Showing papers on "Open quantum system published in 2001"
TL;DR: It is shown that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors and are robust against errors from photon loss and detector inefficiency.
Abstract: Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.
5,236 citations
TL;DR: It is shown that the communication efficiency scales polynomially with the channel length, and hence the scheme should be operable over very long distances.
Abstract: Quantum communication holds promise for absolutely secure transmission of secret messages and the faithful transfer of unknown quantum states. Photonic channels appear to be very attractive for the physical implementation of quantum communication. However, owing to losses and decoherence in the channel, the communication fidelity decreases exponentially with the channel length. Here we describe a scheme that allows the implementation of robust quantum communication over long lossy channels. The scheme involves laser manipulation of atomic ensembles, beam splitters, and single-photon detectors with moderate efficiencies, and is therefore compatible with current experimental technology. We show that the communication efficiency scales polynomially with the channel length, and hence the scheme should be operable over very long distances.
3,126 citations
TL;DR: A technique for manipulating quantum information stored in collective states of mesoscopic ensembles by optical excitation into states with strong dipole-dipole interactions that can be employed for controlled generation of collective atomic spin states as well as nonclassical photonic states and for scalable quantum logic gates is described.
Abstract: We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting "dipole blockade" can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as nonclassical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed.
1,310 citations
01 Jan 2001
TL;DR: The Standard Statistical Model of Quantum Mechanics (SSMMLM) as discussed by the authors is a well-known model of quantum mechanics and is used in many aspects of quantum physics, e.g., evolution of an open system.
Abstract: The Standard Statistical Model of Quantum Mechanics.- Statistics of Quantum Measurements.- Evolution of an Open System.- Repeated and Continuous Measurement Processes.- Processes in Fock Space.
795 citations
Book•
21 Dec 2001
TL;DR: Operational Quantum Physics as discussed by the authors offers a systematic presentation of quantum mechanics which makes exhaustive use of the full probabilistic structure of this theory and explains the notion of an observable as a positive operator valued (POV) measure.
Abstract: Operational Quantum Physics offers a systematic presentation of quantum mechanics which makes exhaustive use of the full probabilistic structure of this theory. Accordingly the notion of an observable as a positive operator valued (POV) measure is explained in great detail, and the ensuing quantum measurement theory is developed and applied both to a resolution of long-standing conceptual and interpretational puzzles in the foundations of quantum mechanics, and to an analysis of various recent fundamental experiments.The book, or different parts of it, may be of interest to advanced students or researchers in quantum physics, to philosophers of physics, and to mathematicians working in operator valued measures.
722 citations
TL;DR: It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry and the correct semiclassical behavior is obtained.
Abstract: It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstration comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained.
717 citations
Book•
01 Jan 2001
TL;DR: This book aims to provide a pedagogical introduction to the subjects of quantum information and computation, including non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault-tolerant quantum computation and quantum cryptography.
Abstract: From the Publisher:
This book aims to provide a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault-tolerant quantum computation as well as some experimental aspects of quantum computation and quantum cryptography. Only knowledge of basic quantum mechanics is assumed. Whenever more advanced concepts and techniques are used, they are introduced carefully. This book is meant to be a self-contained overview. While basic concepts are discussed in detail, unnecessary technical details are excluded. It is well-suited for a wide audience ranging from physics graduate students to advanced researchers.
507 citations
TL;DR: Utilizing the entangled nature of a two-photon state, the experimental results have beaten the classical diffraction limit by a factor of 2 and are a quantum mechanical two- photon phenomenon but not a violation of the uncertainty principle.
Abstract: We report a proof-of-principle experimental demonstration of quantum lithography. Utilizing the entangled nature of a two-photon state, the experimental results have beaten the classical diffraction limit by a factor of 2. This is a quantum mechanical two-photon phenomenon but not a violation of the uncertainty principle.
505 citations
TL;DR: In this paper, the authors study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems, and study this robustness using numerical simulations of the algorithm.
Abstract: We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic computation against two kinds of errors, unitary control errors and decoherence, and we study this robustness using numerical simulations of the algorithm.
424 citations
TL;DR: A semiclassical interpretation of the results indicates that electron motion in the rings is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots, opening a way to experiments where even more complex structures can be investigated at a quantum mechanical level.
Abstract: Quantum mechanical experiments in ring geometries have long fascinated physicists. Open rings connected to leads, for example, allow the observation of the Aharonov-Bohm effect, one of the best examples of quantum mechanical phase coherence. The phase coherence of electrons travelling through a quantum dot embedded in one arm of an open ring has also been demonstrated. The energy spectra of closed rings have only recently been studied by optical spectroscopy. The prediction that they allow persistent current has been explored in various experiments. Here we report magnetotransport experiments on closed rings in the Coulomb blockade regime. Our experiments show that a microscopic understanding of energy levels, so far limited to few-electron quantum dots, can be extended to a many-electron system. A semiclassical interpretation of our results indicates that electron motion in the rings is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots. This opens a way to experiments where even more complex structures can be investigated at a quantum mechanical level.
418 citations
TL;DR: This work investigates the simulation of fermionic systems on a quantum computer and shows in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity.
Abstract: We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity. The key to our demonstration is the spin-particle connection (or generalized Jordan-Wigner transformation) that allows exact algebraic invertible mappings of operators with different statistical properties. We give an explicit implementation of a simple problem using a quantum computer based on standard qubits.
Book•
06 Sep 2001
TL;DR: In this article, basic tools for quantum mechanics are presented, including algebraic tools, deterministic dynamics, spin chains, Fermionic dynamical systems, and quantum irreversibility.
Abstract: Preface 1. Introduction 2. Basic tools for quantum mechanics 3. Deterministic dynamics 4. Spin chains 5. Algebraic tools 6. Fermionic dynamical systems 7. Ergodic theory 8. Quantum irreversibility 9. Entropy 10. Dynamical entropy 11. Classical dynamical entropy 12. Finite quantum systems 13. Model systems 14. Epilogue Index Bibliography
TL;DR: A general method based on quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation, which needs only a single entangled state as input.
Abstract: Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement We present a general method based on quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation As input the method needs only a single entangled state The feasibility of the technique for the electromagnetic field is shown, and the experimental setup is illustrated based on homodyne tomography of a twin beam
TL;DR: The production of photon fields with a fixed photon number on demand is discussed based on a cavity quantum electrodynamics scheme using the strong coupling between excited atoms and a single-mode cavity field.
Abstract: Many applications in quantum information or quantum computing require radiation with a fixed number of photons. This increased the demand for systems able to produce such fields. We discuss the production of photon fields with a fixed photon number on demand. The first experimental demonstration of the device is described. This setup is based on a cavity quantum electrodynamics scheme using the strong coupling between excited atoms and a single-mode cavity field.
14 Oct 2001
TL;DR: In this paper, the authors analyze the computational power and limitations of the recently proposed "quantum adiabatic evolution algorithm" and show that the usual query complexity arguments cannot be used to rule out a polynomial time solution.
Abstract: The authors analyze the computational power and limitations of the recently proposed 'quantum adiabatic evolution algorithm'. Adiabatic quantum computation is a novel paradigm for the design of quantum algorithms; it is truly quantum in the sense that it can be used to speed up searching by a quadratic factor over any classical algorithm. On the question of whether this new paradigm may be used to efficiently solve NP-complete problems on a quantum computer, we show that the usual query complexity arguments cannot be used to rule out a polynomial time solution. On the other hand, we argue that the adiabatic approach may be thought of as a kind of 'quantum local search'. We design a family of minimization problems that is hard for such local search heuristics, and establish an exponential lower bound for the adiabatic algorithm for these problems. This provides insights into the limitations of this approach. It remains an open question whether adiabatic quantum computation can establish an exponential speed-up over traditional computing or if there exists a classical algorithm that can simulate the quantum adiabatic process efficiently.
TL;DR: The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set A of operationally relevant observables, and the notion of compoundness for quantum systems is accordingly relativized.
Abstract: The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set A of operationally relevant observables. The algebraic structure of A selects a preferred tensor product structure, i.e., a partition into subsystems. The notion of compoundness for quantum systems is accordingly relativized. Universal control over virtual subsystems can be achieved by using quantum noncommutative holonomies
TL;DR: In this article, sufficient conditions for complete controllability of N-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established and applied in particular to Morse and harmonic-oscillator systems.
Abstract: Sufficient conditions for complete controllability of N-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Controllability of these model systems is of special interest since they have many applications in physics, e.g., Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.
TL;DR: In this article, the authors introduce spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity and topological quantum field theories.
Abstract: This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path integral quantum gravity, lattice field theory, matrix models, category theory and statistical mechanics. We describe the general formalism and ideas of spin foam models, the picture of quantum geometry emerging from them, and give a review of the results obtained so far, in both the Euclidean and Lorentzian cases. We focus in particular on the Barrett-Crane model for four-dimensional quantum gravity.
TL;DR: The notion of entanglement can be naturally extended from quantum states to the level of general quantum evolutions by considering multipartite unitary transformations as elements of a multipartitite Hilbert space and then extended to general quantum operations as mentioned in this paper.
Abstract: The notion of entanglement can be naturally extended from quantum states to the level of general quantum evolutions. This is achieved by considering multipartite unitary transformations as elements of a multipartite Hilbert space and then extended to general quantum operations. We show some connection between this entanglement and the entangling capabilities of the quantum evolution.
TL;DR: In this paper, the authors demonstrate how this procedure can be implemented with a nuclear magnetic resonance quantum computer and test an important assumption underlying many models of quantum error correction, the independence of errors on different qubits.
Abstract: Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-NOT logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying many models of quantum error correction, the independence of errors on different qubits.
TL;DR: In this paper, it was shown that a very different model involving only projective measurements, quantum memory, and the ability to prepare the |0> state is also universal for quantum computation.
Abstract: What resources are universal for quantum computation? In the standard model, a quantum computer consists of a sequence of unitary gates acting coherently on the qubits making up the computer. This paper shows that a very different model involving only projective measurements, quantum memory, and the ability to prepare the |0> state is also universal for quantum computation. In particular, no coherent unitary dynamics are involved in the computation.
TL;DR: The ability to perform measurements on a quantum system, combined with the ability to feed back the measurement results via coherent control, allows one to control the system to follow any desired coherent or incoherent quantum dynamics as discussed by the authors.
Abstract: The ability to perform measurements on a quantum system, combined with the ability to feed back the measurement results via coherent control, allows one to control the system to follow any desired coherent or incoherent quantum dynamics. Such universal dynamical control can be achieved, in principle, through the repeated application of only two coherent control operations and a simple ``Yes-No'' measurement. As a consequence, a quantum computer can simulate an arbitrary open-system dynamics using just one qubit more than required to simulate closed-system dynamics.
TL;DR: In this paper, the authors discuss the criteria presently used for evaluating the efficiency of quantum teleportation schemes for continuous variables and show that a fidelity value larger than 2/3 warrants that the teleported state is the best possible remaining copy of the input state.
Abstract: We discuss the criteria presently used for evaluating the efficiency of quantum teleportation schemes for continuous variables. Using an argument based upon the difference between 1-to-2 quantum cloning (quantum duplication) and 1-to-infinity cloning (classical measurement), we show that a fidelity value larger than 2/3 warrants that the teleported state is the best possible remaining copy of the input state. This value has not been reached experimentally so far.
Abstract: We consider the problem of continuous quantum measurement of coherent oscillations between two quantum states of an individual two-state system. It is shown that the interplay between the information acquisition and the backaction dephasing of the oscillations by the detector imposes a fundamental limit, equal to four, on the signal-to-noise ratio of the measurement. The limit is universal, e.g., independent of the coupling strength between the detector and system, and results from the tendency of quantum measurement to localize the system in one of the measured eigenstates.
TL;DR: In this article, the authors define the information gain in a quantum measurement using the notion of Shannon information, which is a natural measure of our ignorance about properties of a system, which can be considered to preexist prior to and independent of observation.
Abstract: In a classical measurement the Shannon information is a natural measure of our ignorance about properties of a system. There, observation removes that ignorance in revealing properties of the system which can be considered to preexist prior to and independent of observation. Because of the completely different root of a quantum measurement as compared to a classical measurement, conceptual difficulties arise when we try to define the information gain in a quantum measurement using the notion of Shannon information. The reason is that, in contrast to classical measurements, quantum measurements, with very few exceptions, cannot be claimed to reveal a property of the individual quantum system existing before the measurement is performed.
TL;DR: In this paper, a measure of entanglement that explicitly takes into account the possibilty of double occupancies is introduced, which is a necessary and sufficient criterion for entangled states.
Abstract: Quantum gates that temporarily increase singlet-triplet splitting in order to swap electronic spins in coupled quantum dots lead inevitably to a finite double-occupancy probability for both dots. By solving the time-dependent Schr\"odinger equation for a coupled dot model, we demonstrate that this does not necessarily lead to quantum computation errors. Instead, the coupled dot ground state evolves quasiadiabatically for typical system parameters so that the double-occupancy probability at the completion of swapping is negligibly small. We introduce a measure of entanglement that explicitly takes into account the possibilty of double occupancies and provides a necessary and sufficient criterion for entangled states.
TL;DR: In this paper, the role of initial correlations between the open system and an environment on quantum dynamics of the open systems is analyzed and a general analysis of the role that initial correlations have on the quantum dynamics is presented.
Abstract: We present a general analysis of the role of initial correlations between the open system and an environment on quantum dynamics of the open system.
TL;DR: A new method for simulating quantum processes in the context of classical molecular dynamics simulations based on solving numerically the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories yields excellent agreement with exact quantum calculations.
Abstract: In this Letter, we present a new method for simulating quantum processes in the context of classical molecular dynamics simulations. The approach is based on solving numerically the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories. Quantum effects arise in this formulation as a breakdown of the statistical independence of the ensemble. New interaction forces between ensemble members are derived, which require the trajectory ensemble representing the state to evolve as an entangled, unified whole. The method is applied to the simulation of quantum tunneling in a one-dimensional model system, yielding excellent agreement with exact quantum calculations.
TL;DR: These steps, which start by discretizing Schrodinger’s equation, are described and a self-contained introduction to quantum computing algorithms from a new perspective is provided.
Abstract: The quantum search algorithm is a technique for searching N possibilities in only O(N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it; these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schrodinger’s equation. This paper also provides a self-contained introduction to quantum computing algorithms from a new perspective.
TL;DR: In this paper, the authors study the time evolution of correlation functions in closed quantum systems for nonequilibrium ensembles of initial conditions and show that generic time-reversal invariant evolutions approach equilibrium at large times.