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The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system, whose hamiltonian is identical to the adjacency matrix of a circulant graph, is periodic if and only if all eigenvalues of the graph are integers (that is, the graph is integral). Motivated by this observation, we focus on relevant properties of integral circulant graphs. Specifically, we bound the number of vertices of integral circulant graphs in terms of their degree, characterize bipartiteness and give exact bounds for their diameter. Additionally, we prove that circulant graphs with odd order do not allow perfect state transfer.
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arxiv:quant-ph/0703236
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Coherent control of bound state processes via the interfering overlapping resonances scenario [Christopher et al., J. Chem. Phys. 123, 064313 (2006)] is developed to control intramolecular vibrational redistribution (IVR). The approach is applied to the flow of population between bonds in a model of chaotic OCS vibrational dynamics, showing the ability to significantly alter the extent and rate of IVR by varying quantum interference contributions.
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arxiv:quant-ph/0703263
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We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the encoding, recovery, or both, and is amenable to approximations that significantly improve computational cost while retaining fidelity. We illustrate our theory numerically for optimized 5-qubit codes, using the standard [5,1,3] code as a benchmark. Our optimized encoding and recovery yields fidelities that are uniformly higher by 1-2 orders of magnitude against random unitary weight-2 errors compared to the [5,1,3] code with standard recovery. We observe similar improvement for a 4-qubit decoherence-free subspace code.
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arxiv:quant-ph/0703274
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Comment on [R.L. Ingraham, Phys. Rev. A 50, 4502 (1994)]. Ingraham suggested ``a delayed-choice experiment with partial, controllable memory erasing''. It is shown that he cannot be right since his predictions contradict relativistic causality. A subtle quantum effect which was overlooked by Ingraham is explained.
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arxiv:quant-ph/9501006
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We prove a powerful scaling property for the extremality condition in the recently developed variational perturbation theory which converts divergent perturbation expansions into exponentially fast convergent ones. The proof is given for the energy eigenvalues of an anharmonic oscillator with an arbitrary $x^p$-potential. The scaling property greatly increases the accuracy of the results.
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arxiv:quant-ph/9502018
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The self-similar representation for the Schr\"{o}dinger equation is derived.
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arxiv:quant-ph/9505013
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We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates.
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arxiv:quant-ph/9505018
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We consider the decoherence of phase space histories in a class of quantum Brownian motion models, consisting of a particle moving in a potential $V(x)$ in interaction with a heat bath at temperature $T$ and dissipation gamma, in the Markovian regime. The evolution of the density operator for this open system is thus described by a non-unitary master equation. The phase space histories of the system are described by a class of quasiprojectors. Generalizing earlier results of Hagedorn and Omn\`es, we show that a phase space projector onto a phase space cell $\Gamma$ is approximately evolved under the master equation into another phase space projector onto the classical dissipative evolution of $\Gamma$, and with a certain amount of degradation due to the noise produced by the environment. We thus show that histories of phase space samplings approximately decohere, and that the probabilities for these histories are peaked about classical dissipative evolution, with a width of peaking depending on the size of the noise.
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arxiv:quant-ph/9506031
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Classical mechanics is based upon a mechanical picture of nature that is fundamentally incorrect. It has been replaced at the basic level by a radically different theory: quantum mechanics. This change entails an enormous shift in our basic conception of nature, one that can profoundly alter the scientific image of man himself. Self-image is the foundation of values, and the replacement of the mechanistic self-image derived from classical mechanics by one concordant with quantum mechanics may provide the foundation of a moral order better suited to our times, a self-image that endows human life with meaning, responsibility, and a deeper linkage to nature as a whole.
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arxiv:quant-ph/9506035
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Schr\"odinger's cat puzzle is resolved. The reason why we do not see a macroscopic superposition of states is cleared in the light of Everett's formulation of quantum mechanics.
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arxiv:quant-ph/9506042
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In a recent review paper [{\em Phys. Reports} {\bf 214} (1992) 339] we proposed, within conventional quantum mechanics, new definitions for the sub-barrier tunnelling and reflection times. \ Aims of the present paper are: \ (i) presenting and analysing the results of various numerical calculations (based on our equations) on the penetration and return times $<\tau_{\, \rm Pen}>$, $<\tau_{\, \rm Ret}>$, during tunnelling {\em inside} a rectangular potential barrier, for various penetration depths $x_{\rm f}$; \ (ii) putting forth and discussing suitable definitions, besides of the mean values, also of the {\em variances} (or dispersions) ${\rm D} \, {\tau_{\rm T}}$ and ${\rm D} \, {\tau_{\, \rm R}}$ for the time durations of transmission and reflection processes; \ (iii) mentioning, moreover, that our definition $<\tau_{\rm T}>$ for the average transmission time results to constitute an {\em improvement} of the ordinary dwell--time ${\ove \tau}^{\rm Dw}$ formula: \ (iv) commenting, at last, on the basis of our {\em new} numerical results, upon some recent criticism by C.R.Leavens. \ \ We stress that our numerical evaluations {\em confirm} that our approach implied, and implies, the existence of the {\em Hartman effect}: an effect that in these days (due to the theoretical connections between tunnelling and evanescent--wave propagation) is receiving ---at Cologne, Berkeley, Florence and Vienna--- indirect, but quite interesting, experimental verifications. \ Eventually, we briefly analyze some other definitions of tunnelling times.
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arxiv:quant-ph/9508010
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We solve the higher order equations of the theory of the strong perturbations in quantum mechanics given in M. Frasca, Phys. Rev. A 45, 43 (1992), by assuming that, at the leading order, the wave function goes adiabatically. This is accomplished by deriving the unitary operator of adiabatic evolution for the leading order. In this way it is possible to show that at least one of the causes of the problem of phase-mixing, whose effect is the polynomial increase in time of the perturbation terms normally called secularities, arises from the shifts of the perturbation energy levels due to the unperturbed part of the hamiltonian. An example is given for a two-level system that, anyway, shows a secularity at second order also in the standard theory of small perturbations. The theory is applied to the quantum analog of a classical problem that can become chaotic, a particle under the effect of two waves of different amplitudes, frequencies and wave numbers.
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arxiv:quant-ph/9508023
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The interaction of a trapped ion with a laser beam in the strong excitation regime is analyzed. In this regime, a variety of non--classical states of motion can be prepared either by using laser pulses of well defined area, or by an adiabatic passage scheme based on the variation of the laser frequency. We show how these states can be used to investigate fundamental properties of quantum mechanics. We also study possible applications of this system to build an ion interferometer.
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arxiv:quant-ph/9509007
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The theory of quantum propagator and time--dependent integrals of motion in quantum optics is reviewed as well as the properties of Wigner function, Q--function, and coherent state representation. Propagators and wave functions of a free particle, harmonic oscillator, and the oscillator with varying frequency are studied using time--dependent linear in position and momentum integrals of motion. Such nonclassical states of light (of quantum systems) as squeezed states, correlated states, even and odd coherent states (Schr\"odinger cat states) are considered. Photon distribution functions of Schr\"odinger cat male and female states are given, and the photon distribution function of squeezed vacuum is derived using the theory of the oscillator with varying parameters. Properties of multivariable Hermite polynomials used for the description of the multimode squeezed and correlated light and polymode Schr\"odinger cats are studied.
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arxiv:quant-ph/9509018
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In previous works Suppes and de Barros used a pure particle model to derive interference effects, where individual photons have well-defined trajectories, and hence no wave properties. In the present paper we extend that description to account for the Casimir effect. We consider that the linear momentum $\sum\frac{1}{2}\hbar {\bf k}$ of the vacuum state in quantum electrodynamics corresponds to the linear momentum of virtual photons. The Casimir effect, in the cases of two parallel plates and the solid ball, is explained in terms of the pressure caused by the photons. Contrary to quantum electrodynamics, we assume a finite number of virtual photons.
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arxiv:quant-ph/9510010
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A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n = 1 - 2H(2t/n) where H(p) is the binary entropy function -p log p - (1-p) log (1-p). Upper bounds on this asymptotic rate are given.
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arxiv:quant-ph/9512032
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In the context of the decoherent histories approach to the quantum mechanics of closed systems, Gell-Mann and Hartle have argued that the variables typically characterizing the quasiclassical domain of a large complex system are the integrals over small volumes of locally conserved densities -- hydrodynamic variables. The aim of this paper is to exhibit some simple models in which approximate decoherence arises as a result of local conservation. We derive a formula which shows the explicit connection between local conservation and approximate decoherence. We then consider a class of models consisting of a large number of weakly interacting components, in which the projections onto local densities may be decomposed into projections onto one of two alternatives of the individual components. The main example we consider is a one-dimensional chain of locally coupled spins, and the projections are onto the total spin in a subsection of the chain. We compute the decoherence functional for histories of local densities, in the limit when the number of components is very large. We find that decoherence requires two things: the smearing volumes must be sufficiently large to ensure approximate conservation, and the local densities must be partitioned into sufficiently large ranges to ensure protection against quantum fluctuations.
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arxiv:quant-ph/9601004
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We consider a class of models describing a quantum oscillator in interaction with an environment. We show that models of continuous spontaneous localization based on a stochastic Schr\"odinger equation can be derived as an approximation to purely deterministic Hamiltonian systems. We show an exponential decay of off-diagonal matrix elements in the energy representation.
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arxiv:quant-ph/9601010
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In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's "measurement probabilities" \it are \rm the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability measure of the process to follow the quantally implemented (via the Born statistical postulate) evolution, then we arrive at the jump process which \it can \rm be interpreted as a Markov process if restricted to a suitable duration time. However, there is no corresponding Markov process consistent with the $Z_2$ event space assumption, if we require its existence for all times $t\in R_+$.
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arxiv:quant-ph/9601016
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We propose a scheme for generating vibrational pair coherent states of the motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is excited bichromatically by three laser beams along different directions in the X-Y plane of the ion trap. We show that if the initial vibrational state is given by a two-mode Fock state, the final steady state, indicated by the extinction of the fluorescence emitted by the ion, is a pure state. The motional state of the ion in the equilibrium realizes that of the highly-correlated pair coherent state.
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arxiv:quant-ph/9604010
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The concepts of the perfect system and degeneracy are introduced. A special symmetry is found which is related to the entropy invariant. The inversion relation of system is obtained which is used to give the oppsite direction of time to classical sencond law of thermodanymics. The nature of time is discussed together with causality relation. A new understanding of quantum mechanics is put forward which describes a new picture of the world.
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arxiv:quant-ph/9605019
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There had been well known claims of ``provably unbreakable'' quantum protocols for bit commitment and coin tossing. However, we, and independently Mayers, showed that all proposed quantum bit commitment (and therefore coin tossing) schemes are, in principle, insecure because the sender, Alice, can always cheat successfully by using an EPR-type of attack and delaying her measurements. One might wonder if secure quantum bit commitment and coin tossing protocols exist at all. Here we prove that an EPR-type of attack by Alice will, in principle, break {\em any} realistic quantum bit commitment and {\em ideal} coin tossing scheme. Therefore, provided that Alice has a quantum computer and is capable of storing quantum signals for an arbitrary length of time, all those schemes are insecure. Since bit commitment and coin tossing are useful primitives for building up more sophisticated protocols such as zero-knowledge proofs, our results cast very serious doubt on the security of quantum cryptography in the so-called ``post-cold-war'' applications.
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arxiv:quant-ph/9605026
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Quantum theory for measurements of energy is introduced and its consequences for the average position of monitored dynamical systems are analyzed. It turns out that energy measurements lead to a localization of the expectation values of other observables. This is manifested, in the case of position, as a damping of the motion without classical analogue. Quantum damping of position for an atom bouncing on a reflecting surface in presence of a homogeneous gravitational field is dealt in detail and the connection with an experiment already performed in the classical regime is studied. We show that quantum damping is testable provided that the same measurement strength obtained in the experimental verification of the quantum Zeno effect in atomic spectroscopy [W. M. Itano et al., Phys. Rev. A {\bf 41}, 2295 (1990)] is made available.
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arxiv:quant-ph/9606024
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We give a quantum algorithm to find the index y in a table T of size N such that in time O(c sqrt N), T[y] is minimum with probability at least 1-1/2^c.
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arxiv:quant-ph/9607014
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After a careful analysis of the feedback model recently proposed by Slosser and Milburn [Phys. Rev. Lett. 75, 418 (1995)], we are led to the conclusion that---under realistic conditions---their scheme is not significantly more effective in the production of linear superpositions of macroscopically distinguishable quantum states than the usual quantum-optical Kerr effect.
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arxiv:quant-ph/9607028
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Quantum trajectory methods can be used for a wide range of open quantum systems to solve the master equation by unraveling the density operator evolution into individual stochastic trajectories in Hilbert space. This C++ class library offers a choice of integration algorithms for three important unravelings of the master equation. Different physical systems are modeled by different Hamiltonians and environment operators. The program achieves flexibility and user friendliness, without sacrificing execution speed, through the way it represents operators and states in Hilbert space. Primary operators, implemented in the form of simple routines acting on single degrees of freedom, can be used to build up arbitrarily complex operators in product Hilbert spaces with arbitrary numbers of components. Standard algebraic notation is used to build operators and to perform arithmetic operations on operators and states. States can be represented in a local moving basis, often leading to dramatic savings of computing resources. The state and operator classes are very general and can be used independently of the quantum trajectory algorithms. Only a rudimentary knowledge of C++ is required to use this package.
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arxiv:quant-ph/9608004
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Interpretational questions that arise in the Consistent Histories formulation of quantum mechanics are illustrated by the familiar example of a beam passing through multiple slits.
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arxiv:quant-ph/9608007
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We perform a systematic WKB expansion to all orders for a one-dimensional system with potential $V(x)=U_0/\cos^2{(\alpha x)}$. We are able to sum the series to the exact energy spectrum. Then we show that at any finite order the error of the WKB approximation measured in the natural units of the mean energy level spacing does not go to zero when the quantum number goes to infinity. Therefore we make the general conclusion that the semiclassical approximations fail to predict the individual energy levels within a vanishing fraction of the mean energy level spacing.
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arxiv:quant-ph/9610027
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Quantum mechanics is nonlocal. Classical mechanics is local. Consequently classical mechanics can not explain all quantum phenomena. Conversely, it is cumbersome to use quantum mechanics to describe classical phenomena. Not only are the computations more complex, but - and this is the main point - it is conceptually more difficult: one has to argue that nonlocality, entanglement and the principle of superposition can be set aside when crossing the "quantum $\rightarrow$ classical" border. Clearly, nonlocality, entanglement and the principle of superposition should become irrelevant in the classical limit. But why should one argue? Shouldn't it just come out of the equations? Does it come out of the equations? This contribution is about the last question. And the answer is: "it depends on which equation".
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arxiv:quant-ph/9611002
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Classical lattice gas automata effectively simulate physical processes such as diffusion and fluid flow (in certain parameter regimes) despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined quantum lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can effectively simulate. Studying the single particle sector of a one dimensional quantum lattice gas we find discrete analogues of plane waves and wave packets, and then investigate their behaviour in the presence of inhomogeneous potentials.
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arxiv:quant-ph/9611005
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We consider a driven damped anharmonic oscillator which classically leads to a bistable steady state and to hysteresis. The quantum counterpart for this system has an exact analytical solution in the steady state which does not display any bistability or hysteresis. We use quantum state diffusion theory to describe this system and to provide a new perspective on the lack of hysteresis in the quantum regime so as to study in detail the quantum to classical transition. The analysis is also relevant to measurements of a single periodically driven electron in a Penning trap where hysteresis has been observed.
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arxiv:quant-ph/9611044
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The quantum theory of ur-objects proposed by C. F. von Weizsaecker has to be interpreted as a quantum theory of information. Ur-objects, or urs, are thought to be the simplest objects in quantum theory. Thus an ur is represented by a two-dimensional Hilbert space with the universal symmetry group SU(2), and can only be characterized as ''one bit of potential information''. In this sense it is not a spatial but an ''information atom''. The physical structure of the ur theory is reviewed, and the philosophical consequences of its interpretation as an information theory are demonstrated by means of some important concepts of physics such as time, space, entropy, energy, and matter, which in ur theory appear to be directly connected with information as ''the'' fundamental substance. This hopefully will help to provide a new understanding of the concept of information.
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arxiv:quant-ph/9611048
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It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first)- class constraints.
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arxiv:quant-ph/9611051
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We consider the Bennett-Brassard cryptographic scheme, which uses two conjugate quantum bases. An eavesdropper who attempts to obtain information on qubits sent in one of the bases causes a disturbance to qubits sent in the other basis. We derive an upper bound to the accessible information in one basis, for a given error rate in the conjugate basis. Independently fixing the error rate in the conjugate bases, we show that both bounds can be attained simultaneously by an optimal eavesdropping probe, consisting of two qubits. The qubits' interaction and their subsequent measurement are described explicitly. These results are combined to give an expression for the optimal information an eavesdropper can obtain for a given average disturbance when her interaction and measurements are performed signal by signal. Finally, the relation between quantum cryptography and violations of Bell's inequalities is discussed.
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arxiv:quant-ph/9701039
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It is shown that the optimum strategy of the eavesdropper, as described in the preceding paper, can be expressed in terms of a quantum circuit in a way which makes it obvious why certain parameters take on particular values, and why obtaining information in one basis gives rise to noise in the conjugate basis.
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arxiv:quant-ph/9702015
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We describe an effective field theory for atomic lasers which reduces to the Jaynes-Cummings model in the non-relativistic, single mode limit. Our action describes a multi-mode system, with general polarizations and Lorentz invariance and can therefore be used in all contexts from the astrophysical to the laboratory. We show how to compute the effective action for this model and perform the calculation explicitly at the one loop level. Our model provides a way of analyzing a many-particle, two-state model with arbitrary boundary conditions.
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arxiv:quant-ph/9703015
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Quasi-exactly solvable rational potentials with known zero-energy solutions of the Schro\" odinger equation are constructed by starting from exactly solvable potentials for which the Schr\" odinger equation admits an so(2,1) potential algebra. For some of them, the zero-energy wave function is shown to be normalizable and to describe a bound state.
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arxiv:quant-ph/9703037
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In classical mechanics, the system of two coupled harmonic oscillators is shown to possess the symmetry of the Lorentz group O(3,3) applicable to a six-dimensional space consisting of three space-like and three time-like coordinates, or SL(4,r) in the four-dimensional phase space consisting of two position and two momentum variables. In quantum mechanics, the symmetry is reduced to that of O(3,2) or Sp(4), which is a subgroup of O(3,3) or SL(4,r) respectively. It is shown that among the six Sp(4)-like subgroups, only one possesses the symmetry which can be translated into the group of unitary transformations in quantum mechanics. In quantum mechanics, there is the lower bound in the size of phase space for each mode determined by the uncertainty principle while there are no restriction on the phase-space size in classical mechanics. This is the reason why the symmetry is smaller in quantum mechanics.
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arxiv:quant-ph/9704005
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A model of a system driven by quantum white noise with singular quadratic self--interaction is considered and an exact solution for the evolution operator is found. It is shown that the renormalized square of the squeezed classical white noise is equivalent to the quantum Poisson process. We describe how equations driven by nonlinear functionals of white noise can be derived in nonlinear quantum optics by using the stochastic approximation.
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arxiv:quant-ph/9704029
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We derive Gamow vectors from S-matrix poles of higher multiplicity in analogy to the Gamow vectors describing resonances from first-order poles. With these vectors we construct a density operator that describes resonances associated with higher order poles that obey an exponential decay law. It turns out that this operator formed by these higher order Gamow vectors has a unique structure.
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arxiv:quant-ph/9705013
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We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.
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arxiv:quant-ph/9705019
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We present Quantum Cloning Machines (QCM) that transform N identical qubits into $M>N$ identical copies and we prove that the fidelity (quality) of these copies is optimal. The connection between cloning and measurement is discussed in detail. When the number of clones M tends towards infinity, the fidelity of each clone tends towards the optimal fidelity that can be obtained by a measurement on the input qubits. More generally, the QCM are universal devices to translate quantum information into classical information.
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arxiv:quant-ph/9705046
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A model for the coherent output coupler of the Bose-Einstein condensed atoms from a trap in the recent MIT experiment (Phys. Rev. Lett., 78 (1997) 582) is established with a simple many-boson system of two states with linear coupling. Its exact solution for the many-body problem shows a factorization of dynamical evolution process, i.e., the wave function initially prepared in a direct product of a vacuum state and a coherent state remains in a direct product of two coherent states at any instance in the evolution of the total system. This conclusion always holds even for a system with a finite average particle number in the initial state. Its thermodynamical limit can be directly dealt with in the Bogoliubov approximation and manifests that an ideal condensate in the trap will remain in a coherent state after the r.f. interaction while the output-coupler pulse of atoms is also in a coherent state, which means a coherent output of atomic beam to form a macroscopic quantum state in a propagating mode.
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arxiv:quant-ph/9706041
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We discuss a scheme for generation of single-mode photon states associated with the two-photon realization of the SU(1,1) algebra. This scheme is based on the process of non-degenerate down-conversion with the signal prepared initially in the squeezed vacuum state and with a measurement of the photon number in one of the output modes. We focus on the generation and properties of single-mode SU(1,1) intelligent states which minimize the uncertainty relations for Hermitian generators of the group. Properties of the intelligent states are studied by using a ``weak'' extension of the analytic representation in the unit disk. Then we are able to obtain exact analytical expressions for expectation values describing quantum statistical properties of the SU(1,1) intelligent states. Attention is mainly devoted to the study of photon statistics and linear and quadratic squeezing.
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arxiv:quant-ph/9707009
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The differential structure of operator bases used in various forms of the Weyl-Wigner-Groenewold-Moyal (WWGM) quantization is analyzed and a derivative-based approach, alternative to the conventional integral-based one is developed. Thus the fundamental quantum relations follow in a simpler and unified manner. An explicit formula for the ordered products of the Heisenberg-Weyl algebra is obtained. The W(infty) -covariance of the WWGM-quantization in its most general form is established. It is shown that the group action of W(infty) that is realized in the classical phase space induces on bases operators in the corresponding Hilbert space a similarity transformation generated by the corresponding quantum W(infty) which provides a projective representation of the former $W_{\infty}$. Explicit expressions for the algebra generators in the classical phase space and in the Hilbert space are given. It is made manifest that this W(infty)-covariance of the WWGM-quantization is a genuine property of the operator bases.
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arxiv:quant-ph/9707040
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In this paper we give a quantum mechanical algorithm that can search a database by a single query, when the number of solutions is more than a quarter. It utilizes modified Grover operator of arbitrary phase.
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arxiv:quant-ph/9708005
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A method to study weakly bound three-body quantum systems in two dimensions is formulated in coordinate space for short-range potentials. Occurrences of spatially extended structures (halos) are investigated. Borromean systems are shown to exist in two dimensions for a certain class of potentials. An extensive numerical investigation shows that a weakly bound two-body state gives rise to two weakly bound three-body states, a reminiscence of the Efimov effect in three dimensions. The properties of these two states in the weak binding limit turn out to be universal. PACS number(s): 03.65.Ge, 21.45.+v, 31.15.Ja, 02.60Nm
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arxiv:quant-ph/9708025
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It is shown that the exponential moments of the canonical phase can be directly sampled from the data recorded in balanced homodyne detection. Analytical expressions for the sampling functions are derived, which are valid for arbitrary states and bridge the gap between quantum and classical phase. The reconstruction of the canonical phase distribution from the experimentally determined exponential moments is discussed.
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arxiv:quant-ph/9708039
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A non-linear quantum state transformation is presented. The transformation, which operates on pairs of spin-1/2, can be used to distinguish optimally between two non-orthogonal states. Similar transformations applied locally on each component of an entangled pair of spin-1/2 can be used to transform a mixed nonlocal state into a quasi-pure maximally entangled singlet state. In both cases the transformation makes use of the basic building block of the quantum computer, namely the quantum-XOR gate.
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arxiv:quant-ph/9708040
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A model for quantum Zeno effect based upon an effective Schr\"odinger equation originated by the path-integral approach is developed and applied to a two-level system simultaneously stimulated by a resonant perturbation. It is shown that inhibition of stimulated transitions between the two levels appears as a consequence of the influence of the meter whenever measurements of energy, either continuous or pulsed, are performed at quantum level of sensitivity. The generality of this approach allows to qualitatively understand the inhibition of spontaneous transitions as the decay of unstable particles, originally presented as a paradox of quantum measurement theory.
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arxiv:quant-ph/9709003
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A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the cases of a harmonic oscillator, a bistable potential and two coupled systems, briefly illustrating their applications.
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arxiv:quant-ph/9709004
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We present a canonical formalism facilitating investigations of the dynamical Casimir effect by means of a response theory approach. We consider a massless scalar field confined inside of an arbitaray domain $G(t)$, which undergoes small displacements for a certain period of time. Under rather general conditions a formula for the number of created particles per mode is derived. The pertubative approach reveals the occurance of two generic processes contributing to the particle production: the squeezing of the vacuum by changing the shape and an acceleration effect due to motion af the boundaries. The method is applied to the configuration of moving mirror(s). Some properties as well as the relation to local Green function methods are discussed. PACS-numbers: 12.20; 42.50; 03.70.+k; 42.65.Vh Keywords: Dynamical Casimir effect; Moving mirrors; Cavity quantum field theory; Vibrating boundary;
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arxiv:quant-ph/9709008
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Quantum mechanics permits nonlocality - both nonlocal correlations and nonlocal equations of motion - while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality: "superquantum" correlations, and nonlocal "jamming" of correlations. These models are consistent with some definitions of nonlocality and causality.
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arxiv:quant-ph/9709026
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The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as generating a Hamiltonian dynamics. Based upon the geometric structure of the quantum phase space we introduce the corresponding natural microcanonical and canonical ensembles. The resulting density matrix for the canonical ensemble differs from density matrix of the conventional approach. As an illustration, the results are applied to the case of a spin one-half particle in a heat bath with an applied magnetic field.
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arxiv:quant-ph/9709048
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It is predicted that in force microscopy the quantum fluctuations responsible for the Casimir force can be directly observed as temperature-independent force fluctuations having spectral density $9\pi/(40\ln(4/e)) \hbar \delta k$, where $\hbar$ is Planck's constant and $\delta k$ is the observed change in spring constant as the microscope tip approaches a sample. For typical operating parameters the predicted force noise is of order $10^{-18}$ Newton in one Hertz of bandwidth. The Second Law is respected via the fluctuation-dissipation theorem. For small tip-sample separations the cantilever damping is predicted to increase as temperature is reduced, a behavior that is reminiscent of the Kondo effect.
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arxiv:quant-ph/9710017
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Two aspects of the physical side of the Church-Turing thesis are discussed. The first issue is a variant of the Eleatic argument against motion, dealing with Zeno squeezed time cycles of computers. The second argument reviews the issue of one-to-one computation, that is, the bijective (unique and reversible) evolution of computations and its relation to the measurement process.
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arxiv:quant-ph/9710052
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This is an "Essay-Review" of a book with the same title, by Jeffrey Bub (Cambridge University Press, 1997).
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arxiv:quant-ph/9711003
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This paper addresses the three following questions. (i) How the structures of group and of chain of groups enter nuclear, atomic and molecular spectroscopy? (ii) How these structures can be exploited, in a quantum- mechanical framework, in the problems of state labelling and (external) symmetry breaking? (iii) How it is possible to associate a Wigner-Racah algebra to a group or a chain of groups for making easier the calculation of quantum-mechanical matrix elements? Numerous examples illustrate the philosophy of qualitative and quantitative applications to spectroscopy.
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arxiv:quant-ph/9711007
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Two important classes of the quantum statistical model, the locally quasi-classical model and the quasi-classical model, are introduced from the estimation theoretical viewpoint, and they are characterized geometrically by the vanishing conditions of the relative phase factor (RPF), implying the close tie between Uhlmann parallel transport and the quantum estimation theory.
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arxiv:quant-ph/9711027
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We show that no source encoding is needed in the definition of the capacity of a quantum channel for carrying quantum information. This allows us to use the coherent information maximized over all sources and and block sizes, but not encodings, to bound the quantum capacity. We perform an explicit calculation of this maximum coherent information for the quantum erasure channel and apply the bound in order find the erasure channel's capacity without relying on an unproven assumption as in an earlier paper.
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arxiv:quant-ph/9711032
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Just at the beginning of quantum stochastic calculus Hudson and Parthasarathy proposed a quantum stochastic Schrodinger equation linked to dilations of quantum dynamical semigroups. Such an equation has found applications in physics, mainly in quantum optics, but not in its full generality. It has been used to give, at least approximately, the dynamics of photoemissive sources such as an atom absorbing and emitting light or matter in an optical cavity, which exchanges light with the surrounding free space. But in these cases the possibility of introducing the gauge (or number) process in the dynamical equation has not been considered. In this paper we show, in the case of the simplest photoemissive source, namely a two-level atom stimulated by a laser, how the full Hudson-Parthasarathy equation allows to describe in a consistent way not only absorption and emission, but also the elastic scattering of the light by the atom. Morever, we study the differential and total cross sections for the scattering of laser light by the atom, as a function of the frequency of the stimulating laser. The resulting line-shape is very interesting. Not only a Lorentzian shape is permitted, but the full variety of Fano profiles can be obtained. The dependence of the line shape on the intensity of the stimulating laser is computed; in particular, the resonance position turns out to be intensity dependent, a phenomenon known as lamp shift.
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arxiv:quant-ph/9711050
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The method of phenomenological damping developed by Pitaevskii for superfluidity near the $\lambda$ point is simulated numerically for the case of a dilute, alkali, inhomogeneous Bose-condensed gas near absolute zero. We study several features of this method in describing the damping of excitations in a Bose-Einstein condensate. In addition, we show that the method may be employed to obtain numerically accurate ground states for a variety of trap potentials.
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arxiv:quant-ph/9801064
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As far as entanglement is concerned, two density matrices of $n$ particles are equivalent if they are on the same orbit of the group of local unitary transformations, $U(d_1)\times...\times U(d_n)$ (where the Hilbert space of particle $r$ has dimension $d_r$). We show that for $n$ greater than or equal to two, the number of independent parameters needed to specify an $n$-particle density matrix up to equivalence is $\Pi_r d_r^2 - \sum_r d_r^2 + n - 1$. For $n$ spin-${1\over 2}$ particles we also show how to characterise generic orbits, both by giving an explicit parametrisation of the orbits and by finding a finite set of polynomial invariants which separate the orbits.
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arxiv:quant-ph/9801076
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Without addressing the measurement problem (i.e. what causes the wave function to ``collapse'', or to ``branch'', or a history to become realized, or a property to actualize), I discuss the problem of the timing of the quantum measurement: assuming that in an appropriate sense a measurement happens, when precisely does it happen? This question can be posed within most interpretations of quantum mechanics. By introducing the operator M, which measures whether or not the quantum measurement has happened, I suggest that, contrary to what is often claimed, quantum mechanics does provide a precise answer to this question, although a somewhat surprising one.
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arxiv:quant-ph/9802020
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Non dispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states and show that the elastic incoherent component (occuring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single photon emissions and the associated rates in the "harmonic approximation", i.e. when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum mechanical calculations, which validates the analytical approach.
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arxiv:quant-ph/9802027
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The environment -- external or internal degrees of freedom coupled to the system -- can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states: Continuous destruction of superpositions leads to environment-induced superselection (einselection). Here I investigate it in the context of quantum chaos (i. e., quantum dynamics of systems which are classically chaotic).
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arxiv:quant-ph/9802054
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Continuous unitary transformations can be used to diagonalize or approximately diagonalize a given Hamiltonian. In the last four years, this method has been applied to a variety of models of condensed matter physics and field theory. With a new generator for the continuous unitary transformation proposed in this paper one can avoid some of the problems of former applications. General properties of the new generator are derived. It turns out that the new generator is especially useful for Hamiltonians with a banded structure. Two examples, the Lipkin model, and the spin--boson model are discussed in detail.
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arxiv:quant-ph/9803040
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The concept of experimental accuracy is investigated in the context of the unbiased joint measurement processes defined by Arthurs and Kelly. A distinction is made between the errors of retrodiction and prediction. Four error-disturbance relationships are derived, analogous to the single error-disturbance relationship derived by Braginsky and Khalili in the context of single measurements of position only. A retrodictive and a predictive error-error relationship are also derived. The connection between these relationships and the extended Uncertainty Principle of Arthurs and Kelly is discussed. The similarities and differences between the quantum mechanical and classical concepts of experimental accuracy are explored. It is argued that these relationships provide grounds for questioning Uffink's conclusion, that the concept of a simultaneous measurement of non-commuting observables is not fruitful.
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arxiv:quant-ph/9803046
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The recent model of Quantum Mechanical Black Holes is discussed and its implications for cosmology, particle structure, low dimensionality and other issues are examined.
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arxiv:quant-ph/9803048
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A relationship between the time scales of quantum coherence loss and short-time solvent response for a solute/bath system is derived for a Gaussian wave packet approximation for the bath. Decoherence and solvent response times are shown to be directly proportional to each other, with the proportionality coefficient given by the ratio of the thermal energy fluctuations to the fluctuations in the system-bath coupling. The relationship allows the prediction of decoherence times for condensed phase chemical systems from well developed experimental methods.
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arxiv:quant-ph/9804004
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Interaction-free measurement is shown to arise from the forward-scattered wave accompanying absorption: a "quantum silhouette" of the absorber. Accordingly, the process is not free of interaction. For a perfect absorber the forward-scattered wave is locked both in amplitude and in phase. For an imperfect one it has a nontrivial phase of dynamical origin (``colored silhouette"), measurable by interferometry. Other examples of quantum silhouettes, all controlled by unitarity, are briefly discussed.
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arxiv:quant-ph/9804058
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Paper is withdrawn
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arxiv:quant-ph/9804068
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Suppose that a quantum source is known to have von Neumann entropy less than or equal to S but is otherwise completely unspecified. We describe a method of universal quantum data compression which will faithfully compress the quantum information of any such source to S qubits per signal (in the limit of large block lengths).
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arxiv:quant-ph/9805017
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The analytic properties of a class of generalized Husimi functions are discussed, with particular reference to the problem of state reconstruction. The class consists of the subset of Wodkiewicz's operational probability distributions for which the filter reference state is a squeezed vacuum state. The fact that the function is analytic means that perfectly precise knowledge of its values over any small region of phase space provides enough information to reconstruct the density matrix. If, however, one only has imprecise knowledge of its values, then the amplification of statistical errors which occurs when one attempts to carry out the continuation seriously limits the amount of information which can be extracted. To take account of this fact a distinction is made between explicate, or experimentally accessible information, and information which is only present in implicate, experimentally inaccessible form. It is shown that an explicate description of various aspects of the system can be found localised on various 2 real dimensional surfaces in complexified phase space. In particular, the continuation of the function to the purely imaginary part of complexified phase space provides an explicate description of the Wigner function.
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arxiv:quant-ph/9805054
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An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum reasoning together with the ``one framework'' rule prevents a logical contradiction, and there is no evidence for any mysterious nonlocal influences. Counterfactual reasoning can support a realistic interpretation of standard quantum theory (measurements reveal what is actually there) under appropriate circumstances.
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arxiv:quant-ph/9805056
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The Lindblad approach to continuous quantum measurements is applied to a system composed of a two-level atom interacting with a stationary quantized electromagnetic field through a dispersive coupling fulfilling quantum nondemolition criteria. Two schemes of measurements are examined. The first one consists in measuring the atomic electric dipole, which indirectly allows one to infer the photon distribution inside the cavity. The second one schematizes a measurement of photon momentum, which permits to describe the atomic level distribution. Decoherence of the corresponding reduced density matrices is studied in detail for both cases, and its relationship to recent experiments is finally discussed.
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arxiv:quant-ph/9805060
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Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically symmetric potential in two dimensions is re-established by the Sturm-Liouville theorem. The critical case, where the Schr\"{o}dinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison with Levinson's theorem in non-critical case, the half bound state for $P$ wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of $P$ wave at zero energy to increase an additional $\pi$.
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arxiv:quant-ph/9806004
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The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy for classical input and quantum output. In 1983, the autho r defined the fully quantum mechanical mutual entropy by means of the relati ve entropy of Umegaki, and he extended it to general quantum systems by the relative entropy of Araki and Uhlmann. When the author introduced the quantu m mutual entropy, he did not indicate that it contains other definitions of the mutual entropy including classical one, so that there exist several misu nderstandings for the use of the mutual entropy (information) to compute the capacity of quantum channels. Therefore in this note we point out that our quantum mutual entropy generalizes others and where the m isuse occurs.
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arxiv:quant-ph/9806042
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The connection between quantum optical nonclassicality and the violation of Bell's inequalities is explored. Bell type inequalities for the electromagnetic field are formulated for general states of quantised radiation and their violation is connected to other nonclassical properties of the field. This is achieved by considering states with an arbitrary number of photons and carefully identifying the hermitian operators whose expectation values do not admit any local hidden variable description. We relate the violation of these multi-photon inequalities to properties of phase space distribution functions such as the diagonal coherent state distribution function and the Wigner function. Finally, the family of 4-mode states with Gaussian Wigner distributions is analysed, bringing out in this case the connection of violation of Bell type inequalities with the nonclassical property of squeezing.
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arxiv:quant-ph/9806049
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We study the generation of photon pulses from thermal field fluctuations through opto-mechanical coupling to a cavity with an oscillatory motion. Pulses are regularly spaced and become sharp for a high finesse cavity.
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arxiv:quant-ph/9806062
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The Levinson theorem for nonrelativistic quantum mechanics in two spatial dimensions is generalized to Dirac particles moving in a central field. The theorem relates the total number of bound states with angular momentum $j$ ($j=\pm 1/2, \pm 3/2, ... $), $n_j$, to the phase shifts $\eta_j(\pm E_k)$ of scattering states at zero momentum as follows: $\eta_j(\mu)+\eta_j(-\mu)= n_j\pi$.
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arxiv:quant-ph/9806075
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We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer multiplication. The quick reader can just read the introduction and the ``Results'' section.
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arxiv:quant-ph/9806084
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We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy which always gives reward if played against any classical strategy.
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arxiv:quant-ph/9806088
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In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such query. It is shown that any decision problem that requires two parallel (non-adaptive) SAT-queries on a classical computer can also be solved exactly by a quantum computer using only one SAT-oracle call, where both computations have polynomial time-complexity. Such a simulation is generally believed to be impossible for a one-query classical computer. The reduction also does not hold if we replace the SAT-oracle by a general black-box. This result gives therefore an example of how a quantum computer is probably more powerful than a classical computer. It also highlights the potential differences between quantum complexity results for general oracles when compared to results for more structured tasks like the SAT-problem.
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arxiv:quant-ph/9806090
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We address the issue of the quantum-classical correspondence in chaotic systems using, as recently done by Zurek [e-print quant-ph/9802054], the solar system as a whole as a case study: this author shows that the classicality of the planetary motion is ensured by the environment-induced decoherence. We show that equivalent results are provided by the theories of spontaneous fluctuations and that these latter theories, in some cases, result in a still faster process of decoherence. We show that, as an additional benefit, the assumption of spontaneous fluctuation makes it possible to genuinely derive thermodynamics from mechanics, namely, without implicitly assuming thermodynamics.
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arxiv:quant-ph/9806092
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A currently discussed interpretation of quantum theory, Time-Symmetrized Quantum Theory, makes certain claims about the properties of systems between pre- and post- selection measurements. These claims are based on a counterfactual usage of the Aharonov-Bergmann-Lebowitz (ABL) rule for calculating the probabilities of measurement outcomes between such measurements. It has been argued by several authors that the counterfactual usage of the ABL rule is, in general, incorrect. This paper examines what might appear to be a loophole in those arguments and shows that this apparent loophole cannot be used to support a counterfactual interpretation of the ABL rule. It is noted that the invalidity of the counterfactual usage of the ABL rule implies that the characterization of those outcomes receiving probability 1 in a counterfactual application of the rule as `elements of reality' is, in general, unfounded.
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arxiv:quant-ph/9807015
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This paper has been withdrawn by the authors.
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arxiv:quant-ph/9807090
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Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.
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arxiv:quant-ph/9807092
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The question has been solved whether Bell's inequalities cover all possible kinds of hidden-variable theories. It has been shown that the given nequalities can be hardly derived when the changing space position of photon-pair source together with the microscopic space structure of measuring devices are taken into account; and when corresponding impact parameters (i.e., exact impact points) of photons in individual measuring devices (polarizers) influence measured values, in addition to usually considered characteristics.
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arxiv:quant-ph/9808005
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Bose-Einstein condensation of a relativistic ideal Bose gas in a rectangular cavity is studied. Finite size corrections to the critical temperature are obtained by the heat kernel method. Using zeta-function regularization of one-loop effective potential, lower dimensional critical temperatures are calculated. In the presence of strong anisotropy, the condensation is shown to occur in multisteps. The criteria of this behavior is that critical temperatures corresponding to lower dimensional systems are smaller than the three dimensional critical temperature.
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arxiv:quant-ph/9808006
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We try to obtain Born's principle as a result of a subquantum heat death, using classical ${\cal H}$-theorem and the definition of a proper quantum ${\cal H}$-theorem, within the framwork of Bohm's theory. We shall show the possibility of solving the problem of action-reaction asymmetry present in Bohm's theory and the arrow of time problem in our procedure.
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arxiv:quant-ph/9808015
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We propose a definition of QNC, the quantum analog of the efficient parallel class NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding and decoding standard quantum error-correcting codes, or more generally any circuit consisting of controlled-not gates, controlled pi-shifts, and Hadamard gates. Finally, while we note the Quantum Fourier Transform can be parallelized to linear depth, we conjecture that an even simpler `staircase' circuit cannot be parallelized to less than linear depth, and might be used to prove that QNC < QP.
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arxiv:quant-ph/9808027
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A potential implementation of quantum-information schemes in semiconductor nanostructures is studied. To this end, the formal theory of quantum encoding for avoiding errors is recalled and the existence of noiseless states for model systems is discussed. Based on this theoretical framework, we analyze the possibility of designing noiseless quantum codes in realistic semiconductor structures. In the specific implementation considered, information is encoded in the lowest energy sector of charge excitations of a linear array of quantum dots. The decoherence channel considered is electron-phonon coupling We show that besides the well-known phonon bottleneck, reducing single-qubit decoherence, suitable many-qubit initial preparation as well as register design may enhance the decoherence time by several orders of magnitude. This behaviour stems from the effective one-dimensional character of the phononic environment in the relevant region of physical parameters.
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arxiv:quant-ph/9808036
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The aim of this paper is to derive explicit formulae for the Riemannian Bures metric on the manifold of (finite dimensional) nondegenerate density matrices. The computation of the Bures metric using the presented equations does not require any diagonalization procedure and uses matrix products, determinants and traces, only.
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arxiv:quant-ph/9808044
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We present a new indirect method to measure the quantum state of a single mode of the electromagnetic field in a cavity. Our proposal combines the idea of (endoscopic) probing and that of tomography in the sense that the signal field is coupled via a quantum-non-demolition Hamiltonian to a meter field on which then quantum state tomography is performed using balanced homodyne detection. This technique provides full information about the signal state. We also discuss the influence of the measurement of the meter on the signal field.
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arxiv:quant-ph/9808052
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Within the context of the usual semi classical investigation of Planck scale Schwarzchild Black Holes, as in Quantum Gravity, and later attempts at a full Quantum Mechanical description in terms of a Kerr-Newman metric including the spinorial behaviour, we attempt to present a formulation that extends from the Planck scale to the Hubble scale. In the process the so called large number coincidences as also the hitherto inexplicable relations between the pion mass and the Hubble Constant, pointed out by Weinberg, turn out to be natural consequences in a consistent description.
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arxiv:quant-ph/9809032
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We propose a novel dynamical method for beating decoherence and dissipation in open quantum systems. We demonstrate the possibility of filtering out the effects of unwanted (not necessarily known) system-environment interactions and show that the noise-suppression procedure can be combined with the capability of retaining control over the effective dynamical evolution of the open quantum system. Implications for quantum information processing are discussed.
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arxiv:quant-ph/9809071
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We suggest a method to perform a quantum logic gate between distant qubits by off-resonant field-atom dispersive interactions. The scheme we present is shown to work ideally even in the presence of errors in the photon channels used for communication. The stability against errors arises from the paradoxical situation that the transmitted photons carry no information about the state of the qubits. In contrast to a previous proposal for ideal communication [Phys. Rev. Lett. 78, 4293 (1997)] our proposal only involves single atoms in the sending and receiving devices.
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arxiv:quant-ph/9810042
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We identify a new parameter that controls the localization length in a driven quantum system. This parameter results from an additional quantum degree of freedom. The center-of-mass motion of a two-level ion stored in a Paul trap and interacting with a standing wave laser field exhibits this phenomenon. We also discuss the influence of spontaneous emission.
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arxiv:quant-ph/9810047
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This is a short introduction to quantum computers, quantum algorithms and quantum error correcting codes. Familiarity with the principles of quantum theory is assumed. Emphasis is put on a concise presentation of the principles avoiding lengthy discussions.
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arxiv:quant-ph/9811006
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