Showing papers on "Open quantum system published in 2003"
TL;DR: A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer Unitary transformations can be performed by moving the excitations around each other Unitary transformation can be done by joining excitations in pairs and observing the result of fusion.
4,920 citations
TL;DR: In this article, it was shown that many of the symptoms of classicality can be induced in quantum systems by their environments, which leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information.
Abstract: as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.
3,499 citations
TL;DR: The results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories.
Abstract: Entanglement, one of the most intriguing features of quantum theory and a main resource in quantum information science, is expected to play a crucial role also in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations. We investigate, through a microscopic calculation, the scaling properties of entanglement in spin chain systems, both near and at a quantum critical point. Our results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories. We explore some of the implications of this connection.
2,522 citations
TL;DR: This work gives a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states, and proves its universality.
Abstract: We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe why its underlying computational model is different from the network model of quantum computation, and relate quantum algorithms to mathematical graphs. Further we investigate the scaling of required resources and give a number of examples for circuits of practical interest such as the circuit for quantum Fourier transformation and for the quantum adder. Finally, we describe computation with clusters of finite size.
1,370 citations
TL;DR: In this article, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has been made explicit, thereby providing a firmer mathematical and conceptual foundation to the subject.
Abstract: Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity. However, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has not been made explicit. The purpose of this paper is to address these issues, thereby providing a firmer mathematical and conceptual foundation to the subject.
794 citations
TL;DR: A number of examples of research programs that could deliver quantum technologies in coming decades including: quantum information technology, quantum electromechanical systems, coherent quantum electronics, quantum optics and coherent matter technology are discussed.
Abstract: We are currently in the midst of a second quantum revolution. The first quantum revolution gave us new rules that govern physical reality. The second quantum revolution will take these rules and use them to develop new technologies. In this review we discuss the principles upon which quantum technology is based and the tools required to develop it. We discuss a number of examples of research programs that could deliver quantum technologies in coming decades including: quantum information technology, quantum electromechanical systems, coherent quantum electronics, quantum optics and coherent matter technology.
718 citations
Journal Article•
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TL;DR: The author describes how such a quantum computer-a computer based on the rules of quantum mechanics-may work, and how it is going to give incredible speed and problem-solving power.
Abstract: Using atoms as digital bits will start a completely new era in computer design. Atoms cannot be simply manipulated and used like the bits built with transistors. The behavior of matter on the atomic scale follows the rules of modern physics. This behavior cannot be understood in terms of our classical description of the world (i. e. Newtonian mechanics or Maxwell's equations in electromagnetics). The physical theory dealing with such behavior is called quantum mechanics. Its use in the computer industry will most probably cause a revolution in the way we use and understand computers. The author describes how such a quantum computer-a computer based on the rules of quantum mechanics-may work, and how it is going to give incredible speed and problem-solving power.
710 citations
Book•
01 Jan 2003
TL;DR: In this article, the authors present a review of concepts of classical quantum mechanics, including operators, eigenfunctions, and eigenvalues, and apply them to problems in three dimensions.
Abstract: I. ELEMENTARY PRINCIPLES AND APPLICATIONS TO PROBLEMS IN ONE DIMENSION. 1. Review of Concepts of Classical Mechanics. 2. Historical Review: Experiments and Theories. 3. The Postulates of Quantum Mechanics: Operators, Eigenfunctions, and Eigenvalues. 4. Preparatory Concepts: Function Spaces and Hermitian Operators. 5. Time Development, Conservation Theorems, and Parity. 6. Time Development, Conservation Theorems, and Parity. 7. Additional One-Dimensional Problems: Bound and Unbound States. 8. Finite Potential Well, Periodic Lattice, and Some Simple Problems with Two Degrees of Freedom. II. FURTHER DEVELOPMENT OF THE THEORY AND APPLICATIONS TO PROBLEMS IN THREE DIMENSIONS. 9. Angular Momentum. 10. Problems in Three Dimensions. 11. Elements of Matrix Mechanics: Spin Wavefunctions. 12. Application to Atomic, Molecular, Solid-State, and Nuclear Physics: Elements of Quantum Statistics. 13. Perturbation Theory. 14. Scattering in Three Dimensions. 15. Relativistic Quantum Mechanics. 16. Quantum Computing. List of Symbols. Appendices. Index. List of Tables. Topical Problems.
633 citations
TL;DR: A brief overview of quantum walks, with emphasis on their algorithmic applications, can be found in this article, where the authors describe quantum walks as quantum counterparts of Markov chains, and present several applications of quantum walk.
Abstract: Quantum walks are quantum counterparts of Markov chains. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications.
TL;DR: The first enabling step in the realization of a protocol for scalable long-distance quantum communication and the distribution of entanglement over quantum networks is reported, namely the observation of quantum correlations for photon pairs generated in the collective emission from an atomic ensemble.
Abstract: Quantum information science attempts to exploit capabilities from the quantum realm to accomplish tasks that are otherwise impossible in the classical domain. Although sufficient conditions have been formulated for the physical resources required to achieve quantum computation and communication, there is a growing understanding of the power of quantum measurement combined with the conditional evolution of quantum states for accomplishing diverse tasks in quantum information science. For example, a protocol has recently been developed for the realization of scalable long-distance quantum communication and the distribution of entanglement over quantum networks. Here we report the first enabling step in the realization of this protocol, namely the observation of quantum correlations for photon pairs generated in the collective emission from an atomic ensemble. The nonclassical character of the fields is demonstrated by the violation of an inequality involving their normalized correlation functions. Compared to previous investigations of non-classical correlations for photon pairs produced in atomic cascades and in parametric down-conversion, our experiment is distinct in that the correlated photons are separated by a programmable time interval (of about 400 nanoseconds in our initial experiments).
TL;DR: The Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition, is considered and an exact solution in the thermodynamic limit is derived, relating this phenomenon to a localization-delocalization transition in which a macroscopic superposition is generated.
Abstract: We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localization-delocalization transition in which a macroscopic superposition is generated. We also describe the classical analogs of this behavior.
Book•
12 Jun 2003
TL;DR: In this article, the authors present an overview of point groups of Molecules with application to Jahn-Teller Systems and a brief review of Point Groups with Application to Quantum Environments.
Abstract: 1. Introduction.- 2. Quantal Phase Factors for Adiabatic Changes.- 3. Spinning Quantum System in an External Magnetic Field.- 4. Quantal Phases for General Cyclic Evolution.- 5. Fiber Bundles and Gauge Theories.- 6. Mathematical Structure of the Geometric Phase I: The Abelian Phase.- 7. Mathematical Structure of the Geometric Phase II: The Non-Abelian Phase.- 8. A Quantum Physical System in a Quantum Environment - The Gauge Theory of Molecular Physics.- 9. Crossing of Potential Energy Surfaces and the Molecular Aharonov-Bohm Effect.- 10. Experimental Detection of Geometric Phases I: Quantum Systems in Classical Environments.- 11. Experimental Detection of Geometric Phases II: Quantum Systems in Quantum Environments.- 12. Geometric Phase in Condensed Matter I: Bloch Bands.- 13. Geometric Phase in Condensed Matter II: The Quantum Hall Effect.- 14. Geometric Phase in Condensed Matter III: Many-Body Systems.- A. An Elementary Introduction to Manifolds and Lie Groups.- B. A Brief Review of Point Groups of Molecules with Application to Jahn-Teller Systems.- References.
TL;DR: In this article, the increasing ability to coherently control quantum systems, designer Hamiltonians can be created to explore new physics and to yield a better understanding of complex phenomena, and they can be used to create new physics models.
Abstract: Thanks to the increasing ability to coherently control quantum systems, designer Hamiltonians can be created to explore new physics and to yield a better understanding of complex phenomena.
Book•
01 Feb 2003
TL;DR: A Brief History of Quantum Tunneling Some Basic Questions Concerning Quantum tunneling Simple Solvable Problems as mentioned in this paper Simple solvable problems Time-Dependence of the Wave Function in One-Dimensional Tunneling Semiclassical Approximations Generalization of the Bohr - Sommerfeld Quantization Rule and its Application to Quantum Tunnelings Gamow's Theory, Complex Eigenvalues, and the wave function of a Decaying State Tunneling in Symmetric and Asymmetric Local Potentials and Tunneling In Nonlocal and Quasi-Solvable Barriers Classical
Abstract: A Brief History of Quantum Tunneling Some Basic Questions Concerning Quantum Tunneling Simple Solvable Problems Time-Dependence of the Wave Function in One-Dimensional Tunneling Semiclassical Approximations Generalization of the Bohr - Sommerfeld Quantization Rule and its Application to Quantum Tunneling Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State Tunneling in Symmetric and Asymmetric Local Potentials and Tunneling in Nonlocal and Quasi-Solvable Barriers Classical Descriptions of Tunneling Tunneling in Time-Dependent Barriers Decay Width and Scattering Theory The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems Path Integral and Its Semi-Classical Approximation in Quantum Tunneling Heisenberg's Equations of Motion for Tunneling Wigner Distribution Function in Quantum Tunneling Decay Widths of Siegert States, Complex Scaling and Dilatation Transformation Multidimensional Quantum Tunneling Group and Signal Velocities Time-Delay, Reflection Time Operator and Minimum Tunneling Time More about Tunneling Time Tunneling of a System with Internal Degrees of Freedom Motion of a Particle in a Waveguide with Variable Cross Section and in a Space Bounded by a Dumbbell-Shaped Object Relativistic Formulation of Quantum Tunneling Inverse Problems of Quantum Tunneling Some Examples of Quantum Tunneling in Atomic and Molecular Physics Some Examples from Condensed Matter Physics Alpha Decay
TL;DR: The Loop Quantum Gravity (LQG) theory as mentioned in this paper is a mathematically rigorous candidate quantum field theory of the gravitational field, which has been shown to have background independence and minimality of structures.
Abstract: Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from other quantum gravity theories are 1) background independence and 2) minimality of structures.
09 Jun 2003
TL;DR: Adiabatic state generation (ASG) as mentioned in this paper is a quantum state generation approach based on Hamiltonians instead of unitary gates, which is equivalent in power to state generation in the standard quantum model.
Abstract: The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to the problem, by studying the problem of 'quantum state generation'.We first show that any problem in Statistical Zero Knowledge (including eg. discrete log, quadratic residuosity and gap closest vector in a lattice) can be reduced to an instance of the quantum state generation problem. Having shown the generality of the state generation problem, we set the foundations for a new paradigm for quantum state generation. We define 'Adiabatic State Generation' (ASG), which is based on Hamiltonians instead of unitary gates. We develop tools for ASG including a very general method for implementing Hamiltonians (The sparse Hamiltonian lemma), and ways to guarantee non negligible spectral gaps (The jagged adiabatic path lemma). We also prove that ASG is equivalent in power to state generation in the standard quantum model. After setting the foundations for ASG, we show how to apply our techniques to generate interesting superpositions related to Markov chains.The ASG approach to quantum algorithms provides intriguing links between quantum computation and many different areas: the analysis of spectral gaps and groundstates of Hamiltonians in physics, rapidly mixing Markov chains, statistical zero knowledge, and quantum random walks. We hope that these links will bring new insights and methods into quantum algorithms.
09 Jan 2003
TL;DR: In this paper, a detailed review of the theory of decoherence-free subspaces and subsystems focusing on their usefulness for preservation of quantum information is provided. But the authors do not consider the decoherent properties of the subsystems.
Abstract: Decoherence is the phenomenon of non-unitary dynamics that arises as a consequence of coupling between a system and its environment. It has important harmful implications for quantum information processing, and various solutions to the problem have been proposed. Here we provide a detailed a review of the theory of decoherence-free subspaces and subsystems, focusing on their usefulness for preservation of quantum information.
TL;DR: In this paper, it was shown that discord determines the difference between the efficiency of quantum and classical Maxwell's demons in extracting work from collections of correlated quantum systems, i.e., entities that can or cannot measure nonlocal observables or carry out conditional quantum operations.
Abstract: Quantum discord was proposed as an information-theoretic measure of the ``quantumness'' of correlations. I show that discord determines the difference between the efficiency of quantum and classical Maxwell's demons---that is, entities that can or cannot measure nonlocal observables or carry out conditional quantum operations---in extracting work from collections of correlated quantum systems.
TL;DR: In this paper, the relevance of the open quantum system formalism for the description of weakly bound nuclei far from the valley of stability, small droplets of neutral atoms, gas of trapped atoms, open microwave cavities and quantum dots is discussed.
TL;DR: In this article, the authors illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle, which can also serve as a simple introduction to many of the ideas and constructions underlying quantum geometry.
Abstract: A programme was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle. The model can also serve as a simple introduction to many of the ideas and constructions underlying quantum geometry. Maxwell fields will be discussed in the second paper of this series which further develops the programme.
TL;DR: A quantum optical closed-loop, including a plant and controller, is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view, in order to facilitate the use of control theory in microscopic world described by quantum theory.
Abstract: This paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators. A quantum optical closed-loop, including a plant and controller, is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view, in order to facilitate the use of control theory in microscopic world described by quantum theory. In particular, an input-output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed. This would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics. This paper is divided into two parts. The first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device, cavity, that can be regarded as a unit of quantum dynamics of bosonic modes. The formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations. The input-output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems. In the follow-up paper, the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory, uncertainty principle, e.g., and some applications are presented.
TL;DR: A close formal analogy is established between the present "classical trajectory" picture over populations of adiabatic states and phase fluctuations of a quantum coherence in spectral line shapes, described by the stochastic Liouville equation.
Abstract: The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary time scale and the corresponding equilibrium free energy difference is generalized to quantum systems. Using the adiabatic representation, we show that this relation holds for isolated systems as well as for systems coupled to a bath described by a master equation. A close formal analogy is established between the present "classical trajectory" picture over populations of adiabatic states and phase fluctuations (dephasing) of a quantum coherence in spectral line shapes, described by the stochastic Liouville equation.
TL;DR: In this paper, the effect of longitudinal (spectral) coherence can be demonstrated by a direct comparison of interferograms obtained with a thermal beam and a velocity selected beam in close analogy to the usua...
Abstract: Wave–particle duality is frequently the first topic students encounter in elementary quantum physics. Although this phenomenon has been demonstrated with photons, electrons, neutrons, and atoms, the dual quantum character of the famous double-slit experiment can be best explained with the largest and most classical objects, which are currently the fullerene molecules. The soccer-ball-shaped carbon cages C60 are large, massive, and appealing objects for which it is clear that they must behave like particles under ordinary circumstances. We present the results of a multislit diffraction experiment with such objects to demonstrate their wave nature. The experiment serves as the basis for a discussion of several quantum concepts such as coherence, randomness, complementarity, and wave–particle duality. In particular, the effect of longitudinal (spectral) coherence can be demonstrated by a direct comparison of interferograms obtained with a thermal beam and a velocity selected beam in close analogy to the usua...
TL;DR: In this article, the authors introduce the concept of biphoton wavepacket and emphasize the very different physics associated with the entangled two-photon system (pure state) and with the individual subsystems (statistical mixture).
Abstract: One of the most surprising consequences of quantum mechanics is the entanglement of two or more distance particles. Even though there are still questions regarding the fundamental issues of quantum theory, quantum entanglement has started to play important roles in practical engineering applications such as quantum information processing, quantum metrology, quantum imaging and quantum lithography. Two-photon states have been the most popular entangled states in fundamental and applied research. Using spontaneous parametric down conversion as an example, this review introduces the concept of biphoton wavepacket and emphasizes the very different physics associated with the entangled two-photon system (pure state) and with the `individual' subsystems (statistical mixture). Experimental approaches for Bell state preparation, pumped by continous wave and ultrashort pulse are discussed.
01 Jan 2003
TL;DR: In this article, a new topology for an Axoim of Quantum Quantum Mechanics is presented, based on the Quantum Quantum Quantum Theory of Irreversibility (QTIR).
Abstract: Quantum Theory of Irreversibility: Open Systems and Continuum Mechanics.- Selected Aspects of Markovian and Non-Markovian Quantum Master Equations.- Aspects of Open Quantum Dynamics.- Concepts and Methods in the Theory of Open Quantum Systems.- Decoherence-Free Subspaces and Subsystems.- Controlled Quantum Open Systems.- Three Different Manifestations of the Quantum Zeno Effect.- Progressive Decoherence and Total Environmental Disentanglement.- Dynamics of Dissipative Quantum Systems: From Path Integrals to Master Equations.- Quantum Entropies in a Classical Context.- Irreversibility and the Foundations of Quantum Mechanics.- An Attempt at Relativistic Spontaneous Localization Theory.- The Quantum Jump Approach and Quantum Trajectories.- Irreversibility, Resonances and Rigged Hilbert Spaces.- Markovian Master Equations and Resonances in Quantum Open Systems.- A New Topology for an Axoim of Quantum Mechanics.- The Importance of Boundary Conditions in Quantum Mechanics.- Time Asymmetric Quantum Mechanics and Relativistic Resonances.- Irreversibility in the Framework of Hermitian and Non-Hermitian Treatments of Resonance States.
TL;DR: This note defines four different notions of controllability of physical interest for multilevel quantum mechanical systems that involve the possibility of driving the evolution operator as well as the state of the system.
Abstract: In this note, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability.
TL;DR: It is shown that electronic spin coherence can be reversibly mapped onto the collective state of the surrounding nuclei and can be used, when combined with standard resonance techniques, to reversibly store coherent superpositions on the time scale of seconds.
Abstract: We describe a technique to create long-lived quantum memory for quantum bits in mesoscopic systems. Specifically we show that electronic spin coherence can be reversibly mapped onto the collective state of the surrounding nuclei. The coherent transfer can be efficient and fast and it can be used, when combined with standard resonance techniques, to reversibly store coherent superpositions on the time scale of seconds. This method can also allow for "engineering" entangled states of nuclear ensembles and efficiently manipulating the stored states. We investigate the feasibility of this method through a detailed analysis of the coherence properties of the system.
TL;DR: In this paper, the experimental implementation of the quantum random-walk algorithm on a nuclear-magnetic-resonance quantum computer is presented, and it is observed that the quantum walk is in sharp contrast to its classical counterpart.
Abstract: The quantum random walk is a possible approach to construct quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper, we present the experimental implementation of the quantum random-walk algorithm on a nuclear-magnetic-resonance quantum computer. We observe that the quantum walk is in sharp contrast to its classical counterpart. In particular, the properties of the quantum walk strongly depends on the quantum entanglement.