Showing papers on "Open quantum system published in 2002"
Book•
29 Aug 2002
TL;DR: Probability in classical and quantum physics has been studied in this article, where classical probability theory and stochastic processes have been applied to quantum optical systems and non-Markovian dynamics in physical systems.
Abstract: PREFACE ACKNOWLEDGEMENTS PART 1: PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS 1. Classical probability theory and stochastic processes 2. Quantum Probability PART 2: DENSITY MATRIX THEORY 3. Quantum Master Equations 4. Decoherence PART 3: STOCHASTIC PROCESSES IN HILBERT SPACE 5. Probability distributions on Hilbert space 6. Stochastic dynamics in Hilbert space 7. The stochastic simulation method 8. Applications to quantum optical systems PART 4: NON-MARKOVIAN QUANTUM PROCESSES 9. Projection operator techniques 10. Non-Markovian dynamics in physical systems PART 5: RELATIVISTIC QUANTUM PROCESSES 11. Measurements in relativistic quantum mechanics 12. Open quantum electrodynamics
6,325 citations
TL;DR: It is demonstrated, for a class of one-dimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point, which connects the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point.
Abstract: Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by macroscopic order. Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant, and are driven by quantum fluctuations. Examples include transitions in quantum Hall systems, localization in Si-MOSFETs (metal oxide silicon field-effect transistors; ref. 4) and the superconductor-insulator transition in two-dimensional systems. Both classical and quantum critical points are governed by a diverging correlation length, although quantum systems possess additional correlations that do not have a classical counterpart. This phenomenon, known as entanglement, is the resource that enables quantum computation and communication. The role of entanglement at a phase transition is not captured by statistical mechanics-a complete classification of the critical many-body state requires the introduction of concepts from quantum information theory. Here we connect the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point. We demonstrate, for a class of one-dimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point.
1,571 citations
TL;DR: This work shows how to achieve massively parallel gate operation in a large-scale quantum computer, based on techniques already demonstrated for manipulating small quantum registers, and uses the use of decoherence-free subspaces to do so.
Abstract: Among the numerous types of architecture being explored for quantum computers are systems utilizing ion traps, in which quantum bits (qubits) are formed from the electronic states of trapped ions and coupled through the Coulomb interaction. Although the elementary requirements for quantum computation have been demonstrated in this system, there exist theoretical and technical obstacles to scaling up the approach to large numbers of qubits. Therefore, recent efforts have been concentrated on using quantum communication to link a number of small ion-trap quantum systems. Developing the array-based approach, we show how to achieve massively parallel gate operation in a large-scale quantum computer, based on techniques already demonstrated for manipulating small quantum registers. The use of decoherence-free subspaces significantly reduces decoherence during ion transport, and removes the requirement of clock synchronization between the interaction regions.
1,469 citations
TL;DR: A superconducting tunnel junction circuit that behaves as a two-level atom that can be programmed with a series of microwave pulses and a projective measurement of the state can be performed by a pulsed readout subcircuit is designed and operated.
Abstract: We have designed and operated a superconducting tunnel junction circuit that behaves as a two-level atom: the "quantronium." An arbitrary evolution of its quantum state can be programmed with a series of microwave pulses, and a projective measurement of the state can be performed by a pulsed readout subcircuit. The measured quality factor of quantum coherence Qphi approximately 25,000 is sufficiently high that a solid-state quantum processor based on this type of circuit can be envisioned.
1,432 citations
Book•
31 May 2002TL;DR: Introduction Classical computation Quantum computation Solutions Elementary number theory Bibliography Index.
Abstract: Introduction Classical computation Quantum computation Solutions Elementary number theory Bibliography Index.
1,209 citations
TL;DR: In this article, the authors show how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission, and show that quantum computers can achieve enhanced speed over their classical counterparts using information-theoretic arguments.
Abstract: Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are in fact intimately related. In this review the author shows how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission. The derivation of many key results differentiates this review from the usual presentation in that they are shown to follow logically from one crucial property of relative entropy. Within the review, optimal bounds on the enhanced speed that quantum computers can achieve over their classical counterparts are outlined using information-theoretic arguments. In addition, important implications of quantum information theory for thermodynamics and quantum measurement are intermittently discussed. A number of simple examples and derivations, including quantum superdense coding, quantum teleportation, and Deutsch's and Grover's algorithms, are also included.
976 citations
TL;DR: It is demonstrated that coherent optical excitations in the quantum-dot two-level system can be converted into deterministic photocurrents and found that this device can function as an optically triggered single-electron turnstile.
Abstract: Present-day information technology is based mainly on incoherent processes in conventional semiconductor devices. To realize concepts for future quantum information technologies, which are based on coherent phenomena, a new type of 'hardware' is required. Semiconductor quantum dots are promising candidates for the basic device units for quantum information processing. One approach is to exploit optical excitations (excitons) in quantum dots. It has already been demonstrated that coherent manipulation between two excitonic energy levels--via so-called Rabi oscillations--can be achieved in single quantum dots by applying electromagnetic fields. Here we make use of this effect by placing an InGaAs quantum dot in a photodiode, which essentially connects it to an electric circuit. We demonstrate that coherent optical excitations in the quantum-dot two-level system can be converted into deterministic photocurrents. For optical excitation with so-called pi-pulses, which completely invert the two-level system, the current is given by I = fe, where f is the repetition frequency of the experiment and e is the elementary charge. We find that this device can function as an optically triggered single-electron turnstile.
702 citations
TL;DR: In this article, a sequence of single photons is emitted on demand from a single three-level atom strongly coupled to a high-finesse optical cavity, generated by an adiabatically driven stimulated Raman transition between two atomic ground states.
Abstract: A sequence of single photons is emitted on demand from a single three-level atom strongly coupled to a high-finesse optical cavity. The photons are generated by an adiabatically driven stimulated Raman transition between two atomic ground states, with the vacuum field of the cavity stimulating one branch of the transition, and laser pulses deterministically driving the other branch. This process is unitary and therefore intrinsically reversible, which is essential for quantum communication and networking, and the photons should be appropriate for all-optical quantum information processing.
684 citations
TL;DR: The purview of cavity QED will continue to grow as researchers build on a rich infrastructure to attack some of the most pressing open questions in micro- and mesoscopic physics.
Abstract: Modern cavity quantum electrodynamics (cavity QED) illuminates the most fundamental aspects of coherence and decoherence in quantum mechanics. Experiments on atoms in cavities can be described by elementary models but reveal intriguing subtleties of the interplay of coherent dynamics with external couplings. Recent activity in this area has pioneered powerful new approaches to the study of quantum coherence and has fueled the growth of quantum information science. In years to come, the purview of cavity QED will continue to grow as researchers build on a rich infrastructure to attack some of the most pressing open questions in micro- and mesoscopic physics.
626 citations
TL;DR: Recent theoretical and experimental advances suggest that cold atoms and individual photons may lead the way towards bigger and better quantum information processors, effectively building mesoscopic versions of 'Schrödinger's cat' from the bottom up.
Abstract: Quantum information processors exploit the quantum features of superposition and entanglement for applications not possible in classical devices, offering the potential for significant improvements in the communication and processing of information. Experimental realization of large-scale quantum information processors remains a long-term vision, as the required nearly pure quantum behaviour is observed only in exotic hardware such as individual laser-cooled atoms and isolated photons. But recent theoretical and experimental advances suggest that cold atoms and individual photons may lead the way towards bigger and better quantum information processors, effectively building mesoscopic versions of 'Schrodinger's cat' from the bottom up.
544 citations
TL;DR: How quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers is reviewed.
Abstract: Quantum theory has found a new field of application in the realm of information and computation during recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some notable aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as examples of the impact of quanta on the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement made possible in information processing by a quantum computer. Finally the authors provide some examples of current experimental realizations for quantum computers and future prospects.
TL;DR: The quantum Zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus.
Abstract: The quantum Zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus. A few significant examples are proposed and their practical relevance discussed. We also focus on decoherence-free subspaces.
Posted Content•
TL;DR: In this regard, no tool appears better calibrated for a direct assault than quantum information theory as discussed by the authors, and this method holds promise precisely because a large part of the structure of quantum theory has always concerned information.
Abstract: In this paper, I try once again to cause some good-natured trouble The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance In this regard, no tool appears better calibrated for a direct assault than quantum information theory Far from a strained application of the latest fad to a time-honored problem, this method holds promise precisely because a large part--but not all--of the structure of quantum theory has always concerned information It is just that the physics community needs reminding
This paper, though taking quant-ph/0106166 as its core, corrects one mistake and offers several observations beyond the previous version In particular, I identify one element of quantum mechanics that I would not label a subjective term in the theory--it is the integer parameter D traditionally ascribed to a quantum system via its Hilbert-space dimension
TL;DR: In this paper, the Bohm Trajectory Approach to Timing Electrons is used for time-energy uncertainty in one-dimensional scattering, as well as a standard quantum-mechanical approach to times of arrival.
Abstract: Characteristic Times in One-Dimensional Scattering.- The Time-Energy Uncertainty Relation.- Jump Time and Passage Time: The Duration ofs a Quantum Transition.- Bohm Trajectory Approach to Timing Electrons.- Decoherent Histories for Space-Time Domains.- Quantum Traversal Time, Path Integrals and "Superluminal" Tunnelling.- Quantum Clocks and Stopwatches.- The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics.- "Standard" Quantum-Mechanical Approach to Times of Arrival.- Experimental Issues in Quantum-Mechanical Time Measurement.- Microwave Experiments on Tunneling Time.- The Two-State Vector Formalism: An Updated Review.
TL;DR: The Fock space of a system of indistinguishable particles is isomorphic (in a nonunique way) to the state space of composite, i.e., many modes, quantum systems as mentioned in this paper.
Abstract: The Fock space of a system of indistinguishable particles is isomorphic (in a nonunique way) to the state space of a composite, i.e., many modes, quantum system. One can then discuss quantum entanglement for fermionic as well as bosonic systems. We exemplify the use of this notion---central in quantum information---by studying some, e.g., Hubbard, lattice fermionic models relevant to condensed matter physics.
TL;DR: In this paper, the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles is introduced and a correlation measure for indistinguishable particles is provided.
TL;DR: It is obtained that any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.
Abstract: We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.
TL;DR: A simple quantum network, based on the controlled-SWAP gate, is presented that can extract certain properties of quantum states without recourse to quantum tomography and is used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator.
Abstract: We present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator. The network has many potential applications ranging from purity tests and eigenvalue estimations to direct characterization of some properties of quantum channels. Experimental realizations of the proposed network are within the reach of quantum technology that is currently being developed.
TL;DR: In this article, the authors studied the interaction of the thermal field and a quantum system composed of two qubits and found that such a chaotic field with minimal information can nevertheless entangle the qubits which are prepared initially in a separable state.
Abstract: A thermal field, which frequently appears in problems of decoherence, provides us with minimal information about the field. We study the interaction of the thermal field and a quantum system composed of two qubits and find that such a chaotic field with minimal information can nevertheless entangle the qubits which are prepared initially in a separable state. This simple model of a quantum register interacting with a noisy environment allows us to understand how memory of the environment affects the state of a quantum register.
TL;DR: In this paper, the authors give a self-contained introduction to the conceptional and mathematical foundations of quantum information theory, including entanglement measures, channel capacities, relations between both, additivity and continuity properties and asymptotic rates of quantum operations.
TL;DR: An experimental demonstration of the power of feedback in quantum metrology, confirming the predicted superior performance of an adaptive homodyne technique for single-shot measurement of optical phase and underscore the importance of real-time feedback for reaching quantum limits in measurement and control.
Abstract: We present an experimental demonstration of the power of feedback in quantum metrology, confirming the predicted [H. M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)] superior performance of an adaptive homodyne technique for single-shot measurement of optical phase. For measurements performed on weak coherent states with no prior knowledge of the signal phase, adaptive homodyne estimation approaches closer to the intrinsic quantum uncertainty than any previous technique. Our results underscore the importance of real-time feedback for reaching quantum limits in measurement and control.
TL;DR: In this paper, the authors exploit the Jordan-Wigner isomorphism between the two algebras and give quantum circuits useful for the efficient evaluation of the physical properties (e.g., spectrum of observables or relevant correlation functions) of an arbitrary system with Hamiltonian H.
Abstract: Physical systems, characterized by an ensemble of interacting constituents, can be represented and studied by different algebras of operators (observables). For example, a fully polarized electronic system can be studied by means of the algebra generated by the usual fermionic creation and annihilation operators or by the algebra of Pauli (spin-1/2) operators. The Jordan-Wigner isomorphism gives the correspondence between the two algebras. As we previously noted, similar isomorphisms enable one to represent any physical system in a quantum computer. In this paper we evolve and exploit this fundamental observation to simulate generic physical phenomena by quantum networks. We give quantum circuits useful for the efficient evaluation of the physical properties (e.g., the spectrum of observables or relevant correlation functions) of an arbitrary system with Hamiltonian H.
IBM1
TL;DR: It is shown that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension.
Abstract: We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant [in Proceedings of the 33rd ACM Symposium on the Theory of Computing (2001), p. 114] corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend the result to noninteracting fermions with arbitrary pairwise interactions, where gates can be conditioned on outcomes of complete von Neumann measurements in the computational basis on other fermionic modes in the circuit. This last result is in remarkable contrast with the case of noninteracting bosons where universal quantum computation can be achieved by allowing gates to be conditioned on classical bits [E. Knill, R. Laflamme, and G. Milburn, Nature (London) 409, 46 (2001)].
TL;DR: Topological quantum field theories (TQFTs) as mentioned in this paper have been used to define a model of computation stronger than the usual quantum model "BQP" and provide a radically different way of looking at quantum computation.
Abstract: Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned “topological models” having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the state is discrete, H≡ 0. These are called topological quantum field theories (TQFTs). These exotic physical systems are proved to be efficiently simulated on a quantum computer. The conclusion is two-fold: 1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model “BQP”. 2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might suggest a new quantum algorithm.
TL;DR: In this article, the authors consider the problem of reversing quantum dynamics, with the goal of preserving an initial state's quantum entanglement or classical correlation with a reference system, and exhibit an approximate reversal operation, adapted to the initial density operator and the "noise" dynamics to be reversed.
Abstract: We consider the problem of reversing quantum dynamics, with the goal of preserving an initial state’s quantum entanglement or classical correlation with a reference system. We exhibit an approximate reversal operation, adapted to the initial density operator and the “noise” dynamics to be reversed. We show that its error in preserving either quantum or classical information is no more than twice that of the optimal reversal operation. Applications to quantum algorithms and information transmission are discussed.
TL;DR: It is shown that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which separate a classical region, an intermediate region, and a fully quantum region.
Abstract: We generalize the quantum prisoner's dilemma to the case where the players share a nonmaximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which separate a classical region, an intermediate region, and a fully quantum region. Furthermore this quantum game is experimentally realized on our nuclear magnetic resonance quantum computer.
Book•
20 Jun 2002
TL;DR: Weinfurter and Zeilinger as discussed by the authors discuss quantum entanglement and quantum communication in terms of quantum information theory, an invitation, and quantum algorithms, applicable algebra and quantum physics.
Abstract: From the foundations of quantum theory to quantum technology - G. Alber quantum information theory, an invitation - R. Werner quantum communication - H. Weinfurter and A. Zeilinger quantum algorithms, applicable algebra and quantum physics - T.H. Beth and M. Rotteler mixed-state entanglement and quantum communication - M. Rotteler and R. Horodecki.
Abstract: Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different “unravelings” of a mixed state master equation. I also comment briefly on the relationship of the theory to the consistent histories formalism and to spontaneous collapse models.