Showing papers on "Open quantum system published in 2005"
TL;DR: The density-matrix renormalization group (DMRG) as mentioned in this paper is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription.
Abstract: The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.
2,341 citations
TL;DR: In this paper, the decoherence program, including its more recent results, and its application and consequences are investigated in the context of the main interpretive approaches of quantum mechanics. But their implications for the quantum measurement problem have remained a matter of great controversy.
Abstract: Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.
1,270 citations
TL;DR: In this paper, the authors considered a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.
Abstract: We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis. In addition, we allow the creation of a one-qubit ancilla in a mixed state rho, which should be regarded as a parameter of the model. Our goal is to determine for which rho universal quantum computation (UQC) can be efficiently simulated. To answer this question, we construct purification protocols that consume several copies of rho and produce a single output qubit with higher polarization. The protocols allow one to increase the polarization only along certain "magic" directions. If the polarization of rho along a magic direction exceeds a threshold value (about 65%), the purification asymptotically yields a pure state, which we call a magic state. We show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The connection of our results with the Gottesman-Knill theorem is discussed.
1,128 citations
28 Jan 2005
1,083 citations
TL;DR: In this article, a broad variety of pulse control and tomographic techniques have been developed for, and used in, NMR quantum computation and many of these will be useful in other quantum systems now being considered for the implementation of quantum information processing tasks.
Abstract: Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to a new level, motivated by the interest in quantum information processing. NMR has been the workhorse for the experimental implementation of quantum protocols, allowing exquisite control of systems up to seven qubits in size. This article surveys and summarizes a broad variety of pulse control and tomographic techniques which have been developed for, and used in, NMR quantum computation. Many of these will be useful in other quantum systems now being considered for the implementation of quantum information processing tasks.
1,068 citations
TL;DR: The implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.
Abstract: Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think about quantum physics. This new model requires qubits to be initialized in a highly entangled cluster state. From this point, the quantum computation proceeds by a sequence of single-qubit measurements with classical feedforward of their outcomes. Because of the essential role of measurement, a one-way quantum computer is irreversible. In the one-way quantum computer, the order and choices of measurements determine the algorithm computed. We have experimentally realized four-qubit cluster states encoded into the polarization state of four photons. We characterize the quantum state fully by implementing experimental four-qubit quantum state tomography. Using this cluster state, we demonstrate the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations. Finally, our implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.
1,058 citations
TL;DR: In this paper, the authors review recent theoretical advances in cold atom physics concentrating on strongly correlated cold atoms in optical lattices and discuss recently developed quantum optical tools for manipulating atoms and show how they can be used to realize a wide range of many body Hamiltonians.
893 citations
TL;DR: Superconducting circuits can behave like atoms making transitions between two levels as mentioned in this paper, and such circuits can test quantum mechanics at macroscopic scales and be used to conduct atomic-physics experiments on a silicon chip.
Abstract: Superconducting circuits can behave like atoms making transitions between two levels. Such circuits can test quantum mechanics at macroscopic scales and be used to conduct atomic-physics experiments on a silicon chip.
864 citations
TL;DR: In this paper, an application of loop quantum cosmology to homogeneous systems, which removes classical singularities, is presented, where the main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory.
Abstract: Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time.
811 citations
TL;DR: In this paper, the authors explore the prospects to control by use of time-dependent fields quantum transport phenomena in nanoscale systems and study for driven conductors the electron current and its noise properties.
605 citations
TL;DR: In this article, the authors show that nanoelectromechanical structures are starting to approach the ultimate quantum mechanical limits for detecting and exciting motion at the nanoscale, and nonclassical states of a mechanical resonator are also on the horizon.
Abstract: Nanoelectromechanical structures are starting to approach the ultimate quantum mechanical limits for detecting and exciting motion at the nanoscale. Nonclassical states of a mechanical resonator are also on the horizon.
TL;DR: In this article, the authors give an operational definition of the quantum, classical and total amounts of correlations in a bipartite quantum state, which can be defined via the amount of work (noise) that is required to erase (destroy) the correlations.
Abstract: We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation we have to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation. As a by-product, we obtain a direct, operational, and elementary proof of strong subadditivity of quantum entropy.
Book•
15 Apr 2005TL;DR: In this paper, the authors present an overview of the history of quantum physics, including the Aharonov-Bergmann-Lebowitz formula, and a discussion of its application in physics.
Abstract: 1 The Uses of Paradox.1.1 Paradox in Physics.1.2 Errors.1.3 Gaps.1.4 Contradictions.1.5 Overview of the Book.References.2 How to Weigh a Quantum.2.1 Why does the Color of the Light Change?2.2 Quanta.2.3 Uncertainty Relations.2.4 The Clock-in-the-Box Paradox.2.5 From Inconsistency to Incompleteness.References.3 Is Quantum Theory Complete?3.1 The Einstein-Podolsky-Rosen Paradox.3.2 Polarized Photons.3.3 Quantum States and Observables.3.4 Bell's Inequality.3.5 Paradox and Beyond.References.4 Phases and Gauges.4.1 Two Paradoxical Procedures.4.2 Classical and Quantum Phases.4.3 Phase Meets Gauge.4.4 The Aharonov-Bohm Effect.4.5 Quantum Consistency and the Aharonov-Bohm Effect.4.6 Flux Quantization.4.7 Magnetoresistance.4.8 Non-Abelian Phases.References.5 Modular Variables.5.1 A Lattice of Solenoids.5.2 Non-overlapping Wave Packets.5.3 Modular Momentum.5.4 The xmod, pmod Representation.5.5 Intimations of Nonlocality.References.6 Nonlocality and Causality.6.1 Causality and a Piston.6.2 Quantum Effects Without Classical Analogues.6.3 Modular Energy.6.4 Reconciling the Irreconcilable.References.7 Quantum Measurements.7.1 The Velocity Paradox.7.2 A Quantum Measurement Paradigm.7.3 Quantum Measurements and Uncertainty Relations.7.4 Paradox Lost.References.8 Measurement and Compensation.8.1 Paradox Regained.8.2 Compensating Forces.8.3 Quantum Measurements of Noncanonical Observables.8.4 Measuring the Electric Field.8.5 Energy and Time.References.9 Quantum Cats.9.1 Schr odinger's Cat.9.2 A Quantum Catalyst.9.3 Quantum Concatenations.9.4 A Quantum Catalog.References.10 A Quantum Arrow of Time?10.1 A Quantum Card Trick.10.2 Time Reversal.10.3 The Aharonov-Bergmann-Lebowitz Formula.10.4 The Arrow of Time Revisited.10.5 Boundary Conditions on the Universe.References.11 Superselection Rules.11.1 Superselection Rule for Angular Momentum?11.2 T and Spin.11.3 The Wick-Wightman-Wigner Argument.11.4 Everything is Relative.11.5 Superposing Charge States.References.12 Quantum Slow Dance.12.1 A Watched Pot Never Boils.12.2 The Adiabatic Approximation.12.3 Feynman Paths.12.4 Classical Analogues.References.13 Charges and Fluxons.13.1 Hidden Momentum?13.2 Duality of the Aharonov-Bohm Effect.13.3 The Aharonov-Bohm Effect and Berry's Phase.13.4 The Aharonov-Casher Effect.References.14 Quantum Measurements and Relativity.14.1 Collapse and Relativity.14.2 Relativistic Constraints on Measurements.14.3 Nonlocal Measurements.14.4 Which Nonlocal Operators are Measurable?14.5 Measuring a Nonlocal Operator.14.6 Collapse and Relativity Revisited.References.15 How to Observe a Quantum Wave.15.1 Dipole Paradox.15.2 How not to Observe a Quantum Wave.15.3 Protective Measurements.15.4 Galilean Dialogue.15.5 Protective Measurements and Causality.15.6 Towards Quantum Field Theory.References.16 Weak Values.16.1 A Weak Measurement.16.2 A Paradox of Errors.16.3 Pre- and Postselected Ensembles.16.4 Weak Measurements and Weak Values.16.5 A Quantum Shell Game.16.6 The Quantum Walk.16.7 Faster than Light.16.8 Galilean Dialogue.References.17 Weak Values and Entanglement.17.1 Interaction-free Paradox.17.2 A Grin Without a Cat.17.3 Alice and Bob in Wonderland.17.4 Galilean Dialogue.17.5 Complex Weak Values.References.18 The Quantum World.18.1 Weak Measurements and Interference.18.2 From Amplitudes to Probabilities.18.3 The Fate of the Universe.18.4 The Role of h.18.5 Causality and Nonlocality as Axioms.18.6 Causality, Nonlocality and Scaling.18.7 What is the Quantum World?References.Index.
TL;DR: A review of coherent and collective quantum optical effects like superradiance and coherent population trapping in mesoscopic systems is presented in this article, with a focus on their role for electronic transport and quantum dissipation.
TL;DR: Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins was proposed in this article, where a fault tolerant architecture was proposed for quantum computing using semiconductor spin spins.
Abstract: Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins
TL;DR: In this paper, the authors proposed a method to solve the problem of "uniformity" in the literature.and.and, and, respectively, the authors' work.
Abstract: and
TL;DR: In this paper, a new route for distributed optical quantum information processing (QIP) based on generalized quantum non-demolition measurements is presented, providing a unified approach for quantum communication and computing.
Abstract: Quantum information processing (QIP) offers the promise of being able to do things that we cannot do with conventional technology. Here we present a new route for distributed optical QIP, based on generalized quantum non-demolition measurements, providing a unified approach for quantum communication and computing. Interactions between photons are generated using weak nonlinearities and intense laser fields—the use of such fields provides for robust distribution of quantum information. Our approach only requires a practical set of resources, and it uses these very efficiently. Thus it promises to be extremely useful for the first quantum technologies, based on scarce resources. Furthermore, in the longer term this approach provides both options and scalability for efficient many-qubit QIP.
TL;DR: The consequences of the time-reversal symmetry for an open dissipative quantum dynamics and a series of subtleties and possible pitfalls are discussed and the path integral methodology is applied to the decay of metastable states assisted by quantum Brownian noise.
Abstract: With this work we elaborate on the physics of quantum noise in thermal equilibrium and in stationary nonequilibrium. Starting out from the celebrated quantum fluctuation-dissipation theorem we discuss some important consequences that must hold for open, dissipative quantum systems in thermal equilibrium. The issue of quantum dissipation is exemplified with the fundamental problem of a damped harmonic quantum oscillator. The role of quantum fluctuations is discussed in the context of both, the nonlinear generalized quantum Langevin equation and the path integral approach. We discuss the consequences of the time-reversal symmetry for an open dissipative quantum dynamics and, furthermore, point to a series of subtleties and possible pitfalls. The path integral methodology is applied to the decay of metastable states assisted by quantum Brownian noise.
TL;DR: A general model for quantum channels with memory is presented and it is shown that it is sufficiently general to encompass all causal automata: any quantum process in which outputs up to some time do not depend on inputs at times can be decomposed into a concatenated memory channel.
Abstract: We present a general model for quantum channels with memory and show that it is sufficiently general to encompass all causal automata: any quantum process in which outputs up to some time $t$ do not depend on inputs at times ${t}^{\ensuremath{'}}gt$ can be decomposed into a concatenated memory channel. We then examine and present different physical setups in which channels with memory may be operated for the transfer of (private) classical and quantum information. These include setups in which either the receiver or a malicious third party have control of the initializing memory. We introduce classical and quantum channel capacities for these settings and give several examples to show that they may or may not coincide. Entropic upper bounds on the various channel capacities are given. For forgetful quantum channels, in which the effect of the initializing memory dies out as time increases, coding theorems are presented to show that these bounds may be saturated. Forgetful quantum channels are shown to be open and dense in the set of quantum memory channels.
Posted Content•
TL;DR: In this article, the authors review different approaches to the modeling of quantum effects in electrostatic collisionless plasmas using the Wigner equation and the Hartree formalism, which is related to the multi-stream approach of classical plasma physics.
Abstract: Traditional plasma physics has mainly focused on regimes characterized by high temperatures and low densities, for which quantum-mechanical effects have virtually no impact. However, recent technological advances (particularly on miniaturized semiconductor devices and nanoscale objects) have made it possible to envisage practical applications of plasma physics where the quantum nature of the particles plays a crucial role. Here, I shall review different approaches to the modeling of quantum effects in electrostatic collisionless plasmas. The full kinetic model is provided by the Wigner equation, which is the quantum analog of the Vlasov equation. The Wigner formalism is particularly attractive, as it recasts quantum mechanics in the familiar classical phase space, although this comes at the cost of dealing with negative distribution functions. Equivalently, the Wigner model can be expressed in terms of $N$ one-particle Schr{o}dinger equations, coupled by Poisson's equation: this is the Hartree formalism, which is related to the `multi-stream' approach of classical plasma physics. In order to reduce the complexity of the above approaches, it is possible to develop a quantum fluid model by taking velocity-space moments of the Wigner equation. Finally, certain regimes at large excitation energies can be described by semiclassical kinetic models (Vlasov-Poisson), provided that the initial ground-state equilibrium is treated quantum-mechanically. The above models are validated and compared both in the linear and nonlinear regimes.
TL;DR: This book surveys proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and "anthropic computing".
Abstract: Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and "anthropic computing." The section on soap bubbles even includes some "experimental" results. While I do not believe that any of the proposals will let us solve NP-complete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics.
TL;DR: The possibility to perform distributed quantum computing using only single-photon sources (atom-cavity-like systems, linear optics, and photon detectors), which does not require explicit qubit-qubit interactions, a priori entangled ancillas, nor the feeding of photons into photon sources.
Abstract: We demonstrate the possibility to perform distributed quantum computing using only single-photon sources (atom-cavity-like systems), linear optics, and photon detectors. The qubits are encoded in stable ground states of the sources. To implement a universal two-qubit gate, two photons should be generated simultaneously and pass through a linear optics network, where a measurement is performed on them. Gate operations can be repeated until a success is heralded without destroying the qubits at any stage of the operation. In contrast with other schemes, this does not require explicit qubit-qubit interactions, a priori entangled ancillas, nor the feeding of photons into photon sources.
Book•
01 Jan 2005
TL;DR: In this article, the authors discuss classical and quantum interference and coherence effects in multi-level systems, including slow and fast light and storage of Photons, quantum interference in phase space, and interference in Atom Optics.
Abstract: Classical and Quantum Interference and Coherence.- Quantum Interference in Atomic Systems: Mathematical Formalism.- Superposition States and Modification of Spontaneous Emission Rates.- Quantum Interference as a Control of Decoherence.- Coherence Effects in Multi-Level Systems.- Field Induced Quantum Interference.- Slow and Fast Light and Storage of Photons.- Quantum Interference in Phase Space.- Quantum Interference in Atom Optics.
Journal Article•
TL;DR: Can NP-complete problems be solved efficiently in the physical universe? as mentioned in this paper survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and anthropic computing.
Abstract: Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and “anthropic computing.” The section on soap bubbles even includes some “experimental” results. While I do not believe that any of the proposals will let us solve NP-complete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics.
TL;DR: A cavity coupling, a charged nanodot, and a fiber can act as a quantum interface, through which a stationary spin qubit and a flying photon qubit can be interconverted via a cavity-assisted Raman process.
Abstract: A cavity coupling, a charged nanodot, and a fiber can act as a quantum interface, through which a stationary spin qubit and a flying photon qubit can be interconverted via a cavity-assisted Raman process. This Raman process can be made to generate or annihilate an arbitrarily shaped single-photon wave packet by pulse shaping the controlling laser field. This quantum interface forms the basis for many essential functions of a quantum network, including sending, receiving, transferring, swapping, and entangling qubits at distributed quantum nodes as well as a deterministic source and an efficient detector of a single-photon wave packet with arbitrarily specified shape and average photon number. Numerical study of errors from noise and system parameters on the operations shows high fidelity and robust tolerance.
01 Jan 2005
TL;DR: This book discusses quantum computing basics, quantum Fourier Transform, and other topics related to quantum computing, as well as some examples of applications.
Abstract: Preface.How to use this book.Acknowledgements.List of Figures.Acronyms.PART I: INTRODUCTION TO QUANTUM COMPUTING.1. Motivations.2. Quantum Computing Basics.3. Measurements.PART II: QUANTUM ALGORITHMS.4. Two Simple Quantum Algorithms.5. Quantum Parallelism.6. Quantum Fourier Transform and its Applications.PART III: QUANTUM-ASSISTED SOLUTIONS OF INFOCOM PROBLEMS.7. Searching in an Unsorted Database.8. Quantum Based Multiuser Detection.9. Quantum Based Code Breaking.10. Quantum Based Key Distribution.11. Surfing the WEB on Quantum Basics.PART IV: APPENDICES.12. Mathematical Background.13. Derivations Related to the Generalized Grover Algorithm.14. Complex Baseband-Equivalent Description of Bandlimited Signals.15. Useful Links.References.Solution of Exercises.Index.
TL;DR: In this article, the geometrical optics of correlated imaging for two kinds of spatial correlations corresponding to a classical thermal light source and a quantum two-photon entangled source were discussed.
Abstract: We discuss the geometrical optics of correlated imaging for two kinds of spatial correlations corresponding, respectively, to a classical thermal light source and a quantum two-photon entangled source. Due to the different features in the second-order spatial correlation, the two sources obey different imaging equations. The quantum entangled source behaves as a mirror, whereas the classical thermal source looks like a phase-conjugate mirror in the correlated imaging.
TL;DR: An inherently open-systems approach is introduced, based on a recent generalization of the adiabatic approximation, that shows that a system may initially be in an adiAbatic regime, but then undergo a transition to a regime where adiABaticity breaks down.
Abstract: We analyze the performance of adiabatic quantum computation (AQC) subject to decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria.
TL;DR: In this paper, the authors generalize the standard quantum adiabatic approximation to the case of open quantum systems and define the limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks.
Abstract: We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks. We then establish validity and invalidity conditions for this approximation and discuss their applicability to superoperators changing slowly in time. As an example, the adiabatic evolution of a two-level open system is analyzed.
Posted Content•
TL;DR: In this paper, a set of lectures in Quantum Optics and Quantum Information (MGAP) were presented at the University of Napoli and University of Milano, with a special emphasis on phase space analysis of quantum dynamics and the role of Gaussian states in continuous variable quantum information.
Abstract: These notes originated out of a set of lectures in Quantum Optics and Quantum Information given by one of us (MGAP) at the University of Napoli and the University of Milano. A quite broad set of issues are covered, ranging from elementary concepts to current research topics, and from fundamental concepts to applications. A special emphasis has been given to the phase space analysis of quantum dynamics and to the role of Gaussian states in continuous variable quantum information.