While the statistical mechanics of small classical systems is relatively well understood, the quantum case still poses challenges. Here, we set up a formalism that allows us to calculate the full probability distribution of energy exchanges between a periodically driven quantum system and a thermalized heat reservoir. The formalism combines Floquet theory with a generalized master equation approach. For a driven two-level system and in the long-time limit, we obtain a universal expression for the distribution, providing clear physical insight into the exchanged energy quanta. We illustrate our approach in two analytically solvable cases and discuss the differences in the corresponding distributions. Our predictions could be directly tested in a variety of systems, including optical cavities and solid-state devices. (paper)
Quantum demolition filtering and optimal control of unstable systems.
Belavkin, V P
2012-11-28
A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one. PMID:23091216
Measures of correlations in infinite-dimensional quantum systems
Shirokov, M. E.
2016-05-01
Several important measures of correlations of the state of a finite-dimensional composite quantum system are defined as linear combinations of marginal entropies of this state. This paper is devoted to infinite-dimensional generalizations of such quantities and to an analysis of their properties. We introduce the notion of faithful extension of a linear combination of marginal entropies and consider several concrete examples, the simplest of which are quantum mutual information and quantum conditional entropy. Then we show that quantum conditional mutual information can be defined uniquely as a lower semicontinuous function on the set of all states of a tripartite infinite-dimensional system possessing all the basic properties valid in finite dimensions. Infinite-dimensional generalizations of some other measures of correlations in multipartite quantum systems are also considered. Applications of the results to the theory of infinite-dimensional quantum channels and their capacities are considered. The existence of a Fawzi-Renner recovery channel reproducing marginal states for all tripartite states (including states with infinite marginal entropies) is shown. Bibliography: 47 titles.
Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach
Using the quantum trajectory approach, we extend the Born-Oppenheimer (BO) approximation from closed to open quantum systems, where the open quantum system is described by a master equation in Lindblad form. The BO approximation is defined and the validity condition is derived. We find that the dissipation in fast variables improves the BO approximation, unlike the dissipation in slow variables. A detailed comparison is presented between this extension and our previous approximation based on the effective Hamiltonian approach [X. L. Huang and X. X. Yi, Phys. Rev. A 80, 032108 (2009)]. Several additional features and advantages are analyzed, which show that the two approximations are complementary to each other. Two examples are described to illustrate our method.
A quantum information perspective of fermionic quantum many-body systems
Kraus, Christina V.
2009-11-02
In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS
A quantum information perspective of fermionic quantum many-body systems
In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS known for spin systems, and they
Numerical approaches to complex quantum, semiclassical and classical systems
In this work we analyse the capabilities of several numerical techniques for the description of different physical systems. Thereby, the considered systems range from quantum over semiclassical to classical and from few- to many-particle systems. In chapter 1 we investigate the behaviour of a single quantum particle in the presence of an external disordered background (static potentials). Starting from the quantum percolation problem, we address the fundamental question of a disorder induced (Anderson-) transition from extended to localised single-particle eigenstates. Distinguishing isolating from conducting states by applying a local distribution approach for the local density of states (LDOS), we detect the quantum percolation threshold in two- and three-dimensions. Extending the quantum percolation model to a quantum random resistor model, we comment on the possible relevance of our results to the influence of disorder on the conductivity in graphene sheets. For the calculation of the LDOS as well as for the Chebyshev expansion of the time evolution operator, the kernel polynomial method (KPM) is the key numerical technique. In chapter 2 we examine how a single quantum particle is influenced by retarded bosonic fields that are inherent to the system. Within the Holstein model, these bosonic degrees of freedom (phonons) give rise to an infinite dimensional Hilbert space, posing a true many-particle problem. Constituting a minimal model for polaron formation, the Holstein model allows us to study the optical absorption and activated transport in polaronic systems. Using a two-dimensional variant of the KPM, we calculate for the first time quasi-exactly the optical absorption and dc-conductivity as a function of temperature. In chapter 3 we come back to the time evolution of a quantum particle in an external, static potential and investigate the capability of semiclassical approximations to it. We address basic quantum effects as tunneling, interference and
Numerical approaches to complex quantum, semiclassical and classical systems
Schubert, Gerald
2008-11-03
In this work we analyse the capabilities of several numerical techniques for the description of different physical systems. Thereby, the considered systems range from quantum over semiclassical to classical and from few- to many-particle systems. In chapter 1 we investigate the behaviour of a single quantum particle in the presence of an external disordered background (static potentials). Starting from the quantum percolation problem, we address the fundamental question of a disorder induced (Anderson-) transition from extended to localised single-particle eigenstates. Distinguishing isolating from conducting states by applying a local distribution approach for the local density of states (LDOS), we detect the quantum percolation threshold in two- and three-dimensions. Extending the quantum percolation model to a quantum random resistor model, we comment on the possible relevance of our results to the influence of disorder on the conductivity in graphene sheets. For the calculation of the LDOS as well as for the Chebyshev expansion of the time evolution operator, the kernel polynomial method (KPM) is the key numerical technique. In chapter 2 we examine how a single quantum particle is influenced by retarded bosonic fields that are inherent to the system. Within the Holstein model, these bosonic degrees of freedom (phonons) give rise to an infinite dimensional Hilbert space, posing a true many-particle problem. Constituting a minimal model for polaron formation, the Holstein model allows us to study the optical absorption and activated transport in polaronic systems. Using a two-dimensional variant of the KPM, we calculate for the first time quasi-exactly the optical absorption and dc-conductivity as a function of temperature. In chapter 3 we come back to the time evolution of a quantum particle in an external, static potential and investigate the capability of semiclassical approximations to it. We address basic quantum effects as tunneling, interference and
Classical and quantum pumping in closed systems
Cohen, Doron
2002-01-01
Pumping of charge (Q) in a closed ring geometry is not quantized even in the strict adiabatic limit. The deviation form exact quantization can be related to the Thouless conductance. We use Kubo formalism as a starting point for the calculation of both the dissipative and the adiabatic contributions to Q. As an application we bring examples for classical dissipative pumping, classical adiabatic pumping, and in particular we make an explicit calculation for quantum pumping in case of the simpl...
Quantum Energy Teleportation in Spin Chain Systems
Hotta, Masahiro
2008-01-01
We propose a protocol for quantum energy teleportation which transports energy in spin chains to distant sites only by local operations and classical communication. By utilizing ground-state entanglement and notion of negative energy density region, energy is teleported without breaking any physical laws including causality and local energy conservation. Because not excited physical entity but classical information is transported in the protocol, the dissipation rate of energy in transport is...
Quantum dynamics of deformed open systems
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model using perturbation theory . The coefficient of the master equation depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation. (author)
Schmidt information and entanglement in quantum systems
Bogdanov, A. Yu.; Bogdanov, Yu. I.; Valiev, K. A.
2005-01-01
The purpose of this paper is to study entanglement of quantum states by means of Schmidt decomposition. The notion of Schmidt information which characterizes the non-randomness of correlations between two observers that conduct measurements of EPR-states is proposed. In two important particular cases - a finite number of Schmidt modes with equal probabilities and Gaussian correlations- Schmidt information is equal to Shannon information. A universal measure of a dependence of two variables is...
Applications of fidelity measures to complex quantum systems.
Wimberger, Sandro
2016-06-13
We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular-chaotic phase space. PMID:27140967
Information theory of quantum systems with some hydrogenic applications
Dehesa, J S; Sánchez-Moreno, P S; Yáñez, R J
2010-01-01
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the quantum-mechanical non-relativistic systems can be quantified by various single (Fisher information, Shannon entropy) and composite (e.g. Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the Schr\\"odinger probability density. First, we examine these concepts and its application to quantum systems with central potentials. Then, we calculate these measures for hydrogenic systems, emphasizing their predictive power for various physical phenomena. Finally, some recent open problems are pointed out.
Communication theory of quantum systems. Ph.D. Thesis, 1970
Yuen, H. P. H.
1971-01-01
Communication theory problems incorporating quantum effects for optical-frequency applications are discussed. Under suitable conditions, a unique quantum channel model corresponding to a given classical space-time varying linear random channel is established. A procedure is described by which a proper density-operator representation applicable to any receiver configuration can be constructed directly from the channel output field. Some examples illustrating the application of our methods to the development of optical quantum channel representations are given. Optimizations of communication system performance under different criteria are considered. In particular, certain necessary and sufficient conditions on the optimal detector in M-ary quantum signal detection are derived. Some examples are presented. Parameter estimation and channel capacity are discussed briefly.
Nexus: A modular workflow management system for quantum simulation codes
Krogel, Jaron T.
2016-01-01
The management of simulation workflows represents a significant task for the individual computational researcher. Automation of the required tasks involved in simulation work can decrease the overall time to solution and reduce sources of human error. A new simulation workflow management system, Nexus, is presented to address these issues. Nexus is capable of automated job management on workstations and resources at several major supercomputing centers. Its modular design allows many quantum simulation codes to be supported within the same framework. Current support includes quantum Monte Carlo calculations with QMCPACK, density functional theory calculations with Quantum Espresso or VASP, and quantum chemical calculations with GAMESS. Users can compose workflows through a transparent, text-based interface, resembling the input file of a typical simulation code. A usage example is provided to illustrate the process.
Effect of Noise on Practical Quantum Communication Systems
Vishal Sharma
2016-03-01
Full Text Available Entanglement is an important resource for various applications of quantum computation. Another important endeavor is to establish the role of entanglement in practical implementation where system of interest is affected by various kinds of noisy channels. Here, a single classical bit is used to send information under the influence of a noisy quantum channel. The entanglement content of quantum states is computed under noisy channels such as amplitude damping, phase damping, squeesed generalised amplitude damping, Pauli channels and various collective noise models on the protocols of quantum key distribution.Defence Science Journal, Vol. 66, No. 2, March 2016, pp. 186-192, DOI: http://dx.doi.org/10.14429/dsj.66.9771
Autonomous quantum thermal machines in atom-cavity systems
Mitchison, Mark T; Prior, Javier; Woods, Mischa P; Plenio, Martin B
2016-01-01
An autonomous quantum thermal machine comprising a trapped atom or ion placed inside an optical cavity is proposed and analysed. Such a machine can operate as a heat engine whose working medium is the quantised atomic motion, or as an absorption refrigerator which cools without any work input. Focusing on the refrigerator mode, we predict that it is possible with state-of-the-art technology to cool a trapped ion almost to its motional ground state using a thermal light source such as sunlight. We nonetheless find that a laser or similar reference system is necessary to stabilise the cavity frequencies. Furthermore, we establish a direct and heretofore unacknowledged connection between the abstract theory of quantum absorption refrigerators and practical sideband cooling techniques. We also highlight and clarify some assumptions underlying several recent theoretical studies on self-contained quantum engines and refrigerators. Our work indicates that cavity quantum electrodynamics is a promising and versatile e...
Quantum and Classical Behavior in Interacting Bosonic Systems
Hertzberg, Mark P
2016-01-01
It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that...
Hidden symmetries enhance quantum transport in Light Harvesting systems
Zech, Tobias; Wellens, Thomas; Buchleitner, Andreas
2012-01-01
For more than 50 years we have known that photosynthetic systems harvest solar energy with almost unit {\\it quantum efficiency}. However, recent experimental evidence of {\\it quantum coherence} during the excitonic energy transport in photosynthetic organisms challenges our understanding of this fundamental biological function. Currently, and despite numerous efforts, the causal connection between coherence and efficiency is still a matter of debate. We show, through the study of extensive simulations of quantum coherent transport on networks, that three dimensional structures characterized by centro-symmetric Hamiltonians are statistically more efficient than random arrangements. Moreover, we demonstrate that the experimental data available for the electronic Hamiltonians of the Fenna-Mathew-Olson (FMO) complex of sulfur bacteria and of the crypophyte PC645 complex of marine algae are consistent with this strong correlation of centro-symmetry with quantum efficiency. These results show that what appears to b...
An Online Banking System Based on Quantum Cryptography Communication
Zhou, Ri-gui; Li, Wei; Huan, Tian-tian; Shen, Chen-yi; Li, Hai-sheng
2014-07-01
In this paper, an online banking system has been built. Based on quantum cryptography communication, this system is proved unconditional secure. Two sets of GHZ states are applied, which can ensure the safety of purchase and payment, respectively. In another word, three trading participants in each triplet state group form an interdependent and interactive relationship. In the meantime, trading authorization and blind signature is introduced by means of controllable quantum teleportation. Thus, an effective monitor is practiced on the premise that the privacy of trading partners is guaranteed. If there is a dispute or deceptive behavior, the system will find out the deceiver immediately according to the relationship mentioned above.
Tunable supercurrent in a triangular triple quantum dot system
The supercurrent in a triangular triple quantum dot system is investigated by using the nonequilibrium Green's function method. It is found that the sign of the supercurrent can be changed from positive to negative with increasing the strength of spin-flip scattering, resulting in the π-junction transition. The supercurrent and the π-junction transition are also modulated by tuning the system parameters such as the gate voltage and the interdot coupling. The tunable π-junction transition is explained in terms of the current carrying density of states. These results provide the ways of manipulating the supercurrent in a triple quantum dot system.
Work and its fluctuations in a driven quantum system
Solinas, Paolo; AVERIN, Dmitri V.; Pekola, Jukka P.
2013-01-01
We analyze work done on a quantum system driven by a control field. The average work depends on the whole dynamics of the system, and is obtained as the integral of the average power operator. As a specific example we focus on a superconducting Cooper-pair box forming a two-level system. We obtain expressions for the average work and work distribution in a closed system, and discuss control field and environment contributions to the average work for an open system.
Phase representation of quantum-optical systems via nonnegative quantum distribution function
We propose a new method for describing phase distributions of nonclassical states in optical systems based on the nonnegative quantum distribution function. A comparison of the proposed method with other known methods such as the Pegg-Barnett and operational ones is given
GRAVITATIONAL WAVES AND EMERGENCE PARAMETER OF CLASSICAL AND QUANTUM SYSTEMS
Trunev A. P.
2014-03-01
Full Text Available It was established that the Fermi-Dirac statistics, Bose-Einstein and Maxwell-Boltzmann distribution can be described by a single equation, which follows from Einstein's equations for systems with central symmetry. Emergence parameter of classical and quantum systems composed by the rays of gravitational waves interacting with gravitational field of the universe has been computed
Coherent Quantum Optics Phenomena in Carbon Low-Dimensional Systems
Dovlatova, Alla; Yerchuck, Dmitri
2011-01-01
Brief review of the theoretical and experimental results, based mainly on the works of authors, in the application of quantum field theory to the study of carbon low-dimensional systems - quasi-1D carbon nanotubes, carbynes and graphene with emphasis on formation of longlived coherent states of joint photon-electron and joint resonance phonon-electron systems of given materials is presented.
Dissipation and entropy production in open quantum systems
Majima, H; Suzuki, A, E-mail: majima@rs.kagu.tus.ac.j, E-mail: asuzuki@rs.kagu.tus.ac.j [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 Japan (Japan)
2010-11-01
A microscopic description of an open system is generally expressed by the Hamiltonian of the form: H{sub tot} = H{sub sys} + H{sub environ} + H{sub sys-environ}. We developed a microscopic theory of entropy and derived a general formula, so-called 'entropy-Hamiltonian relation' (EHR), that connects the entropy of the system to the interaction Hamiltonian represented by H{sub sys-environ} for a nonequilibrium open quantum system. To derive the EHR formula, we mapped the open quantum system to the representation space of the Liouville-space formulation or thermo field dynamics (TFD), and thus worked on the representation space L := H x H-tilde, where H denotes the ordinary Hilbert space while H-tilde the tilde Hilbert space conjugates to H. We show that the natural transformation (mapping) of nonequilibrium open quantum systems is accomplished within the theoretical structure of TFD. By using the obtained EHR formula, we also derived the equation of motion for the distribution function of the system. We demonstrated that by knowing the microscopic description of the interaction, namely, the specific form of H{sub sys-environ} on the representation space L, the EHR formulas enable us to evaluate the entropy of the system and to gain some information about entropy for nonequilibrium open quantum systems.
Dissipation and entropy production in open quantum systems
Majima, H.; Suzuki, A.
2010-11-01
A microscopic description of an open system is generally expressed by the Hamiltonian of the form: Htot = Hsys + Henviron + Hsys-environ. We developed a microscopic theory of entropy and derived a general formula, so-called "entropy-Hamiltonian relation" (EHR), that connects the entropy of the system to the interaction Hamiltonian represented by Hsys-environ for a nonequilibrium open quantum system. To derive the EHR formula, we mapped the open quantum system to the representation space of the Liouville-space formulation or thermo field dynamics (TFD), and thus worked on the representation space Script L := Script H otimes , where Script H denotes the ordinary Hilbert space while the tilde Hilbert space conjugates to Script H. We show that the natural transformation (mapping) of nonequilibrium open quantum systems is accomplished within the theoretical structure of TFD. By using the obtained EHR formula, we also derived the equation of motion for the distribution function of the system. We demonstrated that by knowing the microscopic description of the interaction, namely, the specific form of Hsys-environ on the representation space Script L, the EHR formulas enable us to evaluate the entropy of the system and to gain some information about entropy for nonequilibrium open quantum systems.
Hidden symmetry of the quantum Calogero-Moser system
Kuzentsov, Vadim b
1996-01-01
The hidden symmetry of the quantum Calogero-Moser system with an inverse-square potential is algebraically demonstrated making use of Dunkl's operators. We find the underlying algebra explaining the super-integrability phenomenon for this system. Applications to related multi-variable Bessel...
The quantum systems control and the optimal control theory
Krotov, V. F.
2008-01-01
Mathematical theory of the quantum systems control is based on some ideas of the optimal control theory. These ideas are developed here as applied to these systems. The results obtained meet the deficiencies in the basis and algorithms of the control synthesis and expand the application of these methods.
Entanglement Routers via Wireless Quantum Network Based on Arbitrary Two Qubit Systems
Metwally, N.
2014-01-01
A wireless quantum network is generated between multi-hop, where each hop consists of two entangled nodes. These nodes share a finite number of entangled two qubit systems randomly. Different types of wireless quantum bridges are generated between the non-connected nodes. The efficiency of these wireless quantum bridges to be used as quantum channels between its terminals to perform quantum teleportation is investigated. We suggest a theoretical wireless quantum communication protocol to tele...
Continuity of the entropy of macroscopic quantum systems.
Swendsen, Robert H
2015-11-01
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics. PMID:26651650
The Kitaev–Feynman clock for open quantum systems
We show that Kitaev's construction of Feynman's clock, in which the time-evolution of a closed quantum system is encoded as a ground state problem, can be extended to open quantum systems. In our formalism, the ground states of an ensemble of non-Hermitian Kitaev–Feynman clock Hamiltonians yield stochastic trajectories, which unravel the evolution of a Lindblad master equation. In this way, one can use the Kitaev–Feynman clock not only to simulate the evolution of a quantum system, but also its interaction with an environment such as a heat bath or measuring apparatus. A simple numerical example of a two-level atom undergoing spontaneous emission is presented and analyzed. (paper)
Controllable quantum information network with a superconducting system
Zhang, Feng-yang, E-mail: zhangfy@mail.dlut.edu.cn [School of Physics and Materials Engineering, Dalian Nationalities University, Dalian 116600 (China); Liu, Bao [Beijing Computational Science Research Center (CSRC), Beijing 100084 (China); Chen, Zi-hong [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Wu, Song-lin [School of Physics and Materials Engineering, Dalian Nationalities University, Dalian 116600 (China); Song, He-shan [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China)
2014-07-15
We propose a controllable and scalable architecture for quantum information processing using a superconducting system network, which is composed of current-biased Josephson junctions (CBJJs) as tunable couplers between the two superconducting transmission line resonators (TLRs), each coupling to multiple superconducting qubits (SQs). We explicitly demonstrate that the entangled state, the phase gate, and the information transfer between any two selected SQs can be implemented, respectively. Lastly, numerical simulation shows that our scheme is robust against the decoherence of the system. -- Highlights: •An architecture for quantum information processing is proposed. •The quantum information transfer between any two selected SQs is implemented. •This proposal is robust against the decoherence of the system. •This architecture can be fabricated on a chip down to the micrometer scale.
Emergent hydrodynamics in integrable quantum systems out of equilibrium
Castro-Alvaredo, Olalla A; Yoshimura, Takato
2016-01-01
Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics. With experiments now able to access the intricate dynamics of many-body quantum systems, it is paramount to develop powerful and widely applicable methods that encode the emergent physics. Up to now, the strong dichotomy observed between integrable and non-integrable evolutions made an overarching theory difficult to build, especially for transport phenomena where space-time profiles show drastically different behaviours. We present a novel framework for studying transport in integrable systems: that of emergent hydrodynamics with infinitely-many conservation laws. This method bridges the conceptual gap between integrable and non-integrable quantum dynamics. We apply it to the description of energy transport between heat baths in interacting integrable systems. We provide for the first time a full description of the current-carrying non-equil...
Locally indistinguishable orthogonal product bases in arbitrary bipartite quantum system
Xu, Guang-Bao; Yang, Ying-Hui; Wen, Qiao-Yan; Qin, Su-Juan; Gao, Fei
2016-08-01
As we know, unextendible product basis (UPB) is an incomplete basis whose members cannot be perfectly distinguished by local operations and classical communication. However, very little is known about those incomplete and locally indistinguishable product bases that are not UPBs. In this paper, we first construct a series of orthogonal product bases that are completable but not locally distinguishable in a general m ⊗ n (m ≥ 3 and n ≥ 3) quantum system. In particular, we give so far the smallest number of locally indistinguishable states of a completable orthogonal product basis in arbitrary quantum systems. Furthermore, we construct a series of small and locally indistinguishable orthogonal product bases in m ⊗ n (m ≥ 3 and n ≥ 3). All the results lead to a better understanding of the structures of locally indistinguishable product bases in arbitrary bipartite quantum system.
Continuity of the entropy of macroscopic quantum systems
Swendsen, Robert H.
2015-11-01
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics.
Quantum ergodicity for a class of non-generic systems
We examine quantum normal typicality and ergodicity properties for quantum systems whose dynamics are generated by Hamiltonians which have residual degeneracy in their spectrum and resonance in their energy gaps. Such systems can be considered atypical in the sense that degeneracy, which is usually a sign of symmetry, is naturally broken in typical systems due to stochastic perturbations. In particular, we prove a version of von Neumann’s quantum ergodic theorem, where a modified condition needs to hold in order to have normal typicality and ergodicity. As a result, we show that degeneracy of spectrum does not considerably modify the condition of the theorem, whereas the existence of resonance is more dominant for obstructing ergodicity. (paper)
Controllable quantum information network with a superconducting system
We propose a controllable and scalable architecture for quantum information processing using a superconducting system network, which is composed of current-biased Josephson junctions (CBJJs) as tunable couplers between the two superconducting transmission line resonators (TLRs), each coupling to multiple superconducting qubits (SQs). We explicitly demonstrate that the entangled state, the phase gate, and the information transfer between any two selected SQs can be implemented, respectively. Lastly, numerical simulation shows that our scheme is robust against the decoherence of the system. -- Highlights: •An architecture for quantum information processing is proposed. •The quantum information transfer between any two selected SQs is implemented. •This proposal is robust against the decoherence of the system. •This architecture can be fabricated on a chip down to the micrometer scale
In this paper we study Spectral Decomposition Theorem (Lasota and Mackey, 1985) and translate it to quantum language by means of the Wigner transform. We obtain a Quantum Version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct goals: First, to rank Quantum Ergodic Hierarchy levels (Castagnino and Lombardi, 2009, Gomez and Castagnino, 2014). Second, to analyze the classical limit in quantum ergodic systems and quantum mixing systems. And third, and maybe most important feature, to find a relevant and simple connection between the first three levels of Quantum Ergodic Hierarchy (ergodic, exact and mixing) and quantum spectrum. Finally, we illustrate the physical relevance of QSDT applying it to two examples: Microwave billiards (Stockmann, 1999, Stoffregen et al. 1995) and a phenomenological Gamow model type (Laura and Castagnino, 1998, Omnès, 1994)
Quantum sweeps, synchronization, and Kibble-Zurek physics in dissipative quantum spin systems
Henriet, Loïc; Le Hur, Karyn
2016-02-01
We address dissipation effects on the nonequilibrium quantum dynamics of an ensemble of spins-1/2 coupled via an Ising interaction. Dissipation is modeled by a (Ohmic) bath of harmonic oscillators at zero temperature and correspond either to the sound modes of a one-dimensional Bose-Einstein (quasi-)condensate or to the zero-point fluctuations of a long transmission line. We consider the dimer comprising two spins and the quantum Ising chain with long-range interactions and develop an (mathematically and numerically) exact stochastic approach to address nonequilibrium protocols in the presence of an environment. For the two-spin case, we first investigate the dissipative quantum phase transition induced by the environment through quantum quenches and study the effect of the environment on the synchronization properties. Then we address Landau-Zener-Stueckelberg-Majorana protocols for two spins and for the spin array. In this latter case, we adopt a stochastic mean-field point of view and present a Kibble-Zurek-type argument to account for interaction effects in the lattice. Such dissipative quantum spin arrays can be realized in ultracold atoms, trapped ions, and mesoscopic systems and are related to Kondo lattice models.
Quantum Simulation of Quantum Field Theory with a Trapped Ion System
Zhang, Xiang; Zhang, Kuan; Shen, Yangchao; Zhang, Jingning; Yung, Man-Hong; Kim, Kihwan; Simon, Julen; Lamata, Lucas; Solano, Enrique; Casanova, Jorge
2015-05-01
We report on the experimental quantum simulation of interacting bosonic and fermionic quantum field modes with a trapped ion system. We consider a basic model of only one fermion and one anti-fermion interacting through a bosonic field mode, which reveals interesting features such as self-interactions, particle creation and annihilation and non-perturbative regimes. We experimentally study these phenomena by manipulating the internal degrees of freedom of a multi-level single 171Yb+ ion and its motional state, based on the proposal of Ref.. Our experimental scheme is a scalable approach and can be extended beyond the limit of classical computation of quantum field theory when more fermions and bosons are included. This work was supported by the National Basic Research Program of China under Grants No. 2011CBA00300 (No. 2011CBA00301), the National Natural Science Foundation of China 11374178.
Novel optical probe for quantum Hall system
Biswajit Karmakar; Brij Mohan Arora
2006-07-01
Surface photovoltage (SPV) spectroscopy has been used for the first time to explore Landau levels of a two-dimensional electron gas (2DEG) in modulation doped InP/InGaAs/InP QW in the quantum Hall regime. The technique gives spectroscopically distinct signals from the bulk Landau levels and the edge states. Evolution of the bulk Landau levels and the edge electronic states is investigated at 2.0 K for magnetic field up to 8 T using SPV spectroscopy.
Integrable quantum systems and classical Lie algebras
Six new infinite series of trigonometric solutions to triangule equations (quantum R-matrices) associated with the nonexceptional simple Lie algebras: sl(N), sp(N), o(N) have been obtained. R-matrices are given in two equivalent representations: in an additive one (as a sum of poles with matrix coefficients) and in a multiplicative one (as a ratio of entire matrix functions). These R-matrices provide an exact integrability of anisotropic generalizations of sl(N), sp(N), o(N) invariant one-dimensional lattice magnetics and two-dimensional periodic Toda lattices associated with the above algebras
Functional methods and mappings of dissipative quantum systems
In the first part of this work we extract the algebraic structure behind the method of the influence functional in the context of dissipative quantum mechanics. Special emphasis was put on the transition from a quantum mechanical description to a classical one, since it allows a deeper understanding of the measurement-process. This is tightly connected with the transition from a microscopic to a macroscopic world where the former one is described by the rules of quantum mechanics whereas the latter follows the rules of classical mechanics. In addition we show how the results of the influence functional method can be interpreted as a stochastical process, which in turn allows an easy comparison with the well known time development of a quantum mechanical system by use of the Schroedinger equation. In the following we examine the tight-binding approximation of models of which their hamiltionian shows discrete eigenstates in position space and where transitions between those states are suppressed so that propagation either is described by tunneling or by thermal activation. In the framework of dissipative quantum mechanics this leads to a tremendous simplification of the effective description of the system since instead of looking at the full history of all paths in the path integral description, we only have to look at all possible jump times and the possible corresponding set of weights for the jump direction, which is much easier to handle both analytically and numerically. In addition we deal with the mapping and the connection of dissipative quantum mechanical models with ones in quantum field theory and in particular models in statistical field theory. As an example we mention conformal invariance in two dimensions which always becomes relevant if a statistical system only has local interaction and is invariant under scaling. (orig.)
van Wezel, Jasper
2007-01-01
In this thesis the connection between Quantum Mechanics and the Classical World, which we see around us every day, is investigated. The quantum origin of large systems turns out to continuously influence their behaviour. One of the consequences discussed in this thesis, is that qubits (the basic building blocks of a future quantum computer) can hold on to their stored quantum information only for a given time. After that time the qubit will be effectively reduced to just an ordinary bit.Another important connection between quantum mechanics and classical physics is the way in which gravity cou
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system have been theoretically studied. In general, we find that the structure parameters of the coupled system significantly affect the optical susceptibilities. The enhancement of the coupling effects between the dot and ring is found to increase considerably the optical susceptibilities and redshift drastically the transition energies. Comparing to the linear susceptibility, the nonlinear optical susceptibility is found to be more sensitive to the variation of the structure parameters. A comprehensive analysis of the electron probability density movement with respect to the modification of the structure parameters is provided, which offers a unique perspective of the ground-state localization. - Highlights: • Optical susceptibilities in a quantum-dot–quantum-ring system are studied. • The structure parameters significantly affect the optical susceptibilities. • The enhancement of the coupling effects increases the optical susceptibilities. • The nonlinear susceptibility is more sensitive to the change in structure parameters. • A comprehensive analysis of the electron probability density movement is provided
Lower bound of local quantum uncertainty for high-dimensional bipartite quantum systems
Wang, Shuhao; Li, Hui; Lu, Xian; Chen, Bin; Long, Gui Lu
2013-01-01
Quantum correlations are of fundamental importance in quantum phenomena and quantum information processing studies. The measure of quantum correlations is one central issue. The recently proposed measure of quantum correlations, the local quantum uncertainty (LQU), satisfies the full physical requirements of a measure of quantum correlations. In this work, by using operator relaxation, a closed form lower bound of the LQU for arbitrary-dimensional bipartite quantum states is derived. We have ...
Keldysh field theory for driven open quantum systems.
Sieberer, L M; Buchhold, M; Diehl, S
2016-09-01
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems. PMID:27482736
Keldysh field theory for driven open quantum systems
Sieberer, L. M.; Buchhold, M.; Diehl, S.
2016-09-01
Recent experimental developments in diverse areas—ranging from cold atomic gases to light-driven semiconductors to microcavity arrays—move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven–dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Aspelmeyer, Markus; Schwab, Keith
2008-09-01
The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanical systems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds—the authors of this editorial are a representative sample—has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the
Perturbation Theory for Open Two-Level Nonlinear Quantum Systems
Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)
Entanglement in Algebraic Quantum Mechanics: Majorana fermion systems
Benatti, F
2016-01-01
Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the associated correlation functions, rather than on particle tensor products. This allows obtaining a complete characterization of non-separable Majorana fermion states. These results may find direct applications in quantum metrology: using Majorana systems, sub-shot noise accuracy in parameter estimations can be achieved without preliminary, resource consuming, state entanglement operations.
Quantum Theory of Large Systems of Non-Relativistic Matter
Froehlich, J.; Studer, U. M.; Thiran, E.
1995-01-01
1. Introduction 2. The Pauli Equation and its Symmetries {2.1} Gauge-Invariant Form of the Pauli Equation {2.2} Aharonov-Bohm Effect {2.3} Aharonov-Casher Effect 3. Gauge Invariance in Non-Relativistic Quantum Many-Particle Systems {3.1} Differential Geometry of the Background {3.2} Systems of Spinning Particles Coupled to External Electromagnetic and Geometric Fields {3.3} Moving Coordinates and Quantum-Mechanical Larmor Theorem 4. Some Key Effects Related to the $U(1) \\times SU(2)$ Gauge In...
Correlations of neutral kaons - an open quantum system approach
Full text: I will present the quantum mechanical model of decaying particles based on the open quantum system approach. I will discuss the decay of a single neutral kaon. In our model the time evolution of the density matrix describing such a kaon is given by the appropriate Lindblad equation. The corresponding Lindblad operators are constructed explicitly in two cases - when we assume CP-invariance and without this assumption. The complete positivity of the time evolution is proved by the explicit construction of the corresponding Krauss operators. We use this results to calculate the correlation function in neutral kaon system. (author)
Arbitrarily Accurate Dynamical Control in Open Quantum Systems
Khodjasteh, Kaveh; Viola, Lorenza
2009-01-01
We show that open-loop dynamical control techniques may be used to synthesize unitary transformations in open quantum systems in such a way that decoherence is perturbatively compensated for to a desired (in principle arbitrarily high) level of accuracy, which depends only on the strength of the relevant errors, and the achievable rate of control modulation. Our constructive and fully analytical solution employs concatenated dynamically corrected gates, and is applicable independently of detailed knowledge of the system-environment interactions and environment dynamics. Explicit implications for boosting quantum gate fidelities are addressed.
Optimized pulse sequences for suppressing unwanted transitions in quantum systems
Schroeder, C A
2010-01-01
We investigate the nature of the pulse sequence so that unwanted transitions in quantum systems can be inhibited optimally. For this purpose we show that the sequence of pulses proposed by Uhrig [Phys. Rev. Lett. \\textbf{98}, 100504 (2007)] in the context of inhibition of environmental dephasing effects is optimal. We derive exact results for inhibiting the transitions and confirm the results numerically. We posit a very significant improvement by usage of the Uhrig sequence over an equidistant sequence in decoupling a quantum system from unwanted transitions. The physics of inhibition is the destructive interference between transition amplitudes before and after each pulse.
Quantum mechanical actuation of microelectromechanical systems by the Casimir force.
Chan, H B; Aksyuk, V A; Kleiman, R N; Bishop, D J; Capasso, F
2001-03-01
The Casimir force is the attraction between uncharged metallic surfaces as a result of quantum mechanical vacuum fluctuations of the electromagnetic field. We demonstrate the Casimir effect in microelectromechanical systems using a micromachined torsional device. Attraction between a polysilicon plate and a spherical metallic surface results in a torque that rotates the plate about two thin torsional rods. The dependence of the rotation angle on the separation between the surfaces is in agreement with calculations of the Casimir force. Our results show that quantum electrodynamical effects play a significant role in such microelectromechanical systems when the separation between components is in the nanometer range. PMID:11239149
A Quantum Spin System with Random Interactions I
Stephen Dias Barreto
2000-11-01
We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of evolution groups $\\{\\mathcal{T}_t()\\}_{\\in}$ of the spin system. The notion of ergodicity of a measure preserving group of automorphisms of the probability space , is used to prove the almost sure independence of the Arveson spectrum $\\mathrm{Sp}(\\mathcal{T}())$ of $\\mathcal{T}_t()$. As a consequence, for any family of $(\\mathcal{T}(), )$-KMS states {ρ()}, the spectrum of the generator of the group of unitaries which implement $\\mathcal{T}()$ in the GNS representation is also almost surely independent of .
Entanglement in algebraic quantum mechanics: Majorana fermion systems
Benatti, F.; Floreanini, R.
2016-07-01
Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the associated correlation functions, rather than on particle tensor products. This allows a complete characterization of non-separable Majorana fermion states to be obtained. These results may have direct application in quantum metrology: using Majorana systems, sub-shot-noise accuracy in parameter estimations can be achieved without preliminary resource-consuming, state entanglement operations.
Quantum algorithm for obtaining the eigenstates of a physical system
Wang, Hefeng
2016-05-01
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how do we obtain the corresponding eigenstate? The algorithm is based on the resonance phenomenon. For a probe qubit coupled to a quantum system, the system exhibits resonance dynamics when the frequency of the probe qubit matches a transition frequency in the system. Therefore the system can be guided to evolve to the eigenstate with a known eigenvalue by inducing the resonance between the probe qubit and a designed transition in the system. This algorithm can also be used to obtain the energy spectrum of a physical system and can achieve even quadratic speedup over the phase estimation algorithm.
Optimized control of multistate quantum systems by composite pulse sequences
We introduce a technique for derivation of high-fidelity composite pulse sequences for two types of multistate quantum systems: systems with the SU(2) and Morris-Shore dynamic symmetries. For the former type, we use the Majorana decomposition to reduce the dynamics to an effective two-state system, which allows us to find the propagator analytically and use the pool of available composite pulses for two-state systems. For the latter type of multistate systems, we use the Morris-Shore decomposition, which reduces the multistate dynamics to a set of two-state systems. We present examples which demonstrate that the multistate composite sequences open a variety of possibilities for coherent control of quantum systems with multiple states.
An initial assumption in quantum mechanics is that particles (or subsystems) can be isolated from the physical world but still behave in a realistic fashion. This paper shows that the above assumption is not only naive but it has far reaching consequences. In particular, time-reversibility, microscopic reversibility and time-energy principles must be reinterpreted for real non-isolated systems. Moreover the new interpretation is far more consistent than that presently accepted for isolated systems. (author)
Quantum teleportation of dynamics and effective interactions between remote systems.
Muschik, Christine A; Hammerer, Klemens; Polzik, Eugene S; Cirac, Ignacio J
2013-07-12
Most protocols for quantum information processing consist of a series of quantum gates, which are applied sequentially. In contrast, interactions between matter and fields, for example, as well as measurements such as homodyne detection of light are typically continuous in time. We show how the ability to perform quantum operations continuously and deterministically can be leveraged for inducing nonlocal dynamics between two separate parties. We introduce a scheme for the engineering of an interaction between two remote systems and present a protocol that induces a dynamics in one of the parties that is controlled by the other one. Both schemes apply to continuous variable systems, run continuously in time, and are based on real-time feedback. PMID:23889374
Generation of cluster states in optomechanical quantum systems
Houhou, Oussama; Aissaoui, Habib; Ferraro, Alessandro
2015-12-01
We consider an optomechanical quantum system composed of a single cavity mode interacting with N mechanical resonators. We propose a scheme for generating continuous-variable graph states of arbitrary size and shape, including the so-called cluster states for universal quantum computation. The main feature of this scheme is that, differently from previous approaches, the graph states are hosted in the mechanical degrees of freedom rather than in the radiative ones. Specifically, via a 2 N -tone drive, we engineer a linear Hamiltonian which is instrumental to dissipatively drive the system to the desired target state. The robustness of this scheme is assessed against finite interaction times and mechanical noise, confirming it as a valuable approach towards quantum state engineering for continuous-variable computation in a solid-state platform.
Enhancing Quantum Effects via Periodic Modulations in Optomechanical Systems
Farace, Alessandro
2012-01-01
Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the oscillator position (or momentum) and the enhancement of entanglement between mechanical and radiation modes. In this paper we further investigate this new modulation regime, considering an optomechanical system with one or more parameters being modulated over time. We first apply a sinusoidal modulation of the mechanical frequency and characterize the optimal regime in which the visibility of purely quantum effects is maximal. We then introduce a second modulation on the input laser intensity and analyze the interplay between the two. We find that an interference pattern shows up, so that different choices of the relative phase between the two modulations can either enhance or cancel the desired quantum effects.
Secret sharing with a single d -level quantum system
Tavakoli, Armin; Herbauts, Isabelle; Żukowski, Marek; Bourennane, Mohamed
2015-09-01
We give an example of a wide class of problems for which quantum-information protocols based on multisystem entanglement can be mapped into much simpler ones involving one system. Secret sharing is a cryptographic primitive which plays a central role in various secure multiparty computation tasks and management of keys in cryptography. In secret sharing protocols, a classical message is divided into shares given to recipient parties in such a way that some number of parties need to collaborate in order to reconstruct the message. Quantum protocols for the task commonly rely on multipartite GHZ entanglement. We present a multiparty secret sharing protocol which requires only sequential communication of a single quantum d -level system (for any prime d ). It has huge advantages in scalability and can be realized with state-of-the-art technology.
Universality of spectra for interacting quantum chaotic systems
Bruzda, Wojciech; Cappellini, Valerio; Sommers, Hans-Juergen; Zyczkowski, Karol
2010-01-01
We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the measurement device, the spectra of the evolution operator exhibit an universal behavior. A generic spectrum consists of a single eigenvalue equal to unity, which corresponds to the invariant state of the system, while all other eigenvalues are contained in a disk in the complex plane. Its radius depends on the number of the Kraus measurement operators, and determines the speed with which an arbitrary initial state converges to the unique invariant state. These spectral properties are characteristic of an ensemble of random quantum maps, which in turn can be described by an ensemble of real random Ginibre matrices. This will be proven in the limit of large dimension.
Natural Light Harvesting Systems: Unraveling the quantum puzzles
Thilagam, A
2013-01-01
In natural light harvesting systems, the sequential quantum events of photon absorption by specialized biological antenna complexes, charge separation, exciton formation and energy transfer to localized reaction centers culminates in the conversion of solar to chemical energy. A notable feature in these processes is the exceptionally high efficiencies (> 95 %) at which excitation is transferred from the illuminated protein complex site to the reaction centers. Such high exciton propagation rates within a system of interwoven biomolecular network structures, is yet to be replicated in artificial light harvesting complexes. A clue to unraveling the quantum puzzles of nature may lie in the observation of long lived coherences lasting several picoseconds in the electronic spectra of photosynthetic complexes, even in noisy environmental baths. A number of experimental and theoretical studies have been devoted to unlocking the links between quantum processes and information protocols, in the hope of finding answers...
Topics in quantum information and the theory of open quantum systems
Oreshkov, Ognyan
2008-01-01
This thesis examines seven topics in the areas of deterministic open-quantum-system dynamics, quantum measurements, and quantum error correction (QEC). The first topic concerns weak measurements and their universality as a means of generating quantum operations. It is shown that every generalized measurement can be implemented as a sequence of weak (infinitesimal) measurements. The second topic is an application of this result to the theory of entanglement. Necessary and sufficient differential conditions for entanglement monotones are derived and are used to find a new entanglement monotone for three-qubit states. The third topic is a study of the performance of different master equations for the description of non-Markovian dynamics. The system studied is a qubit coupled to a spin bath via the Ising interaction. The fourth topic investigates continuous QEC in the presence of non-Markovian noise. It is shown that due to the existence of a Zeno regime in non-Markovian dynamics, the performance of continuous Q...
Quantum correlations play vital roles in the quantum features in quantum information processing tasks. Among the measures of quantum correlations, quantum discord (QD) and entanglement of formation (EOF) are two significant ones. Recent research has shown that there exists a relation between QD and EOF, which makes QD more significant in quantum information theory. However, until now, there exists no general method of characterizing quantum discord in high-dimensional quantum systems. In this paper, we have proposed a general method for calculating quantum discord in arbitrary-dimensional bipartite quantum systems in terms of Hurwitz's theory. Applications including the Werner state, the spin-1 XXZ model thermal equilibrium state, the Horodecki state, and the separable-bound-free entanglement state are investigated. We present the method of obtaining the EOF of arbitrary-dimensional bipartite quantum states via purification, and the relationship between QD and EOF. (general)
Chen Li-Bing; Lu Hong; Jin Rui-Bo
2007-01-01
We present a systematic simple method to implement a generalized quantum control-NOT (CNOT) gate on two d-dimensional distributed systems. First, we show how the nonlocal generalized quantum CNOT gate can be implemented with unity fidelity and unity probability by using a maximally entangled pair of qudits as a quantum channel. We also put forward a scheme for probabilistically implementing the nonlocal operation with unity fidelity by employing a partially entangled qudit pair as a quantum channel. Analysis of the scheme indicates that the use of partially entangled quantum channel for implementing the nonlocal generalized quantum CNOT gate leads to the CNOT gate can be used in the entanglement swapping between particles belonging to distant users in a communication network and distributed quantum computer.
Large quantum systems: a mathematical and numerical perspective
This thesis is devoted to the mathematical study of variational models for large quantum systems. The mathematical methods are that of nonlinear analysis, calculus of variations, partial differential equations, spectral theory, and numerical analysis. The first part contains some results on finite systems. We study several approximations of the N-body Schroedinger equation for electrons in an atom or a molecule, and then the so-called Hartree-Fock- Bogoliubov model for a system of fermions interacting via the gravitational force. In a second part, we propose a new method allowing to prove the existence of the thermodynamic limit of Coulomb quantum systems. Then, we construct two Hartree-Fock-type models for infinite systems. The first is a relativistic theory deduced from Quantum Electrodynamics, allowing to describe the behavior of electrons, coupled to that of Dirac's vacuum which can become polarized. The second model describes a nonrelativistic quantum crystal in the presence of a charged defect. A new numerical method is also proposed. The last part of the thesis is devoted to spectral pollution, a phenomenon which is observed when trying to approximate eigenvalues in a gap of the essential spectrum of a self-adjoint operator, for instance for periodic Schroedinger operators or Dirac operators. (author)
Integrated System Technologies for Modular Trapped Ion Quantum Information Processing
Crain, Stephen G.
Although trapped ion technology is well-suited for quantum information science, scalability of the system remains one of the main challenges. One of the challenges associated with scaling the ion trap quantum computer is the ability to individually manipulate the increasing number of qubits. Using micro-mirrors fabricated with micro-electromechanical systems (MEMS) technology, laser beams are focused on individual ions in a linear chain and steer the focal point in two dimensions. Multiple single qubit gates are demonstrated on trapped 171Yb+ qubits and the gate performance is characterized using quantum state tomography. The system features negligible crosstalk to neighboring ions (detectors (SNSPD), which provide a higher detector efficiency (69%) compared to traditional photomultiplier tubes (35%). The total system photon collection efficiency is increased from 2.2% to 3.4%, which allows for fast state detection of the qubit. For a detection beam intensity of 11 mW/cm 2, the average detection time is 23.7 mus with 99.885(7)% detection fidelity. The technologies demonstrated in this thesis can be integrated to form a single quantum register with all of the necessary resources to perform local gates as well as high fidelity readout and provide a photon link to other systems.
The classical limit of non-integrable quantum systems
Castagnino, M; Castagnino, Mario; Lombardi, Olimpia
2005-01-01
The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced decoherence approach and the corresponding classical limit are generalized from integrable to non-integrable systems. In this approach, the lost of information, usually conceived as the result of a coarse-graining or the trace of an environment, is produced by a particular choice of the algebra of observables and the systematic use of mean values, that project the unitary evolution onto an effective non-unitary one. The decoherence times computed with this approach coincide with those of the literature. By means of our method, we can obtain the classical limit of the quantum state of a non-integrable system, which turns out to be a set of unstable, potentially chaotic classical trajectories contained in the Wigner transformation of the quantum state.
Construction of the Gibbs states of quantum lattice systems.
Глоба, Сергей Александрович
2013-01-01
A scheme for construction of temperature states of quantum lattice systems in terms of a functional integral has been proposed. Existence of such states for a concrete class of models with one-particle has been proved with the help of the indicated scheme.
Chaotic Dynamics and Transport in Classical and Quantum Systems
NONE
2003-07-01
The aim of this summer school is to provide a set of extended and pedagogical lectures, on the major present-day topics in dynamical systems and statistical mechanics including applications. Some articles are dedicated to chaotic transport in plasma turbulence and to quantum chaos. This document gathers the summaries of some presentations.
Geometrical and Algebraic Structures in Quantum Hall Systems
Wallet, J. C.
2005-01-01
We review the main features of a mathematical framework encompassing some of the salient quantum mechanical and geometrical aspects of Hall systems with finite size and general boundary conditions. Geometrical as well as algebraic structures controlling possibly the integral or fractional quantization of the Hall conductivity are discussed.
Optimal control of quantum systems by chirped pulses
Amstrup, Bjarne; Doll, J. D.; Sauerbrey, R. A.;
1993-01-01
Research on optimal control of quantum systems has been severely restricted by the lack of experimentally feasible control pulses. Here, to overcome this obstacle, optimal control is considered with the help of chirped pulses. Simulated annealing is used as the optimizing procedure. The examples...
Precision of electromagnetic control of a quantum system
Coherent control of a quantum system is limited both by the decoherence due to environment and the quantum nature of the control agent. The high fidelity of control demanded by fault-tolerant quantum computation and the intrinsic interest in nonclassical effects from the interplay between control and dissipation are motivations for a detailed study of the interaction dynamics between the quantum system and the macroscopic environment and control agent. We present a detailed time-evolution study of a two-level system interacting with a laser pulse and the electromagnetic vacuum in the multimode Jaynes-Cummings model. A diagrammatic formalism allows easy identification of coherent dynamics and relaxation of the two-level system. We demonstrate a computational method of dynamics with precise error bounds for fast operations versus slow decoherence, spanning the Markovian and non-Markovian regimes. Comparison against an exact model solution of our results with existing approximations of the master equation shows the lack of accuracy in the latter.
Instantaneous Spreading Versus Space Localization for Nonrelativistic Quantum Systems
Coutinho, F. A. B.; Wreszinski, W. F.
2016-08-01
A theorem of Hegerfeldt (Kielanowski et al. 1998) establishes, for a class of quantum systems, a dichotomy between those which are permanently localized in a bounded region of space, and those exhibiting instantaneous spreading. We analyze in some detail the physical inconsistencies which follow from both of these options, and formulate which, in our view, are the basic open problems.
Existence of the thermodynamic limit for disordered quantum Coulomb systems
Blanc, Xavier
2012-01-01
Following a recent method introduced by C. Hainzl, J.P. Solovej and the second author of this article, we prove the existence of the thermodynamic limit for a system made of quantum electrons, and classical nuclei whose positions and charges are randomly perturbed in an ergodic fashion. All the particles interact through Coulomb forces.
Performance of Photon-Pair Quantum Key Distribution Systems
Walton, Z D; Atatüre, M; Saleh, B E A; Teich, M C
2001-01-01
We analyze the quantitative improvement in performance provided by a novel quantum key distribution (QKD) system that employs a correlated photon source (CPS) and a photon-number resolving detector (PNR). Our calculations suggest that given current technology, the CPR implementation offers an improvement of several orders of magnitude in secure bit rate over previously described implementations.
Crossover from coherent to incoherent dynamics in damped quantum systems
Egger, Reinhold; Grabert, Hermann; Weiss, Ulrich
1997-01-01
The destruction of quantum coherence by environmental influences is investigated taking the damped harmonic oscillator and the dissipative two-state system as prototypical examples. It is shown that the location of the coherent-incoherent transition depends to a large degree on the dynamical quantity under consideration.
Perfect Parallel Repetition Theorem for Quantum Xor Proof Systems
Unger, F.P.; Cleve, R.E.; Slofstra, W.; Upadhyay, S.
2008-01-01
We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier's verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to coordinate their behavior using a shared entangled quantum st
Perfect parallel repetition theorem for quantum XOR proof systems
R. Cleve; W. Slofstra; F. Unger; S. Upadhyay
2008-01-01
We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier’s verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to coordinate their behavior using a shared entangled quantum st
Symmetry of quantum phase space in a degenerate Hamiltonian system
The structure of the global ''quantum phase space'' is analyzed for the harmonic oscillator perturbed by a monochromatic wave in the limit when the perturbation amplitude is small. Usually, the phenomenon of quantum resonance was studied in nondegenerate [G. M. Zaslavsky, Chaos in Dynamic Systems (Harwood Academic, Chur, 1985)] and degenerate [Demikhovskii, Kamenev, and Luna-Acosta, Phys. Rev. E 52, 3351 (1995)] classically chaotic systems only in the particular regions of the classical phase space, such as the center of the resonance or near the separatrix. The system under consideration is degenerate, and even an infinitely small perturbation generates in the classical phase space an infinite number of the resonant cells which are arranged in the pattern with the axial symmetry of the order 2μ (where μ is the resonance number). We show analytically that the Husimi functions of all Floquet states (the quantum phase space) have the same symmetry as the classical phase space. This correspondence is demonstrated numerically for the Husimi functions of the Floquet states corresponding to the motion near the elliptic stable points (centers of the classical resonance cells). The derived results are valid in the resonance approximation when the perturbation amplitude is small enough, and the stochastic layers in the classical phase space are exponentially thin. The developed approach can be used for studying a global symmetry of more complicated quantum systems with chaotic behavior. (c) 2000 American Institute of Physics
Chaotic Dynamics and Transport in Classical and Quantum Systems
The aim of this summer school is to provide a set of extended and pedagogical lectures, on the major present-day topics in dynamical systems and statistical mechanics including applications. Some articles are dedicated to chaotic transport in plasma turbulence and to quantum chaos. This document gathers the summaries of some presentations
Transport of quantum states of periodically driven systems
Breuer, H. P.; Dietz, K.; Holthaus, M.
1990-01-01
We discuss the transport of quantum states on quasi-energy surfaces of periodically driven systems and establish their non-trivial structure. The latter is shown to be caused by diabatic transitions at lines of narrow avoided crossings. Some experimental consequences pertaining to adiabatic transport and Landau-Zener transitions among Floquet states are briefly sketched.
Quantum Communication in the Ion-Trapped System
Xu, Xiong
2016-03-01
A theoretical scheme of quantum communication is proposed in the context of ion-trapped systems. According to the results, the receiver can obtain different secret messages in a deterministic way. Our scheme is insensitive to both the initial vibrational state and heating. The probability of the success in our scheme is 1.0.
Post-processing procedure for industrial quantum key distribution systems
Kiktenko, E. O.; Trushechkin, A. S.; Kurochkin, Y. V.; Fedorov, A. K.
2016-01-01
We present algorithmic solutions aimed on post-processing for industrial quantum key distribution systems with hardware sifting. The main steps of the procedure are error correction, parameter estimation, and privacy amplification. Authentication of a classical public communication channel is also considered.
A note on Borromean correlations in multipartite quantum systems
Zapatrin, Roman R.
2001-01-01
If a pure state of a multipartite quantum system is Borromean, that is, its density matrix becomes product after tracing out any its component then the initial state is product itself. This shows the essentially classical nature of Borromean correlations which can not be achieved by entangled pure states.
Correlations in complex nonlinear systems and quantum information theory
Guehne, Otfried [Institut fuer Quantenoptik und Quanteninformation, Oesterreichische Akademie der Wissenschaften, Innsbruck (Austria); Galla, Tobias [School of Physics and Astronomy, University of Manchester (United Kingdom)
2010-07-01
The dynamical evolution of classical complex systems such as coupled logistic maps or simple models of lattice gases and cellular automata can result in correlations between distant parts of the system. For the understanding of these systems, it is crucial to develop methods to characterize and quantify these multi-party correlations. On the other hand, the study of correlations between distant particles is also a central problem in the field of quantum information theory. There, correlations are often viewed as a resource and many tools have been developed for their characterization. In this talk, we explore the extent to which the tools from quantum information can be applied to study classical complex systems and whether they allow to study complex systems from a different perspective.
Correlations in complex nonlinear systems and quantum information theory
The dynamical evolution of classical complex systems such as coupled logistic maps or simple models of lattice gases and cellular automata can result in correlations between distant parts of the system. For the understanding of these systems, it is crucial to develop methods to characterize and quantify these multi-party correlations. On the other hand, the study of correlations between distant particles is also a central problem in the field of quantum information theory. There, correlations are often viewed as a resource and many tools have been developed for their characterization. In this talk, we explore the extent to which the tools from quantum information can be applied to study classical complex systems and whether they allow to study complex systems from a different perspective.
Entropy of open quantum systems and the Poisson distribution
The entropy of the harmonic oscillator and the Klein-Gordan-Fock quantum field with a static source, located in a coherent state, is considered. The expressions for the entropy in both cases coincide with the accuracy up to the numerical multiplier with the entropy for a black hole. Such a coincidence along with the known property of the gravitational field to provide for a decoherence of the quantum system, placed therein, makes it possible to suppose that the vacuum in the black hole vicinity is in a coherent state
Manifolds of Equal Entanglement for Composite Quantum Systems
Quantum entanglement remains invariant with respect to unitary transformations performed locally in each subsystem. Local orbits of a state of an N x N bi-partite quantum system are analyzed. For a pure state their dimensions depend on the degeneracy of the vector of coefficients arising by the Schmidt decomposition. For instance, the generic orbit of a pure state has 2N2 - N - 1 dimensions, the set of separable states is 4(N - 1) dimensional, while the manifold of maximally entangled states has N2 - 1 dimensions. (author)
Formal Analysis of Quantum Systems using Process Calculus
Timothy A.S. Davidson
2011-07-01
Full Text Available Quantum communication and cryptographic protocols are well on the way to becoming an important practical technology. Although a large amount of successful research has been done on proving their correctness, most of this work does not make use of familiar techniques from formal methods, such as formal logics for specification, formal modelling languages, separation of levels of abstraction, and compositional analysis. We argue that these techniques will be necessary for the analysis of large-scale systems that combine quantum and classical components, and summarize the results of initial investigation using behavioural equivalence in process calculus. This paper is a summary of Simon Gay's invited talk at ICE'11.
Formal Analysis of Quantum Systems using Process Calculus
Davidson, Timothy A S; Nagarajan, Rajagopal; 10.4204/EPTCS.59.9
2011-01-01
Quantum communication and cryptographic protocols are well on the way to becoming an important practical technology. Although a large amount of successful research has been done on proving their correctness, most of this work does not make use of familiar techniques from formal methods, such as formal logics for specification, formal modelling languages, separation of levels of abstraction, and compositional analysis. We argue that these techniques will be necessary for the analysis of large-scale systems that combine quantum and classical components, and summarize the results of initial investigation using behavioural equivalence in process calculus. This paper is a summary of Simon Gay's invited talk at ICE'11.
Hall Drag in Correlated Double Layer Quantum Hall Systems
Yang, Kun
1998-01-01
We show that in the limit of zero temperature, double layer quantum Hall systems exhibit a novel phenomena called Hall drag, namely a current driven in one layer induces a voltage drop in the other layer, in the direction perpendicular to the driving current. The two-by-two Hall resistivity tensor is quantized and proportional to the ${\\bf K}$ matrix that describes the topological order of the quantum Hall state, even when the ${\\bf K}$ matrix contains a zero eigenvalue, in which case the Hal...
A quantum CISC compiler and scalable assembler for quantum computing on large systems
Using the cutting edge high-speed parallel cluster HLRB-II (with a total LINPACK performance of 63.3 TFlops/s) we present a quantum CISC compiler into time-optimised or decoherence-protected complex instruction sets. They comprise effective multi-qubit interactions with up to 10 qubits. We show how to assemble these medium-sized CISC-modules in a scalable way for quantum computation on large systems. Extending the toolbox of universal gates by optimised complex multi-qubit instruction sets paves the way to fight decoherence in realistic Markovian and non-Markovian settings. The advantage of quantum CISC compilation over standard RISC compilations into one- and two-qubit universal gates is demonstrated inter alia for the quantum Fourier transform (QFT) and for multiply-controlled NOT gates. The speed-up is up to factor of six thus giving significantly better performance under decoherence. - Implications for upper limits to time complexities are also derived
Quantum Entanglement of Matter and Geometry in Large Systems
Hogan, Craig J
2014-01-01
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard quantum field theory with general relativity on macroscopic scales can be reconciled by nonstandard, nonlocal entanglement of field states with quantum states of geometry. Wave functions of particle world lines are used to estimate scales of geometrical entanglement and emergent locality. Simple models of entanglement predict coherent fluctuations in position of massive bodies, of Planck scale origin, measurable on a laboratory scale, and may account for the fact that the information density of long lived position states in Standard Model fields, which is determined by the strong interactions, is the same as that determined holographically by the cosmological constant.
Practical Entanglement Estimation for Spin-System Quantum Simulators
Marty, O.; Cramer, M.; Plenio, M. B.
2016-03-01
We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focusing on long- and short-range Ising-type Hamiltonians, we introduce schemes that are applicable under realistic experimental conditions including mixedness due to, e.g., noise or temperature. In particular, we identify a single observable whose expectation value serves as a lower bound to entanglement and that may be obtained by a simple quantum circuit. As such circuits are not (yet) available for every platform, we investigate the performance of routinely measured observables as quantitative entanglement witnesses. Possible applications include experimental studies of entanglement scaling in critical systems and the reliable benchmarking of quantum simulators.
Practical Entanglement Estimation for Spin-System Quantum Simulators.
Marty, O; Cramer, M; Plenio, M B
2016-03-11
We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focusing on long- and short-range Ising-type Hamiltonians, we introduce schemes that are applicable under realistic experimental conditions including mixedness due to, e.g., noise or temperature. In particular, we identify a single observable whose expectation value serves as a lower bound to entanglement and that may be obtained by a simple quantum circuit. As such circuits are not (yet) available for every platform, we investigate the performance of routinely measured observables as quantitative entanglement witnesses. Possible applications include experimental studies of entanglement scaling in critical systems and the reliable benchmarking of quantum simulators. PMID:27015489
Topos-Based Logic for Quantum Systems and Bi-Heyting Algebras
Doering, Andreas
2012-01-01
To each quantum system, described by a von Neumann algebra of physical quantities, we associate a complete bi-Heyting algebra. The elements of this algebra represent contextualised propositions about the values of the physical quantities of the quantum system.
Quantum information entropy for one-dimensional system undergoing quantum phase transition
Xu-Dong, Song; Shi-Hai, Dong; Yu, Zhang
2016-05-01
Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic “Landau” potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy Sx and the momentum entropy Sp at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition. Project supported by the National Natural Science Foundation of China (Grant No. 11375005) and partially by 20150964-SIP-IPN, Mexico.
Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack
Huang, Jing-Zheng; Weedbrook, Christian; Yin, Zhen-Qiang; Wang, Shuang; Li, Hong-Wei; Chen, Wei; Guo, Guang-Can; Han, Zheng-Fu
2013-06-01
The security proofs of continuous-variable quantum key distribution are based on the assumptions that the eavesdropper can neither act on the local oscillator nor control Bob's beam splitter. These assumptions may be invalid in practice due to potential imperfections in the implementations of such protocols. In this paper, we consider the problem of transmitting the local oscillator in a public channel and propose a wavelength attack which allows the eavesdropper to control the intensity transmission of Bob's beam splitter by switching the wavelength of the input light. Specifically we target continuous-variable quantum key distribution systems that use the heterodyne detection protocol using either direct or reverse reconciliation. Our attack is proved to be feasible and renders all of the final keys shared between the legitimate parties insecure, even if they have monitored the intensity of the local oscillator. To prevent our attack on commercial systems, a simple wavelength filter should be randomly added before performing monitoring detection.
Zippilli, S.; Johanning, M.; Giampaolo, S. M.; Wunderlich, Ch.; Illuminati, F.
2013-01-01
We investigate theoretically systems of ions in segmented linear Paul traps for the quantum simulation of quantum spin models with tunable interactions. The scheme is entirely general and can be applied to the realization of arbitrary spin-spin interactions. As a specific application we discuss in detail the quantum simulation of models that exhibit long-distance entanglement in the ground state. We show how tailoring of the axial trapping potential allows for generating spin-spin coupling pa...
Quantum cloning machines and their implementation in physical systems
We review the basic theory of approximate quantum cloning for discrete variables and some schemes for implementing quantum cloning machines. Several types of approximate quantum clones and their expansive quantum clones are introduced. As for the implementation of quantum cloning machines, we review some design methods and recent experimental results. (topical review - quantum information)
Transforming quantum operations: quantum supermaps
Chiribella, G.; D'Ariano, G. M.; Perinotti, P.
2008-01-01
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any sup...
Toward engineered quantum many-body phonon systems
Soykal, Ö. O.; Tahan, Charles
2013-01-01
Arrays of coupled phonon cavities each including an impurity qubit in silicon are considered. We study experimentally feasible architectures that can exhibit quantum many-body phase transitions of phonons, e.g. Mott insulator and superfluid states, due to a strong phonon-phonon interaction (which is mediated by the impurity qubit-cavity phonon coupling). We investigate closed equilibrium systems as well as driven dissipative non-equilibrium systems at zero and non-zero temperatures. Our resul...
Purity of states in the theory of open quantum systems
Isar, A.
2006-01-01
The condition of purity of states for a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, the correlated coherent states are shown to be the only states which remain pure all the time during the evolution of the considered system. These states are also the most stable under evolution in the presence of the environment.
Geometry of adiabatic Hamiltonians for two-level quantum systems
We present the formulation of the problem of the coherent dynamics of quantum mechanical two-level systems in the adiabatic region in terms of the differential geometry of plane curves. We show that there is a natural plane curve corresponding to the Hamiltonian of the system for which the geometrical quantities have a simple physical interpretation. In particular, the curvature of the curve has the role of the nonadiabatic coupling. (paper)
A Model for a Quantum Level System-Apparatus Interaction
Bracken, Paul
2016-01-01
A quantum system is investigated which consists of a two-state spin which interacts with a model apparatus consisting of a large number of bosons. The Hamiltonian which describes the interaction of system and apparatus is defined and the evolution of an initial state of the two by means of an evolution operator over time is calculated. Some insights into the nature of such measurement processes can be made.
Theory of ground state factorization in quantum cooperative systems
Giampaolo, S. M.; Adesso, G.; Illuminati, F.
2008-01-01
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows to determine rigorously existence, location, and exact form of separable ground states in a large variety of, generally non-exactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary ...