Showing papers on "Quantum state published in 1998"
Book•
01 Jun 1998TL;DR: In this article, the generation of entanglement of trapped atomic ions is discussed and several possible decoherence mechanisms are examined and what may be the more important of these are identified, as well as potential applications for entangled states of trapped-ions which lie outside the immediate realm of quantum computation.
Abstract: Methods for, and limitations to, the generation of entangled states of trapped atomic ions are examined. As much as possible, state manipulations are described in terms of quantum logic operations since the conditional dynamics implicit in quantum logic is central to the creation of entanglement. Keeping with current interest, some experimental issues in the proposal for trappedion quantum computation by J. I. Cirac and P. Zoller (University of Innsbruck) are discussed. Several possible decoherence mechanisms are examined and what may be the more important of these are identified. Some potential applications for entangled states of trapped-ions which lie outside the immediate realm of quantum computation are also discussed.
522 citations
TL;DR: Wave function engineering techniques were used to monitor and control a nonstationary quantum mechanical state composed of a superposition of eigenstates to extend the concept of coherent control in semiconductors to the limit of a single quantum system in a zero-dimensional quantum dot.
Abstract: Picosecond optical excitation was used to coherently control the excitation in a single quantum dot on a time scale that is short compared with the time scale for loss of quantum coherence. The excitonic wave function was manipulated by controlling the optical phase of the two-pulse sequence through timing and polarization. Wave function engineering techniques, developed in atomic and molecular systems, were used to monitor and control a nonstationary quantum mechanical state composed of a superposition of eigenstates. The results extend the concept of coherent control in semiconductors to the limit of a single quantum system in a zero-dimensional quantum dot.
505 citations
TL;DR: In this article, the Schrodinger-Newton equations for the spherically-symmetric case are considered and numerical evidence for a discrete family of solutions, everywhere regular, and with normalizable wavefunctions.
Abstract: As part of a programme in which quantum state reduction is understood as a gravitational phenomenon, we consider the Schrodinger-Newton equations. For a single particle, this is a coupled system consisting of the Schrodinger equation for the particle moving in its own gravitational field, where this is generated by its own probability density via the Poisson equation. Restricting to the spherically-symmetric case, we find numerical evidence for a discrete family of solutions, everywhere regular, and with normalizable wavefunctions. The solutions are labelled by the non-negative integers, the nth solution having n zeros in the wavefunction. Furthermore, these are the only globally defined solutions. Analytical support is provided for some of the features found numerically.
401 citations
TL;DR: In this paper, a nonlinear stochastic Schrodinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-markovian master equations is presented, providing an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators.
Abstract: A nonlinear stochastic Schr\"odinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including measurementlike situations, dissipation, and quantum Brownian motion. Some examples treat this environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In such a quasiperiodic case we see the reversible decay of a macroscopic quantum-superposition (``Schr\"odinger cat''). Finally, our description of open systems is compatible with different positions of the ``Heisenberg cut'' between system and environment.
361 citations
TL;DR: The experiments demonstrate the importance of vacuum fluctuations in the environment for quantum dot devices and potential design constraints for their use for preparing long-lived quantum states.
Abstract: A double quantum dot device is a tunable two-level system for electronic energy states. A dc electron current was used to directly measure the rates for elastic and inelastic transitions between the two levels. For inelastic transitions, energy is exchanged with bosonic degrees of freedom in the environment. The inelastic transition rates are well described by the Einstein coefficients, relating absorption with stimulated and spontaneous emission. The most effectively coupled bosons in the specific environment of the semiconductor device used here were acoustic phonons. The experiments demonstrate the importance of vacuum fluctuations in the environment for quantum dot devices and potential design constraints for their use for preparing long-lived quantum states.
316 citations
TL;DR: The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states as mentioned in this paper, and it has been shown that only linearly independent states can be reliably discriminated.
312 citations
TL;DR: In this article, the authors derived a tight upper bound for the fidelity of a universal qubit cloner, where the output of the cloner is required to be supported on the symmetric subspace.
Abstract: We derive a tight upper bound for the fidelity of a universal $N\ensuremath{\rightarrow}M$ qubit cloner, valid for any $M\ensuremath{\ge}N$, where the output of the cloner is required to be supported on the symmetric subspace. Our proof is based on the concatenation of two cloners and the connection between quantum cloning and quantum state estimation. We generalize the operation of a quantum cloner to mixed and/or entangled input qubits described by a density matrix supported on the symmetric subspace of the constituent qubits. We also extend the validity of optimal state estimation methods to inputs of this kind.
228 citations
Book•
31 Jan 1998
TL;DR: In this article, the authors introduce the Birkhoff-Von Neumann concept of quantum logic and the problem of Hidden Variables in Quantum Field Theory. But they do not discuss the relation between quantum conditional probabilities and quantum conditional probability.
Abstract: Preface. 1. Introduction. 2. Observables and States in the Hilbert Space Formalism of Quantum Mechanics. 3. Lattice Theoretic Notions. 4. Hilbert Lattice. 5. Physical Theory in Semantic Approach. 6. Von Neumann Lattices. 7. The Birkhoff-Von Neumann Concept of Quantum Logic. 8. Quantum Conditional and Quantum Conditional Probability. 9. The Problem of Hidden Variables. 10. Violation of Bell's Inequality in Quantum Field Theory. 11. Independence in Quantum Logic Approach. 12. Reichenbach's Common Cause Principle and Quantum Field Theory. References. Index.
218 citations
TL;DR: In this paper, the authors studied the means of preparing and coherently manipulating atomic wave packets in optical lattices, with particular emphasis on alkali-metal atoms in the far-detuned limit.
Abstract: We study the means of preparing and coherently manipulating atomic wave packets in optical lattices, with particular emphasis on alkali-metal atoms in the far-detuned limit. We derive a general, basis-independent expression for the lattice potential operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well-controlled fluctuations in the potential, making the atom-lattice system attractive for the study of decoherence and the connection between classical and quantum physics. @S1050-2947~98!00803-8#
206 citations
TL;DR: In this paper, a special aspect of quantum mechanics, namely the possibility of entanglement between two or more particles, is discussed, and the basic properties of entagglement using quantum state teleportation are established.
Abstract: Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more particles. We will establish the basic properties of entanglement using quantum state teleportation. These principles will then allow us to formulate quantitative measures of entanglement. Finally we will show that the same general principles can also be used to prove seemingly difficult questions regarding entanglement dynamics very easily. This will be used to motivate the hope that we can construct a thermodynamics of entanglement.
201 citations
TL;DR: In this paper, the authors extend the kinematical framework for diffeomorphism-invariant theories of connections for compact gauge groups to the case of a diffeomorphic invariant quantum field theory which includes, besides connections, also fermions and Higgs fields.
Abstract: We extend the recently developed kinematical framework for diffeomorphism-invariant theories of connections for compact gauge groups to the case of a diffeomorphism-invariant quantum field theory which includes, besides connections, also fermions and Higgs fields. This framework is appropriate for coupling matter to quantum gravity. The presence of diffeomorphism invariance forces us to choose a representation which is a rather non-Fock-like one: the elementary excitations of the connection are along open or closed strings, while those of the fermions or Higgs fields are at the end points of the string. Nevertheless we are able to promote the classical reality conditions to quantum adjointness relations which, in turn, uniquely fixes the gauge- and diffeomorphism-invariant probability measure that underlies the Hilbert space. Most of the fermionic part of this work is independent of the recent preprint by Baez and Krasnov and earlier work by Rovelli and Morales-Tecotl because we use new canonical fermionic variables, so-called Grassman-valued half-densities, which enable us to solve the difficult fermionic adjointness relations.
Posted Content•
TL;DR: In this paper, the authors show that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements.
Abstract: The Kochen-Specker theorem asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context come naturally from the topos theory of presheaves.
The first step in our theory is to demonstrate that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements. We then show how the use of ideas drawn from the theory of presheaves leads to the definition of a generalized valuation in quantum theory whose values are sieves of operators. In particular, we show how each quantum state leads to such a generalized valuation.
TL;DR: In this paper, a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system is presented, which specifies a physically realizable (i.e., finite) positive operator valued measurement on a finite number of identically prepared systems.
Abstract: We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable (i.e., finite) positive operator valued measurement on a finite number of identically prepared systems. We illustrate the general formalism by applying it to different scenarios of the state estimation of $N$ independent and identically prepared two-level systems (qubits).
TL;DR: In this paper, the authors study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic and prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations.
Abstract: We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann–Husimi representations for quantum states as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of zeros of the Husimi density). We rigorously prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations. We deduce from this property a universal behavior for the phase patterns of chaotic Bargmann eigenfunctions which is reminiscent of the WKB approximation for eigenstates of integrable systems (though in a weaker sense). In order to obtain more precise information on “chaotic eigenconstellations,” we then model their properties by ensembles of random states, generalizing former results on the 2-sphere to the torus geometry. This approach yields statistical predictions for the constellations which fit quite well the chaotic data. We finally observe that specific dynamical information, e.g., the presence of high peaks (like scars) in Husimi densities, can be recovered from the knowledge of a few long-wavelength Fourier coefficients, which therefore appear as valuable order parameters at the level of individual chaotic eigenfunctions.
TL;DR: In this paper, the authors discuss how quantum entanglement is the key to protecting quantum states from decoherence in a manner which, in a theoretical sense, is as effective as the protection of digital data from bit noise.
TL;DR: In this paper, the authors proposed to measure the quantum state by coupling a single-electron transistor to the $q$-bit and analyzed the time evolution of the density matrix of the transistor and the quantum bit when a voltage is turned on.
Abstract: Low-capacitance Josephson junction systems as well as coupled quantum dots, in a parameter range where single charges can be controlled, provide physical realizations of quantum bits, discussed in connection with quantum computing. The necessary manipulation of the quantum states can be controlled by applied gate voltages. In addition, the state of the system has to be read out. Here we suggest to measure the quantum state by coupling a single-electron transistor to the $q$-bit. As long as no transport voltage is applied, the transistor influences the quantum dynamics of the $q$-bit only weakly. We have analyzed the time evolution of the density matrix of the transistor and $q$-bit when a voltage is turned on. For values of the capacitances and temperatures which can be realized by modern nanotechniques, the process constitutes a quantum measurement process.
17 Feb 1998
TL;DR: This work considers the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state and proves linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability.
Abstract: We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability. Our proofs employ a novel kind of "quantum" reduction from a quantum information theory problem to the problem of computing the inner product. The communication required for the former problem can then be bounded by an application of Holevo's theorem. We also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit.
TL;DR: In this paper, the authors describe a wave function that can always be written as a superposition of quantum states, each characterized by a complex probability amplitude, where interference between these amplitudes occurs when the particle can follow several indistinguishable paths.
Abstract: Quantum mechanics is very puzzling. A particle can be delocalized, it can be simultaneously in several energy states and it can even have several different identities at once. This schizophrenic behavior is encoded in its wavefunction, which can always be written as a superposition of quantum states, each characterized by a complex probability amplitude. Interferences between these amplitudes occur when the particle can follow several indistinguishable paths. Any attempt to determine which trajectory it “actually takes” destroys these interferences. This is a manifestation of wave—particle complementarity, which has recently been illustrated in textbook fashion by several beautiful experiments.
TL;DR: In this paper, the precise quantum state of two trapped, coupled Bose-Einstein condensates in the two-mode approximation was considered and a representation of the state in terms of a Wigner-like distribution on the twomode Bloch sphere was obtained using a selfconsistent rotation of the unknown state to the south pole of the sphere.
Abstract: We consider the precise quantum state of two trapped, coupled Bose-Einstein condensates in the two-mode approximation. We seek a representation of the state in terms of a Wigner-like distribution on the two-mode Bloch sphere. The problem is solved using a self-consistent rotation of the unknown state to the south pole of the sphere. The two-mode Hamiltonian is projected onto the harmonic-oscillator phase plane, where it can be solved by standard techniques. Our results show how the number of atoms in each trap and the squeezing in the number difference depend on the physical parameters. Considering negative scattering lengths, we show that there is a regime of squeezing in the relative phase of the condensates which occurs for weaker interactions than the superposition states found by Cirac et al. (quant-ph/9706034). The phase squeezing is also apparent in mildly asymmetric trap configurations.
TL;DR: In this article, a family of asymmetric Pauli-cloning machines for quantum states is introduced, and the tradeoff between the quality of these copies is shown to result from a complementarity akin to Heisenberg uncertainty principle.
Abstract: A family of asymmetric cloning machines for $N$-dimensional quantum states is introduced. These machines produce two imperfect copies of a single state that emerge from two distinct Heisenberg channels. The tradeoff between the quality of these copies is shown to result from a complementarity akin to Heisenberg uncertainty principle. A no-cloning inequality is derived for isotropic cloners: if $\pi_a$ and $\pi_b$ are the depolarizing fractions associated with the two copies, the domain in $(\sqrt{\pi_a},\sqrt{\pi_b})$-space located inside a particular ellipse representing close-to-perfect cloning is forbidden. More generally, a no-cloning uncertainty relation is discussed, quantifying the impossibility of copying imposed by quantum mechanics. Finally, an asymmetric Pauli cloning machine is defined that makes two approximate copies of a quantum bit, while the input-to-output operation underlying each copy is a (distinct) Pauli channel. The class of symmetric Pauli cloning machines is shown to provide an upper bound on the quantum capacity of the Pauli channel of probabilities $p_x$, $p_y$ and $p_z$.
14 Sep 1998
TL;DR: In this article, the authors investigate the teleportation of a quantum state using three-particle entanglement to either one of two receivers in such a way that, generally, either one or both receivers can fully reconstruct the quantum state conditioned on the measurement outcome of the other.
Abstract: We investigate the ``teleportation'' of a quantum state using three-particle entanglement to either one of two receivers in such a way that, generally, either one of the two, but only one, can fully reconstruct the quantum state conditioned on the measurement outcome of the other. We furthermore delineate the similarities between this process and a quantum nondemolition measurement.
TL;DR: In this paper, the mixed quantum-classical dynamics of a system containing both bound and continuum quantum states were simulated using a surface hopping method, in the limit where the quantum wave function is made up of only contributions from the continuum, this method reduces to mean-field dynamics.
Abstract: We present a method that allows the mixed quantum-classical dynamics of a system containing both bound and continuum quantum states to be simulated using a surface hopping method. In the limit where the quantum wave function is made up of only contributions from the continuum, this method reduces to mean-field (Ehrenfest) dynamics. We demonstrate the new technique by simulating a simple model of a quantum wave packet colliding with an adsorbed particle on a solid surface. By calculating the mixed quantum-classical evolution of this problem with both mean-field dynamics and our generalized surface hopping scheme and comparing these results to fully quantum solutions, we show that the surface hopping approach can avoid some of the inaccuracies that are common features of mean-field calculations.
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TL;DR: In this article, a new family of indecomposable positive linear maps based on entangled quantum states is introduced, and the notion of an unextendible product basis is introduced.
Abstract: We introduce a new family of indecomposable positive linear maps based on entangled quantum states. Central to our construction is the notion of an unextendible product basis. The construction lets us create indecomposable positive linear maps in matrix algebras of arbitrary high dimension.
TL;DR: The exact lower bound on the sum of the information entropies is obtained for arbitrary pairs of observables in two-dimensional Hilbert space for the particular case of real transformation matrices and state vectors.
TL;DR: In this article, the authors formulate the principles of classical statistical inference in a natural geometric setting, and establish generalisations of the classical Cramer-Rao and Bhattacharyya inequalities, described in terms of the geometry of the underlying real Hilbert space.
Abstract: A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the space of all square–integrable functions. More precisely, by consideration of the square–root density function we can regard M as a submanifold of the unit sphere S in a real Hilbert space H . Therefore, H embodies the ‘state space’ of the probability distributions, and the geometry of the given statistical model can be described in terms of the embedding of M in S . The geometry in question is characterised by a natural Riemannian metric (the Fisher–Rao metric), thus allowing us to formulate the principles of classical statistical inference in a natural geometric setting. In particular, we focus attention on the variance lower bounds for statistical estimation, and establish generalisations of the classical Cramer–Rao and Bhattacharyya inequalities, described in terms of the geometry of the underlying real Hilbert space. As a comprehensive illustration of the utility of the geometric framework, the statistical model M is then specialised to the case of a submanifold of the state space of a quantum mechanical system. This is pursued by introducing a compatible complex structure on the underlying real Hilbert space, which allows the operations of ordinary quantum mechanics to be reinterpreted in the language of real Hilbert space geometry. The application of generalised variance bounds in the case of quantum statistical estimation leads to a set of higher order corrections to the Heisenberg uncertainty relations for canonically conjugate observables.
TL;DR: For a two-particle two-state system, a set of compatible propositions exist for which quantum mechanics and noncontextual hidden-variable theories make conflicting predictions for every individual system, regardless of its quantum state.
Abstract: For a two-particle two-state system, sets of compatible propositions exist for which quantum mechanics and noncontextual hidden-variable theories make conflicting predictions for every individual system whatever its quantum state. This permits a simple all-or-nothing state-independent experimental verification of the Bell-Kochen-Specker theorem.
TL;DR: In this paper, the authors consider intermediate measurements which interpolate between these extremes and derive a general lower bound on the combination of errors and inconclusive results, and describe a family of measurement strategies which attains this limit.
Abstract: Any measurement strategy designed to discriminate between nonorthogonal quantum states will have a finite probability of yielding erroneous or inconclusive results. The lower bounds on these probabilities for conclusive and error-free strategies are given by the Helstrom and Ivanovic–Feres limits respectively. We consider intermediate measurements which interpolate between these extremes and derive a general lower bound on the combination of errors and inconclusive results. We also describe a family of measurement strategies which attains this limit.
TL;DR: In this paper, the authors demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements, and show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadratures phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors.
Abstract: We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.
TL;DR: In this article, a generalized quantum Fokker-planck theory in a non-Gaussian-Markovian model bath is developed, which is applicable to the study of quantum coherence and relaxation in various dynamic systems.
Abstract: We develop a generalized quantum Fokker-Planck theory in a non-Gaussian-Markovian model bath. The semiclassical bath adopted in this work is charactered by three parameters. One denotes the strength of system-bath coupling and the other two are chosen to interpolate smoothly the solvation dynamics between the long- and short-time regimes. The fluctuation-dissipation relation in this model bath is analyzed in detail. Based on this model bath, we derive two sets of coupled Fokker-Planck equations. These two equation sets are equivalent in the second order of system-bath coupling but different in the higher orders. The corresponding reduced Liouville equation in one set of the Fokker-Planck formulation is characterized by a memory relaxation kernel, while that in the other is by a local-time relaxation tensor. Each resulting set of Fokker-Planck equations involves only the reduced density operator and a series of well-characterized Hilbert-space relaxation operators. The present theory is valid for arbitrary time-dependent Hamiltonians and is applicable to the study of quantum coherence and relaxation in various dynamic systems.
TL;DR: In this article, the authors consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices.
Abstract: We consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices. We study the time-dependent expectation values of these observables, assuming that the system is in a definite (but arbitrary) pure quantum state. We induce a probability distribution for the expectation values by treating the zero of time as a uniformly distributed random variable. We show explicitly that if an observable has a nonequilibrium expectation value at some particular moment, then it is overwhelmingly likely to move towards equilibrium, both forwards and backwards in time. For deviations from equilibrium that are not much larger than a typical quantum or thermal fluctuation, we find that the time dependence of the move towards equilibrium is given by the Kubo correlation function, in agreement with Onsager's postulate. These results are independent of the details of the system's quantum state.