Showing papers on "Quantum state published in 2004"
TL;DR: In this article, the authors translate the TEBD algorithm into the language of matrix product states in order to both highlight and exploit its resemblances to the widely used density-matrix renormalization-group (DMRG) algorithms.
Abstract: An algorithm for the simulation of the evolution of slightly entangled quantum states has been recently proposed as a tool to study time-dependent phenomena in one-dimensional quantum systems. Its key feature is a time-evolving block-decimation (TEBD) procedure to identify and dynamically update the relevant, conveniently small, subregion of the otherwise exponentially large Hilbert space. Potential applications of the TEBD algorithm are the simulation of time-dependent Hamiltonians, transport in quantum systems far from equilibrium and dissipative quantum mechanics. In this paper we translate the TEBD algorithm into the language of matrix product states in order to both highlight and exploit its resemblances to the widely used density-matrix renormalization-group (DMRG) algorithms. The TEBD algorithm, being based on updating a matrix product state in time, is very accessible to the DMRG community and it can be enhanced by using well-known DMRG techniques, for instance in the event of good quantum numbers. More importantly, we show how it can be simply incorporated into existing DMRG implementations to produce a remarkably effective and versatile 'adaptive time-dependent DMRG' variant, that we also test and compare to previous proposals.
888 citations
TL;DR: In this article, a measure of non-classicality of quantum states based on the volume of the negative part of the Wigner function is proposed, and the authors analyse this quantity for Fock states and cat-like states defined as coherent superposition of two Gaussian wavepackets.
Abstract: A measure of non-classicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyse this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wavepackets.
637 citations
TL;DR: Direct experimental evidence for passive (or intrinsic) optical cooling of a micromechanical resonator is reported and cavity-induced photothermal pressure is exploited to quench the brownian vibrational fluctuations of a gold-coated silicon microlever from room temperature down to an effective temperature of 18 K.
Abstract: The prospect of realizing entangled quantum states between macroscopic objects and photons1 has recently stimulated interest in new laser-cooling schemes2,3. For example, laser-cooling of the vibrational modes of a mirror can be achieved by subjecting it to a radiation2 or photothermal4 pressure, actively controlled through a servo loop adjusted to oppose its brownian thermal motion within a preset frequency window. In contrast, atoms can be laser-cooled passively without such active feedback, because their random motion is intrinsically damped through their interaction with radiation5,6,7,8. Here we report direct experimental evidence for passive (or intrinsic) optical cooling of a micromechanical resonator. We exploit cavity-induced photothermal pressure to quench the brownian vibrational fluctuations of a gold-coated silicon microlever from room temperature down to an effective temperature of 18 K. Extending this method to optical-cavity-induced radiation pressure might enable the quantum limit to be attained, opening the way for experimental investigations of macroscopic quantum superposition states1 involving numbers of atoms of the order of 1014.
627 citations
TL;DR: Recent studies of semiconductor bilayer systems that provide clear evidence for exciton condensation in the quantum Hall regime are reviewed and why this phenomenon is as likely to occur in electron–electron bilayers as in electron-hole bilayers is explained.
Abstract: An exciton is the particle-like entity that forms when an electron is bound to a positively charged 'hole'. An ordered electronic state in which excitons condense into a single quantum state was proposed as a theoretical possibility many years ago. We review recent studies of semiconductor bilayer systems that provide clear evidence for this phenomenon and explain why exciton condensation in the quantum Hall regime, where these experiments were performed, is as likely to occur in electron–electron bilayers as in electron–hole bilayers. In current quantum Hall excitonic condensates, disorder induces mobile vortices that flow in response to a supercurrent and limit the extremely large bilayer counterflow conductivity.
605 citations
TL;DR: In this article, the authors translate the TEBD algorithm into the language of matrix product states in order to both highlight and exploit its resemblances to the widely used densitymatrix renormalization-group (DMRG) algorithms.
Abstract: An algorithm for the simulation of the evolution of slightly entangled quantum states has been recently proposed as a tool to study time-dependent phenomena in one-dimensional quantum systems. Its key feature is a time-evolving block-decimation (TEBD) procedure to identify and dynamically update the relevant, conveniently small subregion of the otherwise exponentially large Hilbert space. Potential applications of the TEBD algorithm are the simulation of time-dependent Hamiltonians, transport in quantum systems far from equilibrium and dissipative quantum mechanics.In this paper we translate the TEBD algorithm into the language of matrix product states in order to both highlight and exploit its resemblances to the widely used density-matrix renormalization-group (DMRG) algorithms. The TEBD algorithm being based on updating a matrix product state in time, it is very accessible to the DMRG community and it can be enhanced by using well-known DMRG techniques, for instance in the event of good quantum numbers. More importantly, we show how it can be simply incorporated into existing DMRG implementations to produce a remarkably effective and versatile ``adaptive time-dependent DMRG'' variant, that we also test and compare to previous proposals.
540 citations
TL;DR: The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half as mentioned in this paper, and the theoretical machinery of quantum wave packet construction leading to the existence of revivals and fractional revivals, in systems with one (or more) quantum number(s), as well as how information on the classical period and revival time is encoded in the energy eigenvalue spectrum.
489 citations
TL;DR: A multipartite protocol to securely distribute and reconstruct a quantum state encoded into a tripartite entangled state and distributed to three players in terms of fidelity, signal transfer, and reconstruction noise is demonstrated.
Abstract: We demonstrate a multipartite protocol to securely distribute and reconstruct a quantum state. A secret quantum state is encoded into a tripartite entangled state and distributed to three players. By collaborating, any two of the three players can reconstruct the state, while individual players obtain nothing. We characterize this (2,3) threshold quantum state sharing scheme in terms of fidelity, signal transfer, and reconstruction noise. We demonstrate a fidelity averaged over all reconstruction permutations of 0.73+/-0.04, a level achievable only using quantum resources.
461 citations
TL;DR: In this article, a measure of nonclassicality of quantum states based on the volume of the negative part of the Wigner function is proposed, and the authors analyze this quantity for Fock states, squeezed displaced Focks states and cat-like states defined as coherent superposition of two Gaussian wave packets.
Abstract: A measure of nonclassicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyze this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wave packets.
449 citations
TL;DR: In this paper, an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having $N$ elements.
Abstract: The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a $2N\ifmmode\times\else\texttimes\fi{}2N$ discrete phase space for a system with $N$ orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having $N$ elements. There exists such a field if and only if $N$ is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our $N\ifmmode\times\else\texttimes\fi{}N$ phase space also leads naturally to a method of constructing a complete set of $N+1$ mutually unbiased bases for the state space.
427 citations
TL;DR: In this article, the authors focus on electronic transport through semiconductor nanostructures which are driven by ac fields and give many examples which demonstrate the possibility of using appropriate ac fields to control/manipulate coherent quantum states.
422 citations
TL;DR: The localizable entanglement in familiar spin systems is analyzed and the results on the hand of the Ising spin model are illustrated, in which characteristic features for a quantum phase transition such as a divergingEntanglement length are observed.
Abstract: We consider pure quantum states of N>>1 spins or qubits and study the average entanglement that can be localized between two separated spins by performing local measurements on the other individual spins. We show that all classical correlation functions provide lower bounds to this localizable entanglement, which follows from the observation that classical correlations can always be increased by doing appropriate local measurements on the other qubits. We analyze the localizable entanglement in familiar spin systems and illustrate the results on the hand of the Ising spin model, in which we observe characteristic features for a quantum phase transition such as a diverging entanglement length.
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TL;DR: This work considers an approach to definition of a scheme with "history", valid for quantization both irreversible and reversible classical CA directly using local transition rules, using language of vectors in Hilbert spaces instead of C*-algebras.
Abstract: In recent work [quant-ph/0405174] by Schumacher and Werner was discussed an abstract algebraic approach to a model of reversible quantum cellular automata (CA) on a lattice. It was used special model of CA based on partitioning scheme and so there is a question about quantum CA derived from more general, standard model of classical CA. In present work is considered an approach to definition of a scheme with "history", valid for quantization both irreversible and reversible classical CA directly using local transition rules. It is used language of vectors in Hilbert spaces instead of C*-algebras, but results may be compared in some cases. Finally, the quantum lattice gases, quantum walk and "bots" are also discussed briefly.
TL;DR: In this paper, a factorization of finite quantum systems in terms of smaller subsystems, based on the Chinese remainder theorem, is studied, and the general formalism is applied to the case of angular momentum.
Abstract: Quantum systems with finite Hilbert space are considered, and phase-space methods like the Heisenberg–Weyl group, symplectic transformations and Wigner and Weyl functions are discussed. A factorization of such systems in terms of smaller subsystems, based on the Chinese remainder theorem, is studied. The general formalism is applied to the case of angular momentum. In this context, SU(2) coherent states are used for analytic representations. Links between the theory of finite quantum systems and other fields of research are discussed.
TL;DR: A general algebraic framework aimed to formalize the partition of a quantum system into subsystems and the emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are developed.
Abstract: It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements The emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are then relative and observable induced We develop a general algebraic framework aimed to formalize this concept
TL;DR: Two results are motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: a definetti theorem for quantum states and a de Fintti theorem forquantum operations.
Abstract: The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In this paper, we motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: Namely a de Finetti theorem for quantum states and a de Finetti theorem for quantum operations. The quantum-state theorem, in a closely analogous fashion to the original de Finetti theorem, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an "unknown quantum state" in quantum-state tomography. Similarly, the quantum-operation theorem gives an operational definition of an "unknown quantum operation" in quantum-process tomography. These results are especially important for a Bayesian interpretation of quantum mechanics, where quantum states and (at least some) quantum operations are taken to be states of belief rather than states of nature.
TL;DR: A lower bound for the concurrence of mixed bipartite quantum states is derived, valid in arbitrary dimensions, from a weaker, purely algebraic estimate, which detects mixed entangled states with a positive partial transpose.
Abstract: We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed entangled states with a positive partial transpose.
TL;DR: This work shows how to implement a mirror inversion of the state of theregister in each excitation subspace with respect to the center of the register to facilitate transfer of data in linear quantum registers.
Abstract: Transfer of data in linear quantum registers can be significantly simplified with preengineered but not dynamically controlled interqubit couplings. We show how to implement a mirror inversion of the state of the register in each excitation subspace with respect to the center of the register. Our construction is especially appealing as it requires no dynamical control over individual interqubit interactions. If, however, individual control of the interactions is available then the mirror inversion operation can be performed on any substring of qubits in the register. In this case, a sequence of mirror inversions can generate any permutation of a quantum state of the involved qubits.
TL;DR: There are (2n+1)-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from n/2 bits to n bits.
Abstract: We show that there exist bipartite quantum states which contain a large locked classical correlation that is unlocked by a disproportionately small amount of classical communication. In particular, there are (2n + 1)-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from n/2 bits to n bits. This phenomenon is impossible classically. However, states exhibiting this behavior need not be entangled. We study the range of states exhibiting this phenomenon and bound its magnitude.
TL;DR: Saturation spectroscopy demonstrates that the neutral exciton behaves as a two-level system and the remaining problem for manipulating excitonic quantum states in this system is spectral fluctuation on a mueV energy scale.
Abstract: We show how the optical properties of a single semiconductor quantum dot can be controlled with a small dc voltage applied to a gate electrode. We find that the transmission spectrum of the neutral exciton exhibits two narrow lines with approximately 2 mueV linewidth. The splitting into two linearly polarized components arises through an exchange interaction within the exciton. The exchange interaction can be turned off by choosing a gate voltage where the dot is occupied with an additional electron. Saturation spectroscopy demonstrates that the neutral exciton behaves as a two-level system. Our experiments show that the remaining problem for manipulating excitonic quantum states in this system is spectral fluctuation on a mueV energy scale.
TL;DR: In this paper, the authors formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability.
Abstract: Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability.
TL;DR: In this article, the quantum Hellinger distance and affinity on the space of probability densities were introduced and applied to characterizing entanglement and to establishing some unusual uncertainty relations relating nonsimultaneous measurements of a single observable in two different quantum states.
Abstract: By formally generalizing the classical Hellinger distance and affinity on the space of probability densities, we introduce their quantum analog on the quantum state space consisting of all density operators. We show that the infinitesimal form of the quantum Hellinger distance is the skew information introduced by Wigner and Yanase in 1963. We compare the Hellinger distance and affinity with the Bures distance and fidelity, and establish a variety of their fundamental properties. We further apply them to characterizing entanglement and to establishing some unusual uncertainty relations relating nonsimultaneous measurements of a single observable in two different quantum states.
TL;DR: This work describes a method for nonobliviously communicating a 2l-qubit quantum state by physically transmitting l+o(l) qubits, and by consuming l ebits of entanglement plus some shared random bits.
Abstract: We describe a method for nonobliviously communicating a 2l-qubit quantum state by physically transmitting l + o(l) qubits, and by consuming l ebits of entanglement plus some shared random bits. In the nonoblivious scenario, the sender has a classical description of the state to be communicated. Our method can be used to communicate states that are pure or entangled with the sender's system; l + o(l) and 3l + o(l) shared random bits are sufficient, respectively.
TL;DR: This work observes a continuous transition from a Kondo state exhibiting a single-peak Kondo resonance to another exhibiting a double peak by increasing the interdot coupling in a parallel-coupled DQD.
Abstract: Strong electron and spin correlations in a double quantum dot (DQD) can give rise to different quantum states. We observe a continuous transition from a Kondo state exhibiting a single-peak Kondo resonance to another exhibiting a double peak by increasing the interdot coupling (t) in a parallel-coupled DQD. The transition into the double-peak state provides evidence for spin entanglement between the excess electrons on each dot. Toward the transition, the peak splitting merges and becomes substantially smaller than t because of strong Coulomb effects. Our device tunability bodes well for future quantum computation applications.
TL;DR: In this paper, the authors studied the dynamics of a Heisenberg $XY$ spin chain with an unknown state coded into one qubit or a pair of entangled qubits, with the rest of the spins being in a polarized state.
Abstract: We study the dynamics of a Heisenberg $XY$ spin chain with an unknown state coded into one qubit or a pair of entangled qubits, with the rest of the spins being in a polarized state. The time evolution involves magnon excitations, and through them the entanglement is transported across the channel. For a large number of qubits, explicit formulas for the concurrences, measures for two-qubit entanglements, and the fidelity for recovering the state some distance away are calculated as functions of time. Initial states with an entangled pair of qubits show better fidelity, which takes its first maximum value at earlier times, compared to initial states with no entangled pair. In particular initial states with a pair of qubits in an unknown state $\ensuremath{\alpha}\ensuremath{\uparrow}\ensuremath{\uparrow}+\ensuremath{\beta}\ensuremath{\downarrow}\ensuremath{\downarrow}$ are best suited for quantum-state transport.
TL;DR: The concept of Localizable entanglement (LE) was introduced in this paper, where the authors consider systems of interacting spins and study the entanglements that can be localized, on average, between two separated spins by performing local measurements on the remaining spins.
Abstract: We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins This concept of Localizable Entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations For both spin-1/2 and spin-1 systems we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins The virtues of LE are illustrated for various spin models In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature
TL;DR: A technique that enables a strong, coherent coupling between isolated neutral atoms and mesoscopic conductors by exciting atoms trapped above the surface of a superconducting transmission line into Rydberg states with large electric dipole moments that induce voltage fluctuations in the transmission line is described.
Abstract: We describe a technique that enables a strong, coherent coupling between isolated neutral atoms and mesoscopic conductors. The coupling is achieved by exciting atoms trapped above the surface of a superconducting transmission line into Rydberg states with large electric dipole moments that induce voltage fluctuations in the transmission line. Using a mechanism analogous to cavity quantum electrodynamics, an atomic state can be transferred to a long-lived mode of the fluctuating voltage, atoms separated by millimeters can be entangled, or the quantum state of a solid-state device can be mapped onto atomic or photonic states.
TL;DR: The concept of the dynamical matrix and the Jamiołkowski isomorphism are explored and an analogous relation is established between the classical maps and an extended space of the discrete probability distributions.
Abstract: We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations, determined by unitary matrices of extended dimensionality, is defined and analyzed. Using the concept of the dynamical matrix and the Jamiolkowski isomorphism we explore the relation between the set of quantum operations (dynamics) and the set of density matrices acting on an extended Hilbert space (kinematics). An analogous relation is established between the classical maps and an extended space of the discrete probability distributions.
TL;DR: In this tutorial review the power of the POVM concept is illustrated on examples relevant to applications in quantum cryptography, including generalized measurements (POVMs) in the Appendices.
Abstract: The problem of discriminating among given nonorthogonal quantum states is underlying many of the schemes that have been suggested for quantum communication and quantum computing. However, quantum mechanics puts severe limitations on our ability to determine the state of a quantum system. In particular, nonorthogonal states cannot be discriminated perfectly, even if they are known, and various strategies for optimum discrimination with respect to some appropriately chosen criteria have been developed. In this article we review recent theoretical progress regarding the two most important optimum discrimination strategies. We also give a detailed introduction with emphasis on the relevant concepts of the quantum theory of measurement. After a brief introduction into the field, the second chapter deals with optimum unambiguous, i. e error-free, discrimination. Ambiguous discrimination with minimum error is the subject of the third chapter. The fourth chapter is devoted to an overview of the recently emerging subfield of discriminating multiparticle states. We conclude with a brief outlook where we attempt to outline directions of research for the immediate future.
TL;DR: In this article, the authors present a review of the theoretical issues and numerical techniques used to describe dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices, from mean-field models to classical and quantum simulations for equilibrium and dynamical properties.
TL;DR: It is shown that an i phi(3) quantum field theory is a physically acceptable model because the spectrum is positive and the theory is unitary.
Abstract: In this Letter it is shown that an i phi(3) quantum field theory is a physically acceptable model because the spectrum is positive and the theory is unitary. The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.