Showing papers on "Quantum state published in 2003"
TL;DR: In this article, the authors review several ideas indicating how such techniques can be used for accurate manipulation of quantum states of atomic ensembles and photons and present possible mechanisms for manipulating the quantum states.
Abstract: Modern optical techniques allow one to accurately control light using atoms and to manipulate atoms using light. In this Colloquium the author reviews several ideas indicating how such techniques can be used for accurate manipulation of quantum states of atomic ensembles and photons. First a technique is discussed that allows one to transfer quantum states between light fields and metastable states of matter. The technique is based on trapping quantum states of photons in coherently driven atomic media, in which the group velocity is adiabatically reduced to zero. Next, possible mechanisms are outlined for manipulating quantum states of atomic ensembles. Specifically, a ``dipole blockade'' technique is considered in which optical excitation of mesoscopic samples into Rydberg states can be used to control the state of ensembles at the level of individual quanta. It is also noted that even simple processes involving atom-photon correlations can be used to effectively manipulate the ensemble states. Potentially these techniques can be used for implementation of important concepts from quantum information science.
959 citations
TL;DR: A capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of Verdu-Han (1994) which are based on the so-called information-spectrum method.
Abstract: The capacity of a classical-quantum channel (or, in other words, the classical capacity of a quantum channel) is considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a channel. A capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of Verdu-Han (1994) which are based on the so-called information-spectrum method. The general results are applied to the stationary memoryless case with or without cost constraint on inputs, whereby a deep relation between the channel coding theory and the hypothesis testing for two quantum states is elucidated.
398 citations
TL;DR: It is demonstrated that the statistical idea underlying the skew information is the Fisher information in the theory of statistical estimation, and a quantum Cramér-Rao inequality and a new uncertainty relation are established, which shed considerable new light on the relationships between quantum measurement and statistical inference.
Abstract: The Wigner-Araki-Yanase theorem puts a limitation on the measurement of observables in the presence of a conserved quantity, and the notion of Wigner-Yanase skew information quantifies the amount of information on the values of observables not commuting with the conserved quantity. We demonstrate that the statistical idea underlying the skew information is the Fisher information in the theory of statistical estimation. A quantum Cramer-Rao inequality and a new uncertainty relation in terms of the skew information are established, which shed considerable new light on the relationships between quantum measurement and statistical inference. The result is applied to estimating the evolution speed of quantum states.
311 citations
TL;DR: This finding is significant because it shows that entanglement, rather than energy-level redistribution, can underlie the magnetic behaviour of a simple insulating quantum spin system.
Abstract: Free magnetic moments usually manifest themselves in Curie laws, where weak external magnetic fields produce magnetizations that vary as the reciprocal of the temperature (1/T). For a variety of materials that do not display static magnetism, including doped semiconductors and certain rare-earth intermetallics, the 1/T law is replaced by a power law T^-α with α < 1. Here we show that a much simpler material system—namely, the insulating magnetic salt LiHo_xY_(1-x)F_4—can also display such a power law. Moreover, by comparing the results of numerical simulations of this system with susceptibility and specific-heat data, we show that both energy-level splitting and quantum entanglement are crucial to describing its behaviour. The second of these quantum mechanical effects—entanglement, where the wavefunction of a system with several degrees of freedom cannot be written as a product of wavefunctions for each degree of freedom—becomes visible for remarkably small tunnelling terms, and is activated well before tunnelling has visible effects on the spectrum. This finding is significant because it shows that entanglement, rather than energy-level redistribution, can underlie the magnetic behaviour of a simple insulating quantum spin system.
310 citations
TL;DR: In this article, the authors study the role of entanglement among subsystems in speeding up the dynamics of a composite system and establish the minimum time it takes for an initial state of mean energy E and energy spread E to move from its initial configuration by a predetermined amount.
Abstract: We establish the minimum time it takes for an initial state of mean energy E and energy spread $\ensuremath{\Delta}E$ to move from its initial configuration by a predetermined amount. Distances in Hilbert space are estimated by the fidelity between the initial and final states. In this context, we study the role of entanglement among subsystems in speeding up the dynamics of a composite system.
305 citations
Posted Content•
TL;DR: In this article, an expression characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel was derived, generalizing both the classical and the quantum capacities of the channel.
Abstract: An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel, generalizing both the classical and quantum capacities of the channel. Although our formula involves regularization, i.e. taking a limit over many copies of the channel, it reduces to a single-letter expression in the case of generalized dephasing channels. Analogous formulae are conjectured for the simultaneous public-private capacity of a quantum channel and for the simultaneously 1-way distillable common randomness and entanglement of a bipartite quantum state.
285 citations
TL;DR: In this article, a scheme for transferring quantum states from the propagating light fields to macroscopic, collective vibrational degree of freedom of a massive mirror by exploiting radiation pressure effects was proposed.
Abstract: We propose a scheme for transferring quantum states from the propagating light fields to macroscopic, collective vibrational degree of freedom of a massive mirror by exploiting radiation pressure effects. This scheme may prepare an Einstein-Podolsky-Rosen state in position and momentum of a pair of distantly separated movable mirrors by utilizing the entangled light fields produced from a nondegenerate optical parametric amplifier.
278 citations
TL;DR: In this paper, the lowest stationary quantum state of neutrons in the Earth's gravitational field is identified in the measurement of neutron transmission between a horizontal mirror on the bottom and an absorber/scatterer on top.
Abstract: The lowest stationary quantum state of neutrons in the Earth's gravitational field is identified in the measurement of neutron transmission between a horizontal mirror on the bottom and an absorber/scatterer on top. Such an assembly is not transparent for neutrons if the absorber height is smaller than the ``height'' of the lowest quantum state.
246 citations
TL;DR: In this article, the concept of quantum spiral bandwidth of the spatial mode function of the two-photon entangled state generated in spontaneous parametric down-conversion was proposed and its dependence with the length of the downconverting crystals and waist of the pump beam was revealed.
Abstract: We put forward the concept of quantum spiral bandwidth of the spatial mode function of the two-photon entangled state generated in spontaneous parametric down-conversion. We obtain the bandwidth using the eigenstates of the orbital angular momentum of the biphoton states, and reveal its dependence with the length of the down-converting crystals and waist of the pump beam. The connection between the quantum spiral bandwidth and the entropy of entanglement of the quantum state is discussed.
210 citations
TL;DR: In this paper, the authors investigated the condition of equality in the monotonicity theorem and its consequences as the strong sub-additivity of von Neumann entropy, the Golden-Thompson trace inequality and the Monotonicity of the Holevo quantitity.
Abstract: Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences as the strong sub-additivity of von Neumann entropy, the Golden–Thompson trace inequality and the monotonicity of the Holevo quantitity. The relation to quantum Markov states is briefly indicated.
188 citations
TL;DR: This work obtains a nonunitary (‘star unitary’), invertible, nondistributive operator Λ (which reduces to the unitary transformation operator U for integrable systems), and shows that irreversible processes and entropy production correspond to irreversible processes creating entropy.
Abstract: Chemical reactions correspond to irreversible processes creating entropy. Chemistry belongs to the class of nonintegrable Poincare systems. In general, chemistry is associated with resonances-transitions of quantum states. We have studied some very simple examples of such processes, like decay of an unstable state, in detail. (In such cases, there are always multiple time scales.) We obtain a nonunitary ("star unitary"), invertible, nondistributive operator A (which reduces to the unitary transformation operator U for integrable systems). The explicit form of A depends on the interaction of each species with all other types of molecules in the system including the solvent. The basic property that results from A is that the fundamental description of nonintegrable systems is no longer in terms of Hamiltonian equations, but in terms of kinetic equations with broken time symmetry. Once we have the kinetic equations, it is easy to show that we have irreversible processes and entropy production.
TL;DR: This work considers the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states, represented by a set of density operators, and shows that the design of the optimal detector can be formulated as a semidefinite programming problem.
Abstract: We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states, represented by a set of density operators. We show that the design of the optimal detector can be formulated as a semidefinite programming problem. Based on this formulation, we derive a set of necessary and sufficient conditions for an optimal quantum measurement. We then show that the optimal measurement can be found by solving a standard (convex) semidefinite program. By exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum, the optimal measurement can be computed very efficiently in polynomial time within any desired accuracy. Using the semidefinite programming formulation, we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator. In particular, if the quantum state ensemble is a pure-state ensemble consisting of (not necessarily independent) rank-one density operators, then we show that the optimal measurement is a pure-state measurement consisting of rank-one measurement operators.
TL;DR: It is found that Aharonov-Anandan phases play the role of classical canonical actions and are conserved in the adiabatic evolution of noneigenstates.
Abstract: We investigate adiabatic evolution of quantum states as governed by the nonlinear Schrodinger equation and provide examples of applications with a nonlinear tunneling model for Bose-Einstein condensates. Our analysis not only spells out conditions for adiabatic evolution of eigenstates but also characterizes the motion of noneigenstates which cannot be obtained from the former in the absence of the superposition principle. We find that Aharonov-Anandan phases play the role of classical canonical actions and are conserved in the adiabatic evolution of noneigenstates.
TL;DR: In this article, the volume of the convex (N 2 − 1)-dimensional set N of density matrices of size N with respect to the Hilbert-Schmidt measure is computed and the hyper-area of the boundary of this set is also found and its ratio to the volume provides information about the structure of N.
Abstract: We compute the volume of the convex (N2 − 1)-dimensional set N of density matrices of size N with respect to the Hilbert–Schmidt measure. The hyper-area of the boundary of this set is also found and its ratio to the volume provides information about the structure of N. Similar investigations are also performed for the smaller set of all real density matrices. As an intermediate step, we analyse volumes of the unitary and orthogonal groups and of the flag manifolds.
TL;DR: In this paper, a scheme for probabilistic and controlled teleportation of the unknown quantum states of both one-particle and twoparticle is proposed, in which the teleportation is not always successful but with certain probability.
TL;DR: It is observed that a mesoscopic field made of several tens of microwave photons exhibits quantum features when interacting with a single Rydberg atom in a high-Q cavity, opening the way to studies of large quantum state superpositions at the quantum-classical boundary.
Abstract: We observe that a mesoscopic field made of several tens of microwave photons exhibits quantum features when interacting with a single Rydberg atom in a high-Q cavity. The field is split into two components whose phases differ by an angle inversely proportional to the square root of the average photon number. The field and the atomic dipole are phase entangled. These manifestations of photon graininess vanish at the classical limit. This experiment opens the way to studies of large quantum state superpositions at the quantum-classical boundary.
TL;DR: In this article, an experimental quantum key distribution that utilizes pulsed homodyne detection, instead of photon counting, to detect weak pulses of coherent light is presented. But the scheme inherently has a finite error rate, and it cannot be used for high-efficiency detection and quantum state measurement.
Abstract: We report an experimental quantum key distribution that utilizes pulsed homodyne detection, instead of photon counting, to detect weak pulses of coherent light. Although our scheme inherently has a finite error rate, homodyne detection allows high-efficiency detection and quantum state measurement of the transmitted light using only conventional devices at room temperature. Our prototype system works at $1.55\ensuremath{\mu}\mathrm{m}$ wavelength and the quantum channel is a 1-km standard optical fiber. The probability distribution of the measured electric-field amplitude has a Gaussian shape. The effect of experimental imperfections such as optical loss and detector noise can be parametrized by the variance and the mean value of the Gaussian distribution.
TL;DR: Coherent quantum bit operations along with quantum state transport open the route towards a "quantum shift register" of individual neutral atoms, which preserves the atomic coherence with slight reduction of coherence time.
Abstract: We have prepared and detected quantum coherences of trapped cesium atoms with long dephasing times. Controlled transport by an "optical conveyor belt" over macroscopic distances preserves the atomic coherence with slight reduction of coherence time. The limiting dephasing effects are experimentally identified, and we present an analytical model of the reversible and irreversible dephasing mechanisms. Our experimental methods are applicable at the single-atom level. Coherent quantum bit operations along with quantum state transport open the route towards a "quantum shift register" of individual neutral atoms.
TL;DR: A formula for the triple resource trade-offs is presented that reduces its calculation to evaluating the data compression trade-off formula and also constructs protocols achieving all the optimal points.
Abstract: We consider the problem of communicating quantum states by simultaneously making use of a noiseless classical channel, a noiseless quantum channel, and shared entanglement. We specifically study the version of the problem in which the sender is given knowledge of the state to be communicated. In this setting, a trade-off arises between the three resources, some portions of which have been investigated previously in the contexts of the quantum-classical trade-off in data compression, remote state preparation, and superdense coding of quantum states, each of which amounts to allowing just two out of these three resources. We present a formula for the triple resource trade-off that reduces its calculation to evaluating the data compression trade-off formula. In the process, we also construct protocols achieving all the optimal points. These turn out to be achievable by trade-off coding and suitable time sharing between optimal protocols for cases involving two resources out of the three mentioned above.
TL;DR: The problem of unambiguous discrimination between a set of linearly independent pure quantum states is considered and the design of the optimal measurement that minimizes the probability of an inconclusive result can be formulated as a semidefinite programming problem.
Abstract: We consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can be formulated as a semidefinite programming problem. Based on this formulation, we develop a set of necessary and sufficient conditions for an optimal quantum measurement. We show that the optimal measurement can be computed very efficiently in polynomial time by exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum. Using the general conditions for optimality, we derive necessary and sufficient conditions so that the measurement that results in an equal probability of an inconclusive result for each one of the quantum states is optimal. We refer to this measurement as the equal-probability measurement (EPM). We then show that for any state set, the prior probabilities of the states can be chosen such that the EPM is optimal. Finally, we consider state sets with strong symmetry properties and equal prior probabilities for which the EPM is optimal. We first consider geometrically uniform (GU) state sets that are defined over a group of unitary matrices and are generated by a single generating vector. We then consider compound GU state sets which are generated by a group of unitary matrices using multiple generating vectors, where the generating vectors satisfy a certain (weighted) norm constraint.
TL;DR: In this paper, a protocol for teleporting an unknown coherent-state superposition within a network consisting of n parties with an arbitrary positive integer is proposed, and the probability of success is shown to be 50%.
Abstract: We propose a protocol for teleporting an unknown coherent-state superposition within a network consisting of ${2}^{N}$ parties with N an arbitrary positive integer. We show explicitly that for moderate and high intensity fields the probability of success is 50%, i.e. the same as in the case of $N=1.$
TL;DR: In this article, the Wigner-Yanase information has been used to give explicit formulas for the geodesic distance and scalar curvatures associated with this metric, and it is shown that this is the only monotone metric for which such an approach is possible.
Abstract: In the search of appropriate Riemannian metrics on quantum state space, the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by Petz. All the elements of this family of geometries can be seen as quantum analogs of Fisher information. Although there exists a number of general theorems shedding light on this subject, many natural questions, also stemming from applications, are still open. In this paper we discuss a particular member of the family, the Wigner–Yanase information. Using a well-known approach that mimics the classical pull-back approach to Fisher information, we are able to give explicit formulas for the geodesic distance, the geodesic path, the sectional and scalar curvatures associated to Wigner–Yanase information. Moreover, we show that this is the only monotone metric for which such an approach is possible.
15 Sep 2003
TL;DR: A single-letter formula for the optimal tradeoff between the extracted common randomness and classical communication rate is obtained for the special case of classical-quantum correlations.
Abstract: The problem of converting noisy quantum correlations between two parties into noiseless classical ones using a limited amount of one-way classical communication is addressed. A single-letter formula for the optimal tradeoff between the extracted common randomness and classical communication rate is obtained for the special case of classical-quantum correlations. The resulting curve is intimately related to the quantum compression with classical side information tradeoff curve Q/sup */(R) of Hayden, Jozsa, and Winter. For a general initial state, we obtain a similar result, with a single-letter formula, when we impose a tensor product restriction on the measurements performed by the sender; without this restriction, the tradeoff is given by the regularization of this function. Of particular interest is a quantity we call "distillable common randomness" of a state: the maximum overhead of the common randomness over the one-way classical communication if the latter is unbounded. It is an operational measure of (total) correlation in a quantum state. For classical-quantum correlations it is given by the Holevo mutual information of its associated ensemble; for pure states it is the entropy of entanglement. In general, it is given by an optimization problem over measurements and regularization; for the case of separable states we show that this can be single-letterized.
TL;DR: In this paper, the authors investigated the effects of decoherence on a quantum game, namely the prisoner dilemma, through three prototype decoding channels, and showed that the Nash equilibria are not changed by the effects for maximally entangled states.
TL;DR: In this article, it was shown that deviations of the quantum state of the inflaton from the thermal vacuum of inflation may leave an imprint in the CMB anisotropies.
Abstract: We show that deviations of the quantum state of the inflaton from the thermal vacuum of inflation may leave an imprint in the CMB anisotropies. The quantum dynamics of the inflaton in such a state produces corrections to the inflationary fluctuations, which may be observable. Because these effects originate from IR physics below the Planck scale, they will dominate over any trans-Planckian imprints in any theory which obeys decoupling. Inflation sweeps away these initial deviations and forces its quantum state closer to the thermal vacuum. We view this as the quantum version of the cosmic no-hair theorem. Such imprints in the CMB may be a useful, independent test of the duration of inflation, or of significant features in the inflaton potential about 60 e-folds before inflation ended, instead of an unlikely discovery of the signatures of quantum gravity. The absence of any such substructure would suggest that inflation lasted uninterrupted much longer than ${\cal O}(100)$ e-folds.
TL;DR: In this article, an isolated, perfectly reflecting, mirror illuminated by an intense laser pulse is studied and the resulting radiation pressure efficiently entangles a mirror vibrational mode with the two reflected optical sideband modes of the incident carrier beam.
Abstract: We study an isolated, perfectly reflecting, mirror illuminated by an intense laser pulse. We show that the resulting radiation pressure efficiently entangles a mirror vibrational mode with the two reflected optical sideband modes of the incident carrier beam. The entanglement of the resulting three-mode state is studied in detail and it is shown to be robust against the mirror mode temperature. We then show how this continuous-variable entanglement can be profitably used to teleport an unknown quantum state of an optical mode onto the vibrational mode of the mirror.
TL;DR: In this article, the authors demonstrate the feasibility of coupling multiple solid-state qubits, and indicate the existence of entangled two-qubit states, and demonstrate a Josephson circuit consisting of two coupled charge qubits.
Abstract: A practical quantum computer, if built, would consist of a set of coupled two-level quantum systems (qubits). Among the variety of qubits implemented, solid-state qubits are of particular interest because of their potential suitability for integrated devices. A variety of qubits based on Josephson junctions have been implemented; these exploit the coherence of Cooper-pair tunnelling in the superconducting state. Despite apparent progress in the implementation of individual solid-state qubits, there have been no experimental reports of multiple qubit gates--a basic requirement for building a real quantum computer. Here we demonstrate a Josephson circuit consisting of two coupled charge qubits. Using a pulse technique, we coherently mix quantum states and observe quantum oscillations, the spectrum of which reflects interaction between the qubits. Our results demonstrate the feasibility of coupling multiple solid-state qubits, and indicate the existence of entangled two-qubit states.
TL;DR: In this paper, it is shown how to map the quantum states of a system of free Bose particles one-to-one onto the states of the complete deterministic model.
Abstract: It is shown how to map the quantum states of a system of free Bose particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group.
TL;DR: In this paper, a general local control theory for manipulating quantum system dynamics is developed, which is based on the realization of monotonous increasing condition of the performance index which is locally (in time domain) defined to major how the present quantum state satisfies the current objective.
Abstract: A general local control theory for manipulating quantum system dynamics is developed. Basic concept of the present theory is lying in the realization of monotonous increasing condition of the performance index, which is locally (in time domain) defined to major how the present quantum state satisfies the current objective. The local control field is designed to satisfy the above condition taking into account the equation of motion of the system. It is found, through the formulation, that the monotonous increasing condition can be achieved as long as the performance index is given as a function of expectation values of time-dependent observable operators, whose equation of motion is governed by the field-free system Hamiltonian or Liouvillian. It is also shown that the present theory is a generalization of the local optimization approach which has been successfully applied to many of molecular dynamics control problems. As for the special cases, performance indices for “transition path control,” “population distribution control,” and “wave packet shaping” are proposed. The theory is applied to vibrational control problems of the one-dimensional model system of hydrogen fluoride. The results show that the present method works effectively for the population dynamics control as well as the wave packet shaping.
TL;DR: In this paper, the quantitative description of the quantum entanglement between a qubit and its environment is consid-ered by a numerical renormalization group treatment of the related anisotropic Kondomodel.
Abstract: Department of Physics, University of Queensland, Brisbane 4072, Australia~Received 7 February 2003; published 5 September 2003!The quantitative description of the quantum entanglement between a qubit and its environment is consid-ered. Specifically, for the ground state of the spin-boson model, the entropy of entanglement of the spin iscalculated as a function of a, the strength of the ohmic coupling to the environment, and «, the levelasymmetry. This is done by a numerical renormalization group treatment of the related anisotropic Kondomodel. For «50, the entanglement increases monotonically with a, until it becomes maximal for a