Showing papers on "Open quantum system published in 2008"

The quantum internet

Abstract: Quantum networks provide opportunities and challenges across a range of intellectual and technical frontiers, including quantum computation, communication and metrology. The realization of quantum networks composed of many nodes and channels requires new scientific capabilities for generating and characterizing quantum coherence and entanglement. Fundamental to this endeavour are quantum interconnects, which convert quantum states from one physical system to those of another in a reversible manner. Such quantum connectivity in networks can be achieved by the optical interactions of single photons and atoms, allowing the distribution of entanglement across the network and the teleportation of quantum states between nodes.

Non-Abelian Anyons and Topological Quantum Computation

Abstract: Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{ u}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{ u}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Thermalization and its mechanism for generic isolated quantum systems

Abstract: It is demonstrated that an isolated generic quantum many-body system does relax to a state well described by the standard statistical mechanical prescription The thermalization happens at the level of individual eigenstates, allowing the computation of thermal averages from knowledge of any eigenstate in the microcanonical energy window An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive Recently, meaningful experimental studies1,2 of the problem have become possible, stimulating theoretical interest3,4,5,6,7 In generic isolated systems, non-equilibrium dynamics is expected8,9 to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible10 For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete11 Some recent studies4,5 even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems Here we demonstrate that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch12 and Srednicki13 A striking consequence of this eigenstate-thermalization scenario, confirmed for our system, is that knowledge of a single many-body eigenstate is sufficient to compute thermal averages—any eigenstate in the microcanonical energy window will do, because they all give the same result

Security of quantum key distribution

Abstract: Quantum Information Theory is an area of physics which studies both fundamental and applied issues in quantum mechanics from an information-theoretical viewpoint. The underlying techniques are, however, often restricted to the analysis of systems which satisfy a certain independence condition. For example, it is assumed that an experiment can be repeated independently many times or that a large physical system consists of many virtually independent parts. Unfortunately, such assumptions are not always justified. This is particularly the case for practical applications — e.g. in quantum cryptography — where parts of a system might have an arbitrary and unknown behavior. We propose an approach which allows us to study general physical systems for which the above mentioned independence condition does not necessarily hold. It is based on an extension of various information-theoretical notions. For example, we introduce new uncertainty measures, called smooth min- and max-entropy, which are generalizations of ...

Quantum discord for two-qubit systems

Abstract: Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.

Quantum states and phases in driven open quantum systems with cold atoms

Abstract: An open quantum system, the time evolution of which is governed by a master equation, can be driven into a given pure quantum state by an appropriate design of the coupling between the system and t ...

Wiring up quantum systems

Abstract: The emerging field of circuit quantum electrodynamics could pave the way for the design of practical quantum computers.

Class of quantum many-body states that can be efficiently simulated.

Abstract: We introduce the multiscale entanglement renormalization ansatz, a class of quantum many-body states on a D-dimensional lattice that can be efficiently simulated with a classical computer, in that the expectation value of local observables can be computed exactly and efficiently. The multiscale entanglement renormalization ansatz is equivalent to a quantum circuit of logarithmic depth that has a very characteristic causal structure. It is also the ansatz underlying entanglement renormalization, a novel coarse-graining scheme for many-body quantum systems on a lattice.

Using measurement-induced disturbance to characterize correlations as classical or quantum

Abstract: In contrast to the seminal entanglement-separability paradigm widely used in quantum information theory, we introduce a quantum-classical dichotomy in order to classify and quantify statistical correlations in bipartite states. This is based on the idea that while in the classical description of nature measurements can be carried out without disturbance, in the quantum description, generic measurements often disturb the system and the disturbance can be exploited to quantify the quantumness of correlations therein. It turns out that certain separable states still possess correlations of a quantum nature and indicates that quantum correlations are more general than entanglement. The results are illustrated in the Werner states and the isotropic states, and are applied to quantify the quantum advantage of the model of quantum computation proposed by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)].

Colloquium: Quantum annealing and analog quantum computation

Abstract: The recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations is reviewed here. The concept is introduced in successive steps through studying the mapping of such computationally hard problems to classical spin-glass problems, quantum spin-glass problems arising with the introduction of quantum fluctuations, and the annealing behavior of the systems as these fluctuations are reduced slowly to zero. This provides a general framework for realizing analog quantum computation.

Quantum optical metrology – the lowdown on high-N00N states

Abstract: Quantum states of light, such as squeezed states or entangled states, can be used to make measurements (metrology), produce images, and sense objects with a precision that far exceeds what is possible classically, and also exceeds what was once thought to be possible quantum mechanically. The primary idea is to exploit quantum effects to beat the shot-noise limit in metrology and the Rayleigh diffraction limit in imaging and sensing. Quantum optical metrology has received a boost in recent years with an influx of ideas from the rapidly evolving field of optical quantum information processing. Both areas of research exploit the creation and manipulation of quantum-entangled states of light. We will review some of the recent theoretical and experimental advances in this exciting new field of quantum optical metrology, focusing on examples that exploit a particular two-mode entangled photon state – the High-N00N state.

Simulating a quantum magnet with trapped ions

Abstract: To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We cannot translate quantum behaviour arising from superposition states or entanglement efficiently into the classical language of conventional computers. The solution to this problem, proposed in 1982 (ref. 1), is simulating the quantum behaviour of interest in a different quantum system where the interactions can be controlled and the outcome detected sufficiently well. Here we study the building blocks for simulating quantum spin Hamiltonians with trapped ions2. We experimentally simulate the adiabatic evolution of the smallest non-trivial spin system from paramagnetic into ferromagnetic order with a quantum magnetization for two spins of 98%. We prove that the transition is not driven by thermal fluctuations but is of quantum-mechanical origin (analogous to quantum fluctuations in quantum phase transitions3). We observe a final superposition state of the two degenerate spin configurations for the ferromagnetic order (|++> + |-->), corresponding to deterministic entanglement achieved with 88% fidelity. This method should allow for scaling to a higher number of coupled spins2, enabling implementation of simulations that are intractable on conventional computers.

Heralded generation of ultrafast single photons in pure quantum states

Abstract: We present an experimental demonstration of heralded single photons prepared in pure quantum states from a parametric down-conversion source. It is shown that, through controlling the modal structure of the photon pair emission, one can generate pairs in factorable states and thence eliminate the need for spectral filters in multiple-source interference schemes. Indistinguishable heralded photons were generated in two independent spectrally engineered sources and Hong-Ou-Mandel interference observed between them without spectral filters. The measured visibility of 94.4% sets a minimum bound on the mean photon purity.

Realization of quantum walks with negligible decoherence in waveguide lattices.

Abstract: Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks. Since waveguide lattices are easily constructed at large scales and display negligible decoherence, they can serve as an ideal and versatile experimental playground for the study of quantum walks and quantum algorithms. We experimentally observe quantum walks in large systems (similar to 100 sites) and confirm quantum walks effects which were studied theoretically, including ballistic propagation, disorder, and boundary related effects.

Robustness of key features of loop quantum cosmology

Abstract: A small simplification based on well-motivated approximations is shown to make loop quantum cosmology of the $k=0$ Friedman-Robertson-Walker model (with a massless scalar field) exactly soluble. Analytical methods are then used i) to show that the quantum bounce is generic; ii) to establish that the matter density has an absolute upper bound which, furthermore, equals the critical density that first emerged in numerical simulations and effective equations; iii) to bring out the precise sense in which the Wheeler-DeWitt theory approximates loop quantum cosmology and the sense in which this approximation fails; and iv) to show that discreteness underlying loop quantum cosmology is fundamental. Finally, the model is compared to analogous discussions in the literature and it is pointed out that some of their expectations do not survive a more careful examination. An effort has been made to make the underlying structure transparent also to those who are not familiar with details of loop quantum gravity.

Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system

Abstract: The field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems1,2,3, has gained new momentum by recent reports of quantum optical experiments with solid-state semiconducting4,5,6,7,8 and superconducting9,10,11 systems. In cavity QED, the observation of the vacuum Rabi mode splitting is used to investigate the nature of matter–light interaction at a quantum-mechanical level. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators12. It has been suggested that an observation of the scaling of the resonant atom–photon coupling strength in the Jaynes–Cummings energy ladder13 with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature14. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous spectroscopic evidence for the quantum nature of the resonant atom–field interaction in cavity QED. We explore atom–photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED set-up15, in which very strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high-quality on-chip microwave cavity. Circuit QED systems also provide a natural quantum interface between flying qubits (photons) and stationary qubits for applications in quantum information processing and communication16.

Quantum many-body phenomena in coupled cavity arrays

Abstract: The increasing level of experimental control over atomic and optical systems gained in the past years have paved the way for the exploration of new physical regimes in quantum optics and atomic physics, characterised by the appearance of quantum many-body phenomena, originally encountered only in condensed-matter physics, and the possibility of experimentally accessing them in a more controlled manner. In this review article we survey recent theoretical studies concerning the use of cavity quantum electrodynamics to create quantum many-body systems. Based on recent experimental progress in the fabrication of arrays of interacting micro-cavities and on their coupling to atomic-like structures in several different physical architectures, we review proposals on the realisation of paradigmatic many-body models in such systems, such as the Bose-Hubbard and the anisotropic Heisenberg models. Such arrays of coupled cavities offer interesting properties as simulators of quantum many-body physics, including the full addressability of individual sites and the accessibility of inhomogeneous models.

Observation of quantum-measurement backaction with an ultracold atomic gas

Abstract: Current research on micromechanical resonators strives for quantum-limited detection of the motion of macroscopic objects. Prerequisite to this goal is the observation of measurement backaction consistent with quantum metrology limits. However, thermal noise currently dominates measurements and precludes ground-state preparation of the resonator. Here, we establish the collective motion of an ultracold atomic gas confined tightly within a Fabry–Perot optical cavity as a system for investigating the quantum mechanics of macroscopic bodies. The cavity-mode structure selects a particular collective vibrational motion that is measured by the cavity’s optical properties, actuated by the cavity optical field and subject to backaction by the quantum force fluctuations of this field. Experimentally, we quantify such fluctuations by measuring the cavity-light-induced heating of the intracavity atomic ensemble. These measurements represent the first observation of backaction on a macroscopic mechanical resonator at the standard quantum limit. Nanoscale beams are one platform for exploring quantum-mechanical phenomena in ever-larger systems. The collective motion of a macroscopic ensemble of ultracold atoms confined in an optical cavity is established as an alternative approach.

Quantum State Engineering and Precision Metrology Using State-Insensitive Light Traps

Abstract: Precision metrology and quantum measurement often demand that matter be prepared in well-defined quantum states for both internal and external degrees of freedom. Laser-cooled neutral atoms localized in a deeply confining optical potential satisfy this requirement. With an appropriate choice of wavelength and polarization for the optical trap, two electronic states of an atom can experience the same trapping potential, permitting coherent control of electronic transitions independent of the atomic center-of-mass motion. Here, we review a number of recent experiments that use this approach to investigate precision quantum metrology for optical atomic clocks and coherent control of optical interactions of single atoms and photons within the context of cavity quantum electrodynamics. We also provide a brief survey of promising prospects for future work.

Quantum magnetism and criticality

Abstract: Quantum magnetism describes systems of magnetic spins in which quantum mechanical effects dominate, often in surprising ways. This review article covers phase transitions between these states, including quantum criticality and entangled electron states.

Solid-state quantum memory using the 31 P nuclear spin

Abstract: The transfer of information between the entities that do the processing and memory is crucial — and problematic — for quantum computation. In classical systems the information transfer can include a copying step, where errors can be spotted and corrected, but in quantum systems copying is fundamentally precluded. Morton et al. demonstrate a technology that could solve the problem: the coherent storage and readout of information between electron-spin processing elements and memory elements based on a nuclear spin. The system utilizes phosphorus-31 spin donors in a silicon-28 crystal. The nuclear spin acts as a memory element that can faithfully store the full state of the electron spin for more than a second, then transfer it back to the electron spin with about 90% efficiency. The transfer of information between processing entities and memory is crucial for quantum computation; it is challenging because the process must remain coherent at all times to preserve the quantum nature of the information. This paper demonstrates coherent storage and readout of information between electron-spin processing elements and memory elements based on a nuclear spin. The transfer of information between different physical forms—for example processing entities and memory—is a central theme in communication and computation. This is crucial in quantum computation1, where great effort2 must be taken to protect the integrity of a fragile quantum bit (qubit). However, transfer of quantum information is particularly challenging, as the process must remain coherent at all times to preserve the quantum nature of the information3. Here we demonstrate the coherent transfer of a superposition state in an electron-spin ‘processing’ qubit to a nuclear-spin ‘memory’ qubit, using a combination of microwave and radio-frequency pulses applied to 31P donors in an isotopically pure 28Si crystal4,5. The state is left in the nuclear spin on a timescale that is long compared with the electron decoherence time, and is then coherently transferred back to the electron spin, thus demonstrating the 31P nuclear spin as a solid-state quantum memory. The overall store–readout fidelity is about 90 per cent, with the loss attributed to imperfect rotations, and can be improved through the use of composite pulses6. The coherence lifetime of the quantum memory element at 5.5 K exceeds 1 s.

Experimentally testable state-independent quantum contextuality.

Abstract: We show that there are Bell-type inequalities for noncontextual theories that are violated by any quantum state. One of these inequalities between the correlations of compatible measurements is particularly suitable for testing this state-independent violation in an experiment.

Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach

Abstract: A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantu...

Quantum Process Tomography: Resource Analysis of Different Strategies

Abstract: Characterization of quantum dynamics is a fundamental problem in quantum physics and quantum-information science. Several methods are known which achieve this goal, namely standard quantum-process tomography (SQPT), ancilla-assisted process tomography, and the recently proposed scheme of direct characterization of quantum dynamics (DCQD). Here, we review these schemes and analyze them with respect to some of the physical resources they require. Although a reliable figure-of-merit for process characterization is not yet available, our analysis can provide a benchmark which is necessary for choosing the scheme that is the most appropriate in a given situation, with given resources. As a result, we conclude that for quantum systems where two-body interactions are not naturally available, SQPT is the most efficient scheme. However, for quantum systems with controllable two-body interactions, the DCQD scheme is more efficient than other known quantum-process tomography schemes in terms of the total number of required elementary quantum operations.

Nonequilibrium quantum field theory

Abstract: Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts and methodology are applied to current research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. Divided into five parts, with each part addressing a particular stage in the conceptual and technical development of the subject, this self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics.

Second law of thermodynamics with discrete quantum feedback control.

Abstract: A new thermodynamic inequality is derived which leads to the maximum work that can be extracted from multi-heat-baths with the assistance of discrete quantum feedback control. The maximum work is determined by the free-energy difference and a generalized mutual information content between the thermodynamic system and the feedback controller. This maximum work can exceed that in conventional thermodynamics and, in the case of a heat cycle with two heat baths, the heat efficiency can be greater than that of the Carnot cycle. The consistency of our results with the second law of thermodynamics is ensured by the fact that work is needed for information processing of the feedback controller.

Quantum Memory for Squeezed Light

Abstract: Introduction Memory for quantum states of light is a necessary component of quantum optical computers and is also required for the implementation of quantum repeaters [1] that would dramatically increase the range of quantum communication. There exists a variety of approaches to implementing quantum optical memory, for example off-resonant interaction of light with spin polarized atomic ensembles [2] and controlled reversible inhomogeneous broadening [3]. One of the most well-studied techniques is adiabatic transfer between optical quantum states and long-lived atomic superposition using electromagnetically induced transparency (EIT) [4]. This method, proposed in 2000 by Fleischhauer and Lukin [5], has been experimentally demonstrated in 2001 with classical light pulses [6]. In 2005, storage and retrieval of single photons, prepared using the Duan-Lukin-Cirac-Zoller

Quantum Circuit Architecture

Abstract: We present a method for optimizing quantum circuits architecture, based on the notion of a quantum comb, which describes a circuit board where one can insert variable subcircuits. Unexplored quantum processing tasks, such as cloning and storing or retrieving of gates, can be optimized, along with setups for tomography and discrimination or estimation of quantum circuits.

Transforming quantum operations: Quantum supermaps

Abstract: We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.