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We describe a new error reconciliation protocol {\it Winnow} based on the exchange of parity and Hamming's ``syndrome'' for $N-$bit subunits of a large data set. {\it Winnow} was developed in the context of quantum key distribution and offers significant advantages and net higher efficiency compared to other widely used protocols within the quantum cryptography community. A detailed mathematical analysis of Winnow is presented in the context of practical implementations of quantum key distribution; in particular, the information overhead required for secure implementation is one of the most important criteria in the evaluation of a particular error reconciliation protocol. The increase in efficiency for Winnow is due largely to the reduction in authenticated public communication required for its implementation.
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arxiv:quant-ph/0203096
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The problem of identifying the dynamical Lie algebras of finite-level quantum systems subject to external control is considered, with special emphasis on systems that are not completely controllable. In particular, it is shown that the dynamical Lie algebra for an N-level system with equally spaced energy levels and uniform transition dipole moments, is a subalgebra for $so(N)$ if $N=2\ell+1$, and a subalgebra of $sp(\ell)$ if $N=2\ell$. General conditions for obtaining either $so(2\ell+1)$ or $sp(\ell)$ are established.
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arxiv:quant-ph/0203104
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We propose a scheme for entangling the motional mode of a trapped atom with a propagating light field via a cavity-mediated parametric interaction. We then show that if this light field is subsequently coupled to a second distant atom via a cavity-mediated linear-mixing interaction, it is possible to transfer the entanglement from the light beam to the motional mode of the second atom to create an EPR-type entangled state of the positions and momenta of two distantly-separated atoms.
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arxiv:quant-ph/0203136
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Based on parity violation in the weak interaction and evidences from neutrino oscillation, a natural choice is that neutrinos may be spacelike particles with a tiny mass. To keep causality for spacelike particles, a kinematic time under a non-standard form of the Lorentz transformation is introduced, which is related to a preferred frame. A Dirac-type equation for spacelike neutrinos is further investigated and its solutions are discussed. This equation can be written in two spinor equations coupled together via nonzero mass while respecting maximum parity violation. As a consequence, parity violation implies that the principle of relativity is violated in the weak interaction.
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arxiv:quant-ph/0204002
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I conjecture that only those states of light whose Wigner function is positive are real states, and give arguments suggesting that this is not a serious restriction. Hence it follows that the Wigner formalism in quantum optics is capable of interpretation as a classical wave field with the addition of a zeropoint contribution. Thus entanglement between pairs of photons with a common origin occurs because the two light signals have amplitudes and phases, both below and above the zeropoint intensity level, which are correlated with each other.
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arxiv:quant-ph/0204020
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Certain quasi-exactly solvable systems exhibit an energy reflection property that relates the energy levels of a potential or of a pair of potentials. We investigate two sister potentials and show the existence of this energy reflection relationship between the two potentials. We establish a relationship between the lowest energy edge in the first potential using the weak coupling expansion and the highest energy level in the sister potential using a WKB approximation carried out to higher order.
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arxiv:quant-ph/0204035
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Based upon the general supercharges which involve not only generators C_j of the Clifford algebra C(4,0) with positive metric, but also operators of third order, C_j C_k C_l, the general form of N=4 supersymmetric quantum mechanics (SSQM), which brings out the richer structures, is realized. Then from them, an one-dimensional physical realization and a new multi-dimensional physical realization of N=4 SSQM are respectively obtained by solving the constraint conditions. As applications, N=4 dynamical superconformal symmetries, which possess both the N=4 supersymmetries and the usual dynamical conformal symmetries, are studied in detail by considering two simple superpotentials k/x and \omega x, and their corresponding superalgebraic structures, which are spanned by eight fermionic generators and six bosonic generators, are established as well.
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arxiv:quant-ph/0204048
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Structures of quantum Fokker-Planck equations are characterized with respect to the properties of complete positivity, covariance under symmetry transformations and satisfaction of equipartition, referring to recent mathematical work on structures of unbounded generators of covariant quantum dynamical semigroups. In particular the quantum optical master-equation and the quantum Brownian motion master-equation are shown to be associated to $\mathrm{U(1)}$ and $\mathrm{R}$ symmetry respectively. Considering the motion of a Brownian particle, where the expression of the quantum Fokker-Planck equation is not completely fixed by the aforementioned requirements, a recently introduced microphysical kinetic model is briefly recalled, where a quantum generalization of the linear Boltzmann equation in the small energy and momentum transfer limit straightforwardly leads to quantum Brownian motion.
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arxiv:quant-ph/0204071
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The remarkable transmission of two bits of information via a single qubit entangled with another at the destination, is presented as an expansion of the unremarkable classical circuit that transmits the bits with two direct qubit-qubit couplings between source and destination
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arxiv:quant-ph/0204107
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The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an $Sp(2,R)$ unitary representation commuting with the SU(3) representation, the infinity of occurrences of each SU(3) irreducible representation can be handled in complete detail. A natural `generating representation' for SU(3), containing each irreducible representation exactly once, is identified within a subspace of the Schwinger construction; and this is shown to be equivalent to an induced representation of SU(3).
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arxiv:quant-ph/0204119
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We show that a mixed state $\rho=\sum_{mn}a_{mn}|m> < n|$ can be realized by an ensemble of pure states $\{p_{k}, |\phi_{k} > \}$ where $|\phi_{k}>=\sum_{m}\sqrt{a_{mm}}e^{i\theta_{m}^{k}}|m>$. Employing this form, we discuss the relative entropy of entanglement of Schmidt correlated states. Also, we calculate the distillable entanglement of a class of mixed states.
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arxiv:quant-ph/0204152
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We discuss techniques for producing, manipulating and measureing qubits encoded optically as vacuum and single photon states. We show that a universal set of non-deterministic gates can be constructed using linear optics and photon counting. We investigate the efficacy of a test gate given realistic detector efficiencies.
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arxiv:quant-ph/0205044
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In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results on symmetry of probability distributions for the Hadamard walk.
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arxiv:quant-ph/0205065
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In this paper we present a state vector analysis of the generation of atomic spin squeezing by measurement of an optical phase shift. The frequency resolution is improved when a spin squeezed sample is used for spectroscopy in place of an uncorrelated sample. When light is transmitted through an atomic sample some photons will be scattered out of the incident beam, and this has a destructive effect on the squeezing. We present quantitative studies for three limiting cases: the case of a sample of atoms of size smaller than the optical wavelength, the case of a large dilute sample and the case of a large dense sample.
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arxiv:quant-ph/0205082
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Environment induced decoherence entails the absence of quantum interference phenomena from the macroworld. The loss of coherence between superposed wave packets depends on their separation. The precise temporal course depends on the relative size of the time scales for decoherence and other processes taking place in the open system and its environment. We use the exactly solvable model of an harmonic oscillator coupled to a bath of oscillators to illustrate various decoherence scenarios: These range from exponential golden-rule decay for microscopic superpositions, system-specific decay for larger separations in a crossover regime, and finally universal interaction-dominated decoherence for ever more macroscopic superpositions.
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arxiv:quant-ph/0205108
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As typically implemented, single photon sources cannot be made to produce single photons with high probability, while simultaneously suppressing the probability of yielding two or more photons. Because of this, single photon sources cannot really produce single photons on demand. We describe a multiplexed system that allows the probabilities of producing one and more photons to be adjusted independently, enabling a much better approximation of a source of single photons on demand.
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arxiv:quant-ph/0205140
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Quantum-cryptography key distribution (QCKD) experiments have been recently reported using polarization-entangled photons. However, in any practical realization, quantum systems suffer from either unwanted or induced interactions with the environment and the quantum measurement system, showing up as quantum and, ultimately, statistical noise. In this paper, we investigate how ideal polarization entanglement in spontaneous parametric downconversion (SPDC) suffers quantum noise in its practical implementation as a secure quantum system, yielding errors in the transmitted bit sequence. Because all SPDC-based QCKD schemes rely on the measurement of coincidence to assert the bit transmission between the two parties, we bundle up the overall quantum and statistical noise in an exhaustive model to calculate the accidental coincidences. This model predicts the quantum-bit error rate and the sifted key and allows comparisons between different security criteria of the hitherto proposed QCKD protocols, resulting in an objective assessment of performances and advantages of different systems.
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arxiv:quant-ph/0205142
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The possibility of revealing non-classical behaviours in the dynamics of a trapped ion via measurements of the mean value of suitable operators is reported. In particular we focus on the manifestation known as `` Parity Effect\rq\rq which may be observed \emph{directly measuring} the expectation value of an appropriate correlation operator. The experimental feasibility of our proposal is discussed.
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arxiv:quant-ph/0205153
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We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein-Podolsky-Rosen ``paradox,'' we demonstrate strong polarization correlations of the entanged photons. Bell's idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of the Clauser, Horne, Shimony and Holt version of the Bell inequality finds $S = 2.307 \pm 0.035$, in clear contradiciton of hidden variable theories. The experiments described can be performed in an afternoon.
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arxiv:quant-ph/0205171
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We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using $2(2^{N-1}-1)$ bosonic harmonic oscillator creation and annihilation operators. We give an explicit construction of all (N-1) Casimirs of SU(N) in terms of these creation and annihilation operators. The SU(N) coherent states belonging to any irreducible representations of SU(N) are labelled by the eigenvalues of the Casimir operators and are characterized by (N-1) complex orthonormal vectors describing the SU(N) manifold. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties.
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arxiv:quant-ph/0206005
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Closed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in general. Some aspects of the spontaneous breakdown of PT symmetry are analysed.
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arxiv:quant-ph/0206032
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We describe an experimental test of whether particle decay causes wave function collapse. The test uses interference between two well separated, but coherent, sources of vector mesons. The short-lived mesons decay before their wave functions can overlap, so any interference must involve identical final states. Unlike previous tests of nonlocality, the interference involves continuous variables, momentum and position. Interference can only occur if the wave function retains amplitudes for all possible decays. The interference can be studied through the transverse momentum spectrum of the reconstructed mesons.
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arxiv:quant-ph/0206060
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We show that a point particle moving in space-time on entwined-pair paths generates Schroedinger's equation in a static potential in the appropriate continuum linit. This provides a new realist context for the Schroedinger equation within the domain of classical stochastic processes. It also suggests that self-quantizing systems may provide considerable insight into conventional quantum mechanics.
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arxiv:quant-ph/0206095
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There are a number of papers dedicated to the description of free particles and antiparticles with zero mass and spin 1/2. A great many equations with different C, P, T properties have been proposed and the impression could be formed that there are many nonequivalent theories for zero-mass particles. The purpose or this paper is to show that it is not the case and to describe all nonequivalent equations.
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arxiv:quant-ph/0206109
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In this work, we consider a 2-state quantum system interacting with a thermal reservoir. By computing the long time limit of the probability for the system to be in the ground state according to the Schrodinger/Von Neumann equation, we reach a contradiction with the prediction of equilibrium statistical mechanics. The most likely explanation is that the Schrodinger equation is incomplete as a description of such systems, because the other assumptions made herein have a wider range of experimental support.
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arxiv:quant-ph/0206120
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The Schr\" odinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring in a supersymmetric approach to these Hamiltonians are consequences of some formulae concerning the general theory of associated special functions. We use this connection in order to obtain a general theory of Schr\" odinger equations exactly solvable in terms of associated special functions, and to extend certain results known in the case of some particular potentials.
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arxiv:quant-ph/0206129
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We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms considered in the canonical decomposition. Our result relies on the fact that states which are mixed by Hadamard operators at any stage of the computation only differ by a phase. This property is a consequence of the structure of the initial state and of the QFT, based on controlled-phase operators and a single action of a Hadamard gate per qubit. As a consequence, Hadamard gates order the probability distribution associated to the quantum state, whereas controlled-phase operators carry all the entanglement but are immaterial to majorization. We also prove that majorization in phase-estimation algorithms follows in a most natural way from unitary evolution, unlike its counterpart in Grover's algorithm.
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arxiv:quant-ph/0206134
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The interaction of coherent light with a nonlinear medium is modeled here by a general quantum anharmonic oscillator. The model is not exactly solvable in a closed analytical form. But we need operator solutions of the equations of motion corresponding to these models in order to study the quantum fluctuations of coherent light in nonlinear media. In the present work we derive approximate operator solutions. From these solutions we observe that there exists an apparent discrepancy between the solutions obtained by different techniques. We compare different solutions and conclude that all correct solutions are equivalent and the apparent discrepancy is due to the use of different ordering of the operators. We use these solutions to investigate the possibilities of observing different optical phenomena in a nonlinear dielectric medium. To be precise, we have studied quantum phase fluctuations of coherent light in a third order inversion symmetric nonlinear medium. Fluctuations in phase space quadrature for the same system are studied and the possibility of generating squeezed state is reported. Fluctuations in photon number are studied and the nonclassical phenomenon of antibunching is predicted. We have generalized the results obtained for third order nonlinear medium and have studied the interaction of an intense laser beam with a general (m-1)-th order nonlinear medium. Aharanov Anandan nonadiabatic geometric phase is also discussed in the context of (m-1)-th order nonlinear medium.
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arxiv:quant-ph/0207034
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The main argument against the reality of the electromagnetic quantum vacuum fluctuations is that they do not activate photon detectors. In order to met this objection I propose a model of photocounting which, in the simple case of a light signal with constant intensity, predicts a counting rate proportional to the intensity, in agreement with the standard quantum result.
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arxiv:quant-ph/0207073
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A new quantum cryptography implementation is presented that combines one-way operation with an autocompensating feature that has hitherto only been available in implementations that require the signal to make a round trip between the users. Using the concept of advanced waves, it is shown that this new implementation is related to the round-trip implementations in the same way that Ekert's two-particle scheme is related to the original one-particle scheme of Bennett and Brassard. The practical advantages and disadvantages of the proposed implementation are discussed in the context of existing schemes.
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arxiv:quant-ph/0207167
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In this contribution we will give a brief overview on the methods used to overcome decoherence in quantum communication protocols. We give an introduction to quantum error correction, entanglement purification and quantum cryptography. It is shown that entanglement purification can be used to create ``private entanglement'', which makes it a useful tool for cryptographic protocols.
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arxiv:quant-ph/0208014
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We investigate cooling and trapping of single atoms inside an optical cavity using a quasi-resonant field and a far-off resonant mode of the Laguerre-Gauss type. The far-off resonant doughnut mode provides an efficient trapping in the case when it shifts the atomic internal ground and excited state in the same way, which is particularly useful for quantum information applications of cavity quantum electrodynamics (QED) systems. Long trapping times can be achieved, as shown by full 3-D simulations of the quasi-classical motion inside the resonator.
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arxiv:quant-ph/0208016
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We investigate the dephasing of ultra cold ^{85}Rb atoms trapped in an optical dipole trap and prepared in a coherent superposition of their two hyperfine ground states by interaction with a microwave pulse. We demonstrate that the dephasing, measured as the Ramsey fringe contrast, can be reversed by stimulating a coherence echo with a pi-pulse between the two pi/2 pulses, in analogy to the photon echo. We also demonstrate that the failure of the echo for certain trap parameters is due to dynamics in the trap, and thereby that ''echo spectroscopy'' can be used to study the quantum dynamics in the trap even when more than 10^6 states are thermally populated, and to study the crossover from quantum (where dynamical decoherence is supressed) to classical dynamics.
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arxiv:quant-ph/0208052
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The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation for this equation. The semiclassical description of the Wigner function in terms of chords, each with its classically defined amplitude and phase, is thus inserted in the integrals, which leads to an explicit differential equation for the Wigner function. All the Lindblad operators are assumed to be represented by smooth phase space functions corresponding to classical variables. In the case that these are real, representing hermitian operators, the semiclassical Lindblad equation can be integrated. There results a simple extension of the unitary evolution of the semiclassical Wigner function, which does not affect the phase of each chord contribution, while dampening its amplitude. This decreases exponentially, as governed by the time integral of the square difference of the Lindblad functions along the classical trajectories of both tips of each chord. The decay of the amplitudes is shown to imply diffusion in energy for initial states that are nearly pure. Projecting the Wigner function onto an orthogonal position or momentum basis, the dampening of long chords emerges as the exponential decay of off-diagonal elements of the density matrix.
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arxiv:quant-ph/0208094
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A suggestion for an observational test of the difference between quantum mechanics and noncontextual hidden variables theories requires the measurement of a product of two commuting observables without measuring either observable separately. A proposal has been made for doing this, but it is shown to be problematic.
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arxiv:quant-ph/0208127
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The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We show that the main parameters of any fundamental model must be theory-independent. They cannot be predicted, because they cannot have internal causes. However, it is possible to describe them in the language of classical mechanics. We invoke philosophical reasons in favor of a specific model, which treats particles as sources of real waves. Experimental considerations for gravitational, electromagnetic, and quantum phenomena are outlined.
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arxiv:quant-ph/0208148
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An experimental scheme for preparing a polarization entangled W states from four photons emitted by parametric down-conversion is proposed. We consider two different configurations and a method of improving the yield by using single photon sources. In the proposed scheme, one uses only linear optical elements and photon detectors, so that this scheme is feasible by current technologies.
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arxiv:quant-ph/0208162
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Can the apparent complexity we observe in the real world be generated from simple initial conditions via simple, deterministic rules?
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arxiv:quant-ph/0209002
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The goal of this brief pedagogical article is to show that Binary Decision Diagrams are a special kind of Bayesian Net. This observation is obvious to workers in these two fields, but it might not be too obvious to others.
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arxiv:quant-ph/0209009
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Here are discussed some problems concerning quant-ph/0208006.
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arxiv:quant-ph/0209024
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Using the spontaneous parametric down-conversion process in a type-I phase matching BBO crystal as single photon source, we perform an all-or-nothing-type Kochen-Specker experiment proposed by Simon \QTR{it}{et al}. [Phys. Rev. Lett. \QTR{bf}{85}, 1783 (2000)] to verify whether noncontextual hidden variables or quantum mechanics is right. The results strongly agree with quantum mechanics.
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arxiv:quant-ph/0209038
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We report a novel Bell-state synthesizer in which an interferometric entanglement concentration scheme is used. An initially mixed polarization state from type-II spontaneous parametric down-conversion becomes entangled after the interferometric entanglement concentrator. This Bell-state synthesizer is universal in the sense that the output polarization state is not affected by spectral filtering, crystal thickness, and, most importantly, the choice of pump source. It is also robust against environmental disturbance and a more general state, partially mixed$-$partially entangled state, can be readily generated as well.
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arxiv:quant-ph/0209041
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A general class of authentication schemes for arbitrary quantum messages is proposed. The class is based on the use of sets of unitary quantum operations in both transmission and reception, and on appending a quantum tag to the quantum message used in transmission. The previous secret between partners required for any authentication is a classical key. We obtain the minimal requirements on the unitary operations that lead to a probability of failure of the scheme less than one. This failure may be caused by someone performing a unitary operation on the message in the channel between the communicating partners, or by a potential forger impersonating the transmitter.
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arxiv:quant-ph/0209061
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A lower bound on the amount of energy needed to carry out an elementary logical operation on a qubit system, with a given accuracy and in a given time, has been recently postulated. This paper is an attempt to formalize this bound and explore the conditions under which it may be expected to hold. This is a work in progress and any contributions will be appreciated.
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arxiv:quant-ph/0209065
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Since Edward Moore, finite automata theory has been inspired by physics, in particular by quantum complementarity. We review automaton complementarity, reversible automata and the connections to generalized urn models. Recent developments in quantum information theory may have appropriate formalizations in the automaton context.
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arxiv:quant-ph/0209089
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We develop a computation model for solving Boolean networks by implementing wires through quantum ground-mode computation and gates through identities following from angular momentum algebra and statistics. Gates are represented by three-dimensional (triplet) symmetries due to particle indistinguishability and are identically satisfied throughout computation being constants of the motion. The relaxation of the wires yields the network solutions. Such gates cost no computation time, which is comparable with that of an easier Boolean network where all the gate constraints implemented as constants of the motion are removed. This model computation is robust with respect to decoherence and yields a generalized quantum speed-up for all NP problems.
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arxiv:quant-ph/0209169
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I comment on the experiment to realize an "on-demand," reversible single-photon source by Kuhn, Hennrich, and Rempe [Phys. Rev. Lett. 89, 067901 (2002)].
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arxiv:quant-ph/0210032
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Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing or eliminating errors, but not one, alone, will serve as a panacea. One must therefore take advantage of the strength of each of these techniques so that we may extend the coherence times of the quantum systems and create more reliable computing devices. To this end we give a general strategy for using dynamical decoupling operations on encoded subspaces. These encodings may be of any form; of particular importance are decoherence-free subspaces and quantum error correction codes. We then give means for empirically determining an appropriate set of dynamical decoupling operations for a given experiment. Using these techniques, we then propose a comprehensive encoding solution to many of the problems of quantum computing proposals which use exchange-type interactions. This uses a decoherence-free subspace and an efficient set of dynamical decoupling operations. It also addresses the problems of controllability in solid state quantum dot devices.
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arxiv:quant-ph/0210072
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We investigate the optical detection of single atoms held in a microscopic atom trap close to a surface. Laser light is guided by optical fibers or optical micro-structures via the atom to a photo-detector. Our results suggest that with present-day technology, micro-cavities can be built around the atom with sufficiently high finesse to permit unambiguous detection of a single atom in the trap with 10 $\mu$s of integration. We compare resonant and non-resonant detection schemes and we discuss the requirements for detecting an atom without causing it to undergo spontaneous emission.
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arxiv:quant-ph/0210090
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We demonstrate one- and two-photon diffraction and interference experiments utilizing parametric down-converted photon pairs (biphotons) and a transmission grating. With two-photon detection, the biphoton exhibits a diffraction-interference pattern equivalent to that of an effective single particle that is associated with half the wavelength of the constituent photons. With one-photon detection, however no diffraction-interference pattern is observed. We show that these phenomena originate from the spatial quantum correlation between the down-converted photons.
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arxiv:quant-ph/0210142
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Charles Bennett's measure of physical complexity for classical objects, namely logical-depth, is used in order to prove that a chaotic classical dynamical system is not physical complex. The natural measure of physical complexity for quantum objects, quantum logical-depth, is then introduced in order to prove that a chaotic quantum dynamical system is not physical complex too.
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arxiv:quant-ph/0210148
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The non-resonant interaction between the high-density excitons in a quantum well and a single mode cavity field is investigated. An analytical expression for the physical spectrum of the excitons is obtained. The spectral properties of the excitons, which are initially prepared in the number states or the superposed states of the two different number states by the resonant femtosecond pulse pumping experiment, are studied. Numerical study of the physical spectrum is carried out and a discussion of the detuning effect is presented.
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arxiv:quant-ph/0210165
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We discuss level schemes of small quantum-dot turnstiles and their applicability in the production of entanglement in two-photon emission. Due to the large energy splitting of the single-electron levels, only one single electron level and one single hole level can be made resonant with the levels in the conduction band and valence band. This results in a model with nine distinct levels, which are split by the Coulomb interactions. We show that the optical selection rules are different for flat and tall cylindrically symmetric dots, and how this affects the quality of the entanglement generated in the decay of the biexciton state. The effect of charge carrier tunneling and of a resonant cavity is included in the model.
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arxiv:quant-ph/0210170
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We establish a necessary and sufficient condition for averages over complex valued weight functions on R^N to be represented as statistical averages over real, non-negative probability weights on C^N. Using this result, we show that many path-integrals for time-ordered expectation values of bosonic degrees of freedom in real-valued time can be expressed as statistical averages over ensembles of paths with complex-valued coordinates, and then speculate on possible consequences of this result for the relation between quantum and classical mechanics.
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arxiv:quant-ph/0210195
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Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental group representations are used to obtain a direct sum of Hilbert spaces, with a Holonomy method for the non simply connected manifolds.The covering spaces of isometric and hence isospectral manifolds are used to obtain the representation of states on orientable and non orientable spaces. Problems of deformations of the operators and the domains are discussed.Possible applications of the geometric and topological effects in physics are mentioned.
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arxiv:quant-ph/0211039
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The explanation presented in [Taichenachev et al, Phys. Rev. A {\bf 61}, 011802 (2000)] according to which the electromagnetically induced absorption (EIA) resonances observed in degenerate two level systems are due to coherence transfer from the excited to the ground state is experimentally tested in a Hanle type experiment observing the parametric resonance on the $% D1$ line of $^{87}$Rb. While EIA occurs in the $F=1\to F^{\prime}=2 $ transition in a cell containing only $Rb$ vapor, collisions with a buffer gas ($30 torr$ of $Ne$) cause the sign reversal of this resonance as a consequence of collisional decoherence of the excited state. A theoretical model in good qualitative agreement with the experimental results is presented.
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arxiv:quant-ph/0211065
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We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction is deteriorated in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing the velocity of the observers if the directions of the measurement are fixed. However, this does not imply a breakdown of non-local correlation since the perfect anti-correlation is maintained in appropriately chosen different directions. We must take account of this relativistic effect in utilizing in moving frames the EPR correlation and the violation of Bell's inequality for quantum communication.
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arxiv:quant-ph/0211177
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We present an optical "enantio-selective switch", that, in two steps, turns a ("racemic") mixture of left-handed and right-handed chiral molecules into the enantiomerically pure state of interest. The optical switch is composed of an "enantio-discriminator" and an "enantio-converter" acting in tandem. The method is robust, insensitive to decay processes, and does not require molecular preorientation. We demonstrate the method on the purification of a racemate of (transiently chiral) D$_2$S$_2$ molecules, performed on the nanosecond timescale.
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arxiv:quant-ph/0211178
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We show that an oracle A that contains either 1/4 or 3/4 of all strings of length n can be used to separate EQP from the counting classes MOD_{p^k}P. Our proof makes use of the degree of a representing polynomial over the finite field of size p^k. We show a linear lower bound on the degree of this polynomial. We also show an upper bound of O(n^{1/log_p m}) on the degree over the ring of integers modulo m, whenever m is a squarefree composite with largest prime factor p.
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arxiv:quant-ph/0211179
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The Fermat principle indicates that light chooses the temporally shortest path. The action for this "motion" is the observed time, and it has no Lorentz invariance. In this paper we show how this action can be obtained from relativistic action, and how the classical wave equation of light can be obtained from this action.
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arxiv:quant-ph/0211181
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In this note we comment on yet another way of describing metric of quantum states with the Lorentzian signature. For this, we consider the metric of quantum states and make successive transformations, exploiting the relationship between S3 and SU(2).
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arxiv:quant-ph/0301070
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We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of few coupled spins: (i) determining the pointer states of the system, and (ii) determining the temporal decay of quantum oscillations. As our results demonstrate, for determining the pointer states, the Chebyshev-based scheme is at least a factor of 8 faster than existing algorithms based on the Suzuki-Trotter decomposition. For the problems of second type, the Chebyshev-based approach has been 3--4 times faster than the Suzuki-Trotter-based schemes. This conclusion holds qualitatively for a wide spectrum of systems, with different spin baths and different Hamiltonians.
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arxiv:quant-ph/0301130
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The controllability condition for finite dimensional quantum systems, the Lie Algebra Rank Condition, has been stated assuming that the right invariant differential system under consideration is bilinear. We remark that this assumption is not necessary and discuss the extension to the general case.
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arxiv:quant-ph/0301144
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We investigate how the dynamical production of quantum entanglement for weakly coupled mapping systems is influenced by the chaotic dynamics of the corresponding classical system. We derive a general perturbative formula for the entanglement production rate which is defined by using the linear entropy of the subsystem. This formula predicts that {\it the increment of the strength of chaos does not enhance the production rate of entanglement} when the coupling is weak enough and the subsystems are strongly chaotic. The prediction is confirmed by numerical experiments for coupled kicked tops and rotors. We also discuss the entanglement production using the Husimi representation of the reduced density matrix.
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arxiv:quant-ph/0302015
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In this paper we propose a Hamiltonian of the n-level system by making use of generalized Pauli matrices.
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arxiv:quant-ph/0302050
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It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wavefunction is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie-Bohm ones, such as crossing of the axis of symmetry.
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arxiv:quant-ph/0302076
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In this short note, we propose a scheme, in which two instances of an equatorial state (or a polar state) can be remotely prepared in one-shot operation to different receivers with prior entanglement and 1 bit of broadcasting. The trade-off curve between the amount of entanglement and the achievable fidelity is derived.
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arxiv:quant-ph/0302170
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We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes an algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that protects against a class of multiple-qubit errors. The code stores two decoherence-free logical qubits in four noisy physical qubits. The computer successfully executes Grover's search algorithm in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.
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arxiv:quant-ph/0302175
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Using the method of shape invariant potentials, a number of exact solutions of one dimensional effective mass Schrodinger equation are obtained. The solutions with equi-spaced spectrum are discussed in detail.
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arxiv:quant-ph/0302191
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Decoherence is the main obstacle to the realization of quantum computers. Until recently it was thought that quantum error correcting codes are the only complete solution to the decoherence problem. Here we present an alternative that is based on a combination of a decoherence-free subspace encoding and the application of strong and fast pulses: ``encoded recoupling and decoupling'' (ERD). This alternative has the advantage of lower encoding overhead (as few as two physical qubits per logical qubit suffice), and direct application to a number of promising proposals for the experimental realization of quantum computers.
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arxiv:quant-ph/0302198
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Can Grover's algorithm speed up search of a physical region - for example a 2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to be needed for each query, just to move amplitude across the grid. Here we show that this problem can be surmounted, refuting a claim to the contrary by Benioff. In particular, we show how to search a d-dimensional hypercube in time O(sqrt n) for d at least 3, or O((sqrt n)(log n)^(3/2)) for d=2. More generally, we introduce a model of quantum query complexity on graphs, motivated by fundamental physical limits on information storage, particularly the holographic principle from black hole thermodynamics. Our results in this model include almost-tight upper and lower bounds for many search tasks; a generalized algorithm that works for any graph with good expansion properties, not just hypercubes; and relationships among several notions of `locality' for unitary matrices acting on graphs. As an application of our results, we give an O(sqrt(n))-qubit communication protocol for the disjointness problem, which improves an upper bound of Hoyer and de Wolf and matches a lower bound of Razborov.
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arxiv:quant-ph/0303041
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It is shown that, concerning the experiment described by the authors, their extension to the situation in which Alice's measurement occurs after Bob's is unnecessary and their interpretation misleading.
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arxiv:quant-ph/0303082
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We show unexpected connection of Set Theoretical Forcing with Quantum Mechanical lattice of projections over some separable Hilbert space. The basic ingredient of the construction is the rule of indistinguishability of Standard and some Nonstandard models of Peano Arithmetic. The ingeneric reals introduced by M. Ozawa will correspond to simultaneous measurement of incompatible observables. We also discuss some results concerning model theoretical analysis of Small Exotic Smooth Structures on topological 4-space. Forcing appears rather naturally in this context and the rule of indistinguishability is crucial again. As an unexpected application we are able to approach Maldacena Conjecture on $AdS/CFT$ correspondence in the case of AdS_5xS^5 and Super YM Conformal Field Theory in 4 dimensions. We conjecture that there is possibility of breaking Supersymetry via sources of gravity generated in 4 dimensions by exotic smooth structures on R^4 emerging in this context.
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arxiv:quant-ph/0303089
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We re-derive the quantum master equation for the decoherence of a massive Brownian particle due to collisions with the lighter particles from a thermal environment. Our careful treatment avoids the occurrence of squares of Dirac delta functions. It leads to a decoherence rate which is smaller by a factor of 2 pi compared to previous findings. This result, which is in agreement with recent experiments, is confirmed by both a physical analysis of the problem and by a perturbative calculation in the weak coupling limit.
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arxiv:quant-ph/0303094
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We calculate the exact transmission coefficient of a quantum wire in the presence of a single point defect at the wire's cut-off frequencies. We show that while the conductance pattern (i.e., the scattering) is strongly affected by the presence of the defect, the pattern is totally independent of the defect's characteristics (i.e., the defect that caused the scattering cannot be identified from that pattern).
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arxiv:quant-ph/0303110
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In an experiment designed to overcome the loophole of observer dependent reality and satisfying the counterfactuality condition, we measured polarization correlations of 1S0 proton pairs produced in 12C(d,2He) and 1H(d,He) reactions in one setting. The results of these measurements are used to test the Bell and Wigner inequalties against the predictions of quantum mechanics.
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arxiv:quant-ph/0303136
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We present a new strategy for multipulse control over decoherence. When a two-level system interacts with a reservoir characterized by a specific frequency, we find that the decoherence is effectively suppressed by synchronizing the pulse-train application with the dynamical motion of the reservoir.
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arxiv:quant-ph/0303144
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We establish conditions under which the experimental verification of quantum error-correcting behavior against a linear set of error operators $\ce$ suffices for the verification of noiseless subsystems of an error algebra $\ca$ contained in $\ce$. From a practical standpoint, our results imply that the verification of a noiseless subsystem need not require the explicit verification of noiseless behavior for all possible initial states of the syndrome subsystem.
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arxiv:quant-ph/0303165
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We show that for a fixed amount of entanglement, two-mode squeezed states are those that maximize Einstein-Podolsky-Rosen-like correlations. We use this fact to determine the entanglement of formation for all symmetric Gaussian states corresponding to two modes. This is the first instance in which this measure has been determined for genuine continuous variable systems.
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arxiv:quant-ph/0304042
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If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical "questions" more efficiently. The existence of one-to-one mappings between different algebras of observables or between different Hilbert spaces allow us to represent and imitate any physical system by any other one (e.g., a bosonic system by a spin-1/2 system). We explain how these mappings can be performed showing quantum networks useful for the efficient evaluation of some physical properties, such as correlation functions and energy spectra.
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arxiv:quant-ph/0304063
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The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved efficiently by quantum computers, it will be demonstrated by means of a simple example, that the detection of more general hidden (two-point) symmetries {$V\{f(x),f(U[x])\}=0$} by a quantum algorithm can also admit an exponential speed-up. E.g., one member of this class of symmetries {$V\{f(x),f(U[x])\}=0$} is discrete self-similarity (or discrete scale invariance). PACS: 03.67.Lx, 89.70.+c.
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arxiv:quant-ph/0304090
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This paper gives a criterion for detecting the entanglement of a quantum state, and uses it to study the relationship between topological and quantum entanglement. It is fundamental to view topological entanglements such as braids as entanglement operators and to associate to them unitary operators that are capable of creating quantum entanglement. The entanglement criterion is used to explore this connection. The paper discusses non-locality in the light of this criterion.
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arxiv:quant-ph/0304091
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We discuss some aspects and examples of applications of dual algebraic pairs $({\cal G}_1,{\cal G}_2)$ in quantum many-body physics. They arise in models whose Hamiltonians $H$ have invariance groups $G_i$. Then one can take ${\cal G}_1 = G_i$ whereas another dual partner ${\cal G}_2= g^D$ is generated by $G_i$ invariants, possesses a Lie-algebraic structure and describes dynamic symmetry of models; herewith polynomial Lie algebras $\hat g = g^D$ appear in models with essentially nonlinear Hamiltonians. Such an approach leads to a geometrization of model kinematics and dynamics.
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arxiv:quant-ph/0304118
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We study the issue of simultaneous estimation of several phase shifts induced by commuting operators on a quantum state. We derive the optimal positive operator-valued measure corresponding to the multiple-phase estimation. In particular, we discuss the explicit case of the optimal detection of double phase for a system of identical qutrits and generalise these results to optimal multiple phase detection for d-dimensional quantum states.
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arxiv:quant-ph/0304126
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A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible representations, both those of higher dimension and orthogonal bases for the trivial representation, are available for error correction. A number of new (non-additive) binary codes are obtained, including two new 7-bit codes and a large family of new 9-bit codes. It is shown that the degeneracy arising from permutational symmetry facilitates the correction of certain types of two-bit errors. The correction of two-bit errors of the same type is considered in detail, but is shown not to be compatible with single-bit error correction using 9-bit codes.
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arxiv:quant-ph/0304153
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An experimental scheme is proposed to test Bell's inequality by using superconducting nanocircuits. In this scheme, quantum entanglement of a pair of charge qubits separated in a sufficient long distance may be created by cavity quantum electrodynamic techniques; the population of qubits is experimentally measurable by dc currents through the probe junctions, and one measured outcome may be recorded for every experiment. Therefore, both locality and detection efficiency loopholes should be closed in the same experiment. We also propose a useful method to measure the amount of entanglement based on the concurrence between Josephson qubits. The measurable variables for Bell's inequality as well as the entanglement are expressed in terms of a useful phase-space Q function.
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arxiv:quant-ph/0304156
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The muon transfer probabilities between muonic hydrogen and an oxygen atom are calculated in a constrained geometry one dimensional model for collision between 10^-6 and 10^3 eV. These estimated rates are discussed in the light of previous model calculations and available experimental data for this process.
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arxiv:quant-ph/0304191
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Simple optical instruments are linear optical networks where the incident light modes are turned into equal numbers of outgoing modes by linear transformations. For example, such instruments are beam splitters, multiports, interferometers, fibre couplers, polarizers, gravitational lenses, parametric amplifiers, phase-conjugating mirrors and also black holes. The article develops the quantum theory of simple optical instruments and applies the theory to a few characteristic situations, to the splitting and interference of photons and to the manifestation of Einstein-Podolsky-Rosen correlations in parametric downconversion. How to model irreversible devices such as absorbers and amplifiers is also shown. Finally, the article develops the theory of Hawking radiation for a simple optical black hole. The paper is intended as a primer, as a nearly self-consistent tutorial. The reader should be familiar with basic quantum mechanics and statistics, and perhaps with optics and some elementary field theory. The quantum theory of light in dielectrics serves as the starting point and, in the concluding section, as a guide to understand quantum black holes.
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arxiv:quant-ph/0305007
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We consider the use of space-filling curves (SFC) in scanning control parameters for quantum chemical systems. First we show that a formally exact SFC must be singular in the control parameters, but a finite discrete generalization can be used with no problem. We then make general observations about the relevance of SFCs in preference to linear scans of the parameters. Finally we present a simple magnetic field example relevant in NMR and show from the calculated autocorrelations that a SFC Peano-Hilbert curve gives a smoother sequence than a linear scan.
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arxiv:quant-ph/0305021
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A recent theoretical calculation shows that the Casimir force between two parallel plates can be repulsive for plates with nontrivial magnetic properties (O. Kenneth et al., Phys. Rev. Lett. 89, 033001 (2002)). According to the authors, the effect may be observed with known materials, such as ferrites and garnets, and it might be possible to engineer micro- or nanoelectromechanical systems (MEMS or NEMS) that could take advantage of a short range repulsive force. Here we show that on the contrary the Casimir force between two parallel plates in vacuum at micron and submicron distance is always attractive.
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arxiv:quant-ph/0305065
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The standard protocol for teleportation of a quantum state requires an entangled pair of particles and the use of two classical bits of information. Here, we present two protocols for teleportation that require only one classical bit. In the first protocol, chained XOR operations are performed on the particles before one of them is removed to the remote location where the state is being teleported. In the second protocol, three entangled particles are used.
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arxiv:quant-ph/0305085
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It is proved that, according to Classical Mechanics and Electrodynamics, the trajectory of the center of mass of a neutral system of electrical charges can be deflected by an inhomogeneous magnetic field, even if its internal angular momentum is zero. This challenges the common view about the function of the Stern-Gerlach apparatus, as resolving the eigen-states of an intrinsic angular momentum. Doubts are cast also on the supposed failure of Schrodinger's theory to explain the properties of atoms in presence of magnetic fields without introducing spin variables.
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arxiv:quant-ph/0305137
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By using local quantum teleportation of a fixed state to one qubit of an entangled pair sent from the other party, it is shown how one party can commit a bit with only classical information as evidence that results in an unconditionally secure protocol. The well-known ``impossibility proof'' does not cover such protocols due to its different commitment and opening prescriptions, which necessitate actual quantum measurements among different possible systems that cannot be entangled as a consequence.
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arxiv:quant-ph/0305142
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We describe a scheme for producing an optical nonlinearity using an interaction with one or more ancilla two-level atomic systems. The nonlinearity, which can be implemented using high efficiency fluorescence shelving measurements, together with general linear transformations is sufficient for simulating arbitrary Hamiltonian evolution on a Fock state qudit. We give two examples of the application of this nonlinearity, one for the creation of nonlinear phase shifts on optical fields as required in single photon quantum computation schemes, and the other for the preparation of optical Schrodinger cat states.
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arxiv:quant-ph/0305167
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Some PT-symmetric non-hermitean Hamiltonians have only real eigenvalues. There is numerical evidence that the associated PT-invariant energy eigenstates satisfy an unconventional completeness relation. An ad hoc scalar product among the states is positive definite only if a recently introduced `charge operator' is included in its definition. A simple derivation of the conjectured completeness and orthonormality relations is given. It exploits the fact that PT-symmetry provides an additional link between the eigenstates of the Hamiltonian and those of its adjoint, which form a dual pair of bases. The `charge operator' emerges naturally upon expressing the properties of the dual bases in terms of one basis only.
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arxiv:quant-ph/0306040
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Recently, it has been observed that the effective dipolar interactions between nuclear spins of spin-carrying molecules of a gas in a closed nano-cavities are independent of the spacing between all spins. We derive exact time-dependent polarization for all spins in spin-1/2 ensemble with spatially independent effective dipolar interactions. If the initial polarization is on a single (first) spin,$P_1(0)= 1$ then the exact spin dynamics of the model is shown to exhibit a periodical short pulses of the polarization of the first spin, the effect being typical of the systems having a large number, $N$, of spins. If $N \gg 1$, then within the period $4\pi/g$ ($2\pi/g$) for odd (even) $N$-spin clusters, with $g$ standing for spin coupling, the polarization of spin 1 switches quickly from unity to the time independent value, 1/3, over the time interval about $(g\sqrt{N})^{-1}$, thus, almost all the time, the spin 1 spends in the time independent condition $P_1(t)= 1/3$. The period and the width of the pulses determine the volume and the form-factor of the ellipsoidal cavity. The formalism is adopted to the case of time varying nano-fluctuations of the volume of the cavitation nano-bubbles. If the volume $V(t)$ is varied by the Gaussian-in-time random noise then the envelope of the polarization peaks goes irreversibly to 1/3. The polarization dynamics of the single spin exhibits the Gaussian (or exponential) time dependence when the correlation time of the fluctuations of the nano-volume is larger (or smaller) than the $<(\delta g)^2 >^{-1/2} $, where the $<(\delta g)^2>$ is the variance of the $g(V(t))$ coupling. Finally, we report the exact calculations of the NMR line shape for the $N$-spin gaseous aggregate.
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arxiv:quant-ph/0306055
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Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as criteria for the validity of quantum mechanics.
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arxiv:quant-ph/0306092
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We report on experiments with cold thermal $^7$Li atoms confined in combined magnetic and electric potentials. A novel type of three-dimensional trap was formed by modulating a magnetic guide using electrostatic fields. We observed atoms trapped in a string of up to six individual such traps, a controlled transport of an atomic cloud over a distance of 400$\mu$m, and a dynamic splitting of a single trap into a double well potential. Applications for quantum information processing are discussed.
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arxiv:quant-ph/0306111
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In the King's Problem, a physicist is asked to prepare a d-state quantum system in any state of her choosing and give it to a king who measures one of (d+1) sets of mutually unbiased observables on it. The physicist is then allowed to make a control measurement on the system, following which the king reveals which set of observables he measured and challenges the physicist to predict correctly all the eigenvalues he found. This paper obtains an upper bound on the physicist's probability of success at this task if she is allowed to make measurements only on the system itself (the "conventional" solution) and not on the system as well as any ancillary systems it may have been coupled to in the preparation phase, as in the perfect solutions proposed recently. An optimal conventional solution, with a success probability of 0.7, is constructed in d = 4; this is to be contrasted with the success probability of 0.902 for the optimal conventional solution in d = 2. The gap between the best conventional solution and the perfect solution grows quite rapidly with increasing d.
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arxiv:quant-ph/0306119
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We study the mathematical structure of superoperators describing quantum measurements, including the \emph{entangling measurement}--the generalization of the standard quantum measurement that results in entanglement between the measurable system and apparatus. It is shown that the coherent information can be effectively used for the analysis of such entangling measurements whose possible applications are discussed as well.
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arxiv:quant-ph/0306120
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