Showing papers in "Physical Review A in 2001"
TL;DR: In this paper, the theory underpinning the measurement of density matrices of a pair of quantum two-level systems is described, and a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation.
Abstract: We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems ~‘‘qubits’’ !. Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction ~in which the density matrix is linearly related to a set of measured quantities ! and a maximum likelihood technique which requires numerical optimization ~but has the advantage of producing density matrices that are always non-negative definite!. In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.
1,838 citations
TL;DR: In this paper, error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables to protect encoded quantum information against shifts in the amplitude or phase of a d-state system.
Abstract: Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.
1,140 citations
TL;DR: In this paper, the authors generalized the spin-flip superoperator to a universal inverter, which acts on quantum systems of arbitrary dimension and introduced the corresponding generalized concurrence for joint pure states of D-1 X D-2 bipartite quantum systems.
Abstract: Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters's concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a universal inverter, which acts on quantum systems of arbitrary dimension, and we introduce the corresponding generalized concurrence for joint pure states of D-1 X D-2 bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. The universal inverter, which is a positive, but not completely positive superoperator, is closely related to the completely positive universal-NOT superoperator, the quantum analogue of a classical NOT gate. We present a physical realization of the universal-NOT Superoperator.
721 citations
TL;DR: In this paper, the authors studied the design of pulse sequences for nuclear magnetic resonance spectroscopy as a problem of time optimal control of the unitary propagator, and gave an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems.
Abstract: In this paper, we study the design of pulse sequences for nuclear magnetic resonance spectroscopy as a problem of time optimal control of the unitary propagator. Radio-frequency pulses are used in coherent spectroscopy to implement a unitary transfer between states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group. What is the minimum time required to steer the system from some initial point to a specified final point? In nuclear magnetic resonance (NMR) spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two-spin system.
660 citations
TL;DR: In this paper, thermal entanglement in the two-qubit isotropic model with a magnetic field and in the anisotropic model with both ferromagnetic and antiferromagnetic cases was investigated.
Abstract: We study the entanglement in the quantum Heisenberg $\mathrm{XY}$ model in which the so-called W entangled states can be generated for 3 or 4 qubits. By the concept of concurrence, we study the entanglement in the time evolution of the $\mathrm{XY}$ model. We investigate the thermal entanglement in the two-qubit isotropic $\mathrm{XY}$ model with a magnetic field and in the anisotropic $\mathrm{XY}$ model, and find that the thermal entanglement exists for both ferromagnetic and antiferromagnetic cases. Some evidences of the quantum phase transition also appear in these simple models.
509 citations
TL;DR: In this paper, a general upper bound on the quantum capacity of a one-mode Gaussian channel with attenuation or amplification and classical noise was derived. But the bounds were not explicitly evaluated for the case of a single-mode channel.
Abstract: We show how to compute or at least to estimate various capacity-related quantities for bosonic Gaussian channels. Among these are the coherent information, the entanglement-assisted classical capacity, the one-shot classical capacity, and a quantity involving the transpose operation, shown to be a general upper bound on the quantum capacity, even allowing for finite errors. All bounds are explicitly evaluated for the case of a one-mode channel with attenuation or amplification and classical noise.
476 citations
TL;DR: In this paper, a set of independent Bell-correlation inequalities for n-partite systems with two dichotomic observables each were constructed, which are complete in the sense that the inequalities are satisfied if and only if the correlations considered allow a local classical model.
Abstract: We construct a set of ${2}^{{2}^{n}}$ independent Bell-correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are satisfied if and only if the correlations considered allow a local classical model. All these inequalities can be summarized in a single, albeit nonlinear inequality. We show that quantum correlations satisfy this condition provided the state has positive partial transpose with respect to any grouping of the n systems into two subsystems. We also provide an efficient algorithm for finding the maximal quantum-mechanical violation of each inequality, and show that the maximum is always attained for the generalized GHZ state.
464 citations
TL;DR: In this article, the authors show how to simplify the computation of the entanglement of formation and the relative entropy for states, which are invariant under a group of local symmetries.
Abstract: We show how to simplify the computation of the entanglement of formation and the relative entropy of entanglement for states, which are invariant under a group of local symmetries. For several examples of groups we characterize the state spaces, which are invariant under these groups. For specific examples we calculate the entanglement measures. In particular, we derive an explicit formula for the entanglement of formation for $(U\ensuremath{\bigotimes}U)$-invariant states, and we find a counterexample of the additivity conjecture for the relative entropy of entanglement.
456 citations
TL;DR: In this article, the decoherence properties of Schrodinger cat states were discussed and a simple protocol that teleports one qubit encoded in Schroda cat states was proposed.
Abstract: When a superposition $(|\ensuremath{\alpha}〉\ensuremath{-}|\ensuremath{-}\ensuremath{\alpha}〉)$ of two coherent states with opposite phase falls upon a 50-50 beam splitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of \ensuremath{\alpha}, as was recently discovered by Hirota and Sasaki [LANL e-print quant-ph/0101018]. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schr\"odinger cat states.
452 citations
TL;DR: In this article, the dynamics of an optical mode in a cavity with a movable mirror subject to quantum Brownian motion was studied, and the phase-noise power spectrum of the output light was described using the quantum Langevin approach.
Abstract: We study the dynamics of an optical mode in a cavity with a movable mirror subject to quantum Brownian motion. We study the phase-noise power spectrum of the output light, and we describe the mirror Brownian motion, which is responsible for the thermal-noise contribution, using the quantum Langevin approach. We show that the standard quantum Langevin equations, supplemented with the appropriate non-Markovian correlation functions, provide an adequate description of Brownian motion.
435 citations
TL;DR: In this article, it was shown that the frequency and space-time correlations of photon pairs generated in the process of spontaneous parametric downconversion possess undesired distinguishing information and that these correlations may be eliminated if certain conditions in the source configuration are satisfied.
Abstract: Multiphoton states constructed from photon pairs generated in the process of spontaneous parametric downconversion possess frequency and space-time correlations that may carry undesired distinguishing information. It is shown that these correlations may be eliminated if certain conditions in the source configuration are satisfied. For the cases in which these conditions cannot be satisfied because of experimental constraints, it is shown that the correlations may be reduced through proper choices of crystal length and pump bandwidth. The advantage of such source engineering is that it yields much higher count rates, since no photon pairs are lost by predetection spectral filtering.
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.
TL;DR: In this article, a necessary and sufficient condition for the existence of decoherence-free (noiseless) subsystems in the Markovian regime is derived for the first time, and a stabilizer formalism for DFSs is developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes.
Abstract: Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of decoherence-free (noiseless) subsystems in the Markovian regime is derived here for the first time. A stabilizer formalism for DFSs is then developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes. Conditions for the existence of Hamiltonians whose induced evolution always preserves a DFS are derived within this stabilizer formalism. Two possible collective decoherence mechanisms arising from permutation symmetries of the system-bath coupling are examined within this framework. It is shown that in both cases universal quantum computation which always preserves the DFS (natural fault-tolerant computation) can be performed using only two-body interactions. This is in marked contrast to standard error correcting codes, where all known constructions using one- or two-body interactions must leave the code space during the on-time of the fault-tolerant gates. A further consequence of our universality construction is that a single exchange Hamiltonian can be used to perform universal quantum computation on an encoded space whose asymptotic coding efficiency is unity. The exchange Hamiltonian, which is naturally present in many quantum systems, is thus asymptotically universal.
TL;DR: In this paper, a simple closed-form analytical expression for ionization rate as a function of instantaneous laser phase was obtained for arbitrary values of the Keldysh parameter within the usual strong-field approximation.
Abstract: We obtain a simple closed-form analytical expression for ionization rate as a function of instantaneous laser phase $\ensuremath{\varphi}(t),$ for arbitrary values of the Keldysh parameter $\ensuremath{\gamma},$ within the usual strong-field approximation. Our analysis allows us to explicitly distinguish multiphoton and tunneling contributions to the total ionization probability. The range of intermediate $\ensuremath{\gamma}\ensuremath{\sim}1,$ which is typical for most current intense field experiments, is the regime of nonadiabatic tunneling. In this regime, the instantaneous laser phase dependence differs dramatically from both quasistatic tunneling and multiphoton limits. For cycle-averaged rates, our results reproduce standard Keldysh-like expressions.
TL;DR: It is proved necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors, which allows a simple verification of the one-error correcting property of codes of length 5 in any dimension.
Abstract: We present a construction for quantum error correcting codes. The basic ingredients are a graph and a finite Abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the one-error correcting property of codes of length 5 in any dimension. As examples, we construct a large class of maximum distance separable codes, i.e. codes saturating the Singleton bound, as well as a code of length 10 detecting three errors.
TL;DR: In this article, the authors characterize and classify quantum correlations in two-fermion systems having $2K$ single-particle states and give a necessary and sufficient condition for a state to have a Slater number 1.
Abstract: We characterize and classify quantum correlations in two-fermion systems having $2K$ single-particle states. For pure states we introduce the Slater decomposition and rank (in analogy to Schmidt decomposition and rank); i.e., we decompose the state into a combination of elementary Slater determinants formed by pairs of mutually orthogonal single-particle states. Mixed states can be characterized by their Slater number which is the minimal Slater rank required to generate them. For $K=2$ we give a necessary and sufficient condition for a state to have a Slater number 1. We introduce a correlation measure for mixed states which can be evaluated analytically for $K=2.$ For higher $K,$ we provide a method of constructing and optimizing Slater number witnesses, i.e., operators that detect Slater numbers for some states.
TL;DR: In this article, the authors present a setup for quantum secret sharing based on energy-time entanglement, which takes advantage of only two entangled photons created via parametric down conversion.
Abstract: We present a setup for quantum secret sharing based on energy-time entanglement. In opposition to known implementations using three particle Greenberger-Horne-Zeilinger ~GHZ! states, our idea takes advantage of only two entangled photons created via parametric down conversion. However, the system comprising the pump plus the two down-converted photons bare the same quantum correlation and can be used to mimic three entangled qubits. The relatively high coincidence count rates found in our setup enable for the first time an application of a quantum communication protocol based on more than two qubits.
TL;DR: In this paper, the zero-temperature phase diagram of bosonic atoms in an optical lattice is presented, which consists of various insulating phases and a superfluid phase, and the nature of the insulating phase is explored by calculating both the quasiparticle and quasihole dispersion relation.
Abstract: We present the zero-temperature phase diagram of bosonic atoms in an optical lattice, using two different mean-field approaches. The phase diagram consists of various insulating phases and a superfluid phase. We explore the nature of the insulating phase by calculating both the quasiparticle and quasihole dispersion relation. We also determine the parameters of our single band Bose-Hubbard model in terms of the microscopic parameters of the atoms in the optical lattice.
TL;DR: It is shown that the information gained by the eavesdropper then simply equals the information lost by the receiver in the resulting quantum cryptographic information versus disturbance trade-off.
Abstract: A continuous key-distribution scheme is proposed that relies on a pair of conjugate quantum variables. It allows two remote parties to share a secret Gaussian key by encoding it into one of the two quadrature components of a single-mode electromagnetic field. The resulting quantum cryptographic information versus disturbance trade-off is investigated for an individual attack based on the optimal continuous cloning machine. It is shown that the information gained by the eavesdropper then simply equals the information lost by the receiver.
TL;DR: In this article, a modified version of Grover's algorithm is presented, where the phase inversion is replaced by phase rotation through angle phi, and the rotation angle is given analytically to be phi = 2 arcsin(sin [pi/(4J+6)]/sin beta), where sin beta = 1/rootN, N is the number of items in the database, and J is any integer equal to or greater than the integer part of [(pi /2)-beta]/(2 beta).
Abstract: In a standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this paper we present a modified version of Grover's algorithm that searches a marked state with full successful rate. The modification is done by replacing the phase inversion by phase rotation through angle phi. The rotation angle is given analytically to be phi = 2 arcsin(sin [pi/(4J+6)]/sin beta), where sin beta = 1/rootN, N is the number of items in the database, and J is any integer equal to or greater than the integer part of [(pi /2)-beta]/(2 beta). Upon measurement at the (J+1)th iteration, the marked state is obtained with certainty.
TL;DR: In this paper, binary atomic collisions in a Bose gas tightly confined in one (axial) direction are discussed and two regimes of scattering are identified: quasi-2D and quasi-3D.
Abstract: We discuss binary atomic collisions in a Bose gas tightly confined in one (axial) direction and identify two regimes of scattering. In the quasi-two-dimensional (quasi-2D) regime, where the confinement frequency ${\ensuremath{\omega}}_{0}$ greatly exceeds the gas temperature $T,$ the scattering rates exhibit 2D features of the particle motion. At temperatures $T\ensuremath{\sim}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0}$ one has a confinement-dominated 3D regime, where the confinement can change the momentum dependence of the scattering amplitudes. We describe the collision-induced energy exchange between the axial and radial degrees of freedom and analyze recent experiments on thermalization and spin-relaxation rates in a tightly (axially) confined gas of Cs atoms.
TL;DR: In this paper, a general unitary operator acting on two qubits in a product state is considered and the conditions such that the state of the qubits after the action is as entangled as possible.
Abstract: We consider a general unitary operator acting on two qubits in a product state. We find the conditions such that the state of the qubits after the action is as entangled as possible. We also consider the possibility of using ancilla qubits to increase the entanglement.
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.
TL;DR: In this paper, the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and how they may be combined to implement a controlled-NOT (CNOT) gate are described.
Abstract: It has previously been shown that probabilistic quantum logic operations may be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they may be combined to implement a controlled-NOT (CNOT) gate. All of these gates may be constructed using polarizing beam splitters that completely transmit one state of polarization and totally reflect the orthogonal state of polarization, which allows a simple explanation of each operation. We also describe a polarizing beam splitter implementation of a CNOT gate that is closely analogous to the quantum teleportation technique previously suggested by Gottesman and Chuang [Nature 402, 390 (1999)]. Finally, our approach has the interesting feature that it makes practical use of a quantum-eraser technique.
TL;DR: In this article, the first study of quantum games with more than two players was presented, and it was shown that entanglement shared among multiple players enables different kinds of cooperative behavior.
Abstract: Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess an alternative form of equilibrium strategy, one which has no analog either in traditional games or even in two-player quantum games. In these ``coherent'' equilibria, entanglement shared among multiple players enables different kinds of cooperative behavior: indeed it can act as a contract, in the sense that it prevents players from successfully betraying one another.
TL;DR: In this paper, the bound states of solitons in a passively mode-locked fiber soliton ring laser are observed and the observed bound states are stable and have discrete, fixed soliton separations that are independent of the experimental conditions.
Abstract: We report on an experimental observation of bound states of solitons in a passively mode-locked fiber soliton ring laser. The observed bound solitons are stable and have discrete, fixed soliton separations that are independent of the experimental conditions.
TL;DR: In this paper, a model of discrete dynamics of entanglement of a bipartite quantum state is considered, which involves a global unitary dynamics of the system and periodic actions of local bistochastic or decaying channel.
Abstract: A model of discrete dynamics of entanglement of a bipartite quantum state is considered. It involves a global unitary dynamics of the system and periodic actions of local bistochastic or decaying channel. For initially pure states the decay of entanglement is accompanied by an increase of von Neumann entropy of the system. We observe and discuss revivals of entanglement due to unitary interaction of subsystems. For some mixed states having different marginal entropies of the subsystems we find an asymmetry in speed of entanglement decay. The entanglement of these states decreases faster, if the depolarizing channel acts on the ``classical'' subsystem, characterized by smaller marginal entropy.
TL;DR: In this article, the superfluidity of Bose-Einstein condensates in optical lattices is investigated and it is shown that a BEC can suffer a dynamical instability, resulting in period doubling and other sorts of symmetry breaking of the system.
Abstract: The superfluidity of Bose-Einstein condensates (BECs) in optical lattices is investigated. Apart from the usual Landau instability, which occurs when a BEC flows faster than the speed of sound, the BEC can also suffer a dynamical instability, resulting in period doubling and other sorts of symmetry breaking of the system. Such an instability plays a crucial role in the dissipative motion of a trapped BEC in an optical lattice recently observed [Burger et al., Phys. Rev. Lett. 86, 4447 (2001)].
TL;DR: This proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q.
Abstract: We prove the security of a quantum key distribution scheme based on transmission of squeezed quantum states of a harmonic oscillator. Our proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q. If the noise in the quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor e r = 1.34) is sufficient in principle to ensure the security of a protocol that is suitably enhanced by classical error correction and privacy amplification. Secure key distribution can be achieved over distances comparable to the attenuation length of the quantum channel.
TL;DR: In this paper, an entangled two-mode coherent state is studied in the framework of 2-dimensional Hilbert space and an entanglement concentration scheme based on joint Bell-state measurements is worked out.
Abstract: An entangled two-mode coherent state is studied within the framework of 2\ifmmode\times\else\texttimes\fi{}2-dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.