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Showing papers on "Quantum state published in 1994"


Journal ArticleDOI
TL;DR: By finding measurements that optimally resolve neighboring quantum states, this work uses statistical distinguishability to define a natural Riemannian metric on the space of quantum-mechanical density operators and to formulate uncertainty principles that are more general and more stringent than standard uncertainty principles.
Abstract: By finding measurements that optimally resolve neighboring quantum states, we use statistical distinguishability to define a natural Riemannian metric on the space of quantum-mechanical density operators and to formulate uncertainty principles that are more general and more stringent than standard uncertainty principles.

2,481 citations


Journal ArticleDOI
TL;DR: In this article, the authors propose a definition of fidelity for mixed quantum states in terms of Uhlmann's transition probability formula F(ϱ1, ϱ2) = {trace [(√ϱ 1ϱ2 × √ ϱ 1)1/2]}2 and give new elementary proofs of its essential properties.
Abstract: We propose a definition of fidelity for mixed quantum states in terms of Uhlmann's ‘transition probability’ formula F(ϱ1, ϱ2) = {trace [(√ϱ1ϱ2 × √ϱ1)1/2]}2 and give new elementary proofs of its essential properties.

1,599 citations


Journal ArticleDOI
TL;DR: In this article, the authors apply the surface-hopping method to proton transfer in solution, where the quantum particle is an atom, using full classical mechanical molecular dynamics for the heavy atom degrees of freedom, including the solvent molecules.
Abstract: We apply ‘‘molecular dynamics with quantum transitions’’ (MDQT), a surface‐hopping method previously used only for electronic transitions, to proton transfer in solution, where the quantum particle is an atom. We use full classical mechanical molecular dynamics for the heavy atom degrees of freedom, including the solvent molecules, and treat the hydrogen motion quantum mechanically. We identify new obstacles that arise in this application of MDQT and present methods for overcoming them. We implement these new methods to demonstrate that application of MDQT to proton transfer in solution is computationally feasible and appears capable of accurately incorporating quantum mechanical phenomena such as tunneling and isotope effects. As an initial application of the method, we employ a model used previously by Azzouz and Borgis to represent the proton transfer reaction AH–B■A−–H+B in liquid methyl chloride, where the AH–B complex corresponds to a typical phenol–amine complex. We have chosen this model, in part, because it exhibits both adiabatic and diabatic behavior, thereby offering a stringent test of the theory. MDQT proves capable of treating both limits, as well as the intermediate regime. Up to four quantum states were included in this simulation, and the method can easily be extended to include additional excited states, so it can be applied to a wide range of processes, such as photoassisted tunneling. In addition, this method is not perturbative, so trajectories can be continued after the barrier is crossed to follow the subsequent dynamics.

1,150 citations


Journal ArticleDOI
Lev Vaidman1
TL;DR: The recent result of Bennett of teleportation of an unknown quantum state is obtained in the framework of nonlocal measurements proposed by Aharonov and Albert, and the latter method is generalized to the teleportation of a quantum state of a system with continuous variables.
Abstract: The recent result of Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)] of teleportation of an unknown quantum state is obtained in the framework of nonlocal measurements proposed by Aharonov and Albert [Phys. Rev. D 21, 3316 (1980); 24, 359 (1981)]. The latter method is generalized to the teleportation of a quantum state of a system with continuous variables.

736 citations


Journal ArticleDOI
TL;DR: The squeezed state formalism provides an interesting framework within which to study the amplification process, but it is concluded that it does not provide us with any new physical results.
Abstract: Inflationary cosmology is analyzed from the point of view of squeezed quantum states. As noted by Grishchuk and Sidorov, the amplification of quantum fluctuations into macroscopic perturbations which occurs during cosmic inflation is a process of quantum squeezing. We carefully develop the squeezed state formalism and derive the equations that govern the evolution of a Gaussian initial state. We derive the power spectrum of density perturbations for a simple inflationary model and discuss its features. We conclude that the squeezed state formalism provides an interesting framework within which to study the amplificaiton process, but, in disagreement with the claims of Grishchuk and Sidorov, that it does not provide us with any new physical results.

307 citations


Journal ArticleDOI
TL;DR: A simple general prescription for a measurement that is typically not optimal but appears to be quite good is considered, which seems to be particularly good when the states to be distinguished are equally likely and almost orthogonal.
Abstract: We address the problem of extracting information from a single quantum system whose state is known to be in one of several possible states. In the generic case, it is notoriously difficult to find the optimal measurement, that is the measurement that provides the most possible information about the system's state. We consider a simple general prescription for a measurement that is typically not optimal but appears to be quite good. It seems to be particularly good when the states to be distinguished are equally likely and almost orthogonal.

306 citations


Journal ArticleDOI
TL;DR: It is shown how suitable boundary conditions, which do not frustrate N\'eel order, allow the study of samples with N=3p+1 spins, and a thorough study of these situations is done in parallel with the more conventional case N= 3p.
Abstract: Exact spectra of periodic samples are computed up to N=36. Evidence of an extensive set of low-lying levels, lower than the softest magnons, is exhibited. These low-lying quantum states are degenerated in the thermodynamic limit; their symmetries and dynamics as well as their finite-size scaling are strong arguments in favor of N\'eel order. It is shown that the N\'eel order parameter agrees with first-order spin-wave calculations. A simple explanation of the low-energy dynamics is given as well as the numerical determinations of the energies, order parameter, and spin susceptibilities of the studied samples. It is shown how suitable boundary conditions, which do not frustrate N\'eel order, allow the study of samples with N=3p+1 spins. A thorough study of these situations is done in parallel with the more conventional case N=3p.

278 citations


Journal ArticleDOI
TL;DR: In this paper, a new decomposition of the Redfield relaxation tensor is proposed for the density matrix of a multilevel quantum-mechanical system interacting with a thermal bath.
Abstract: We present a new method for solving the Redfield equation, which describes the evolution of the reduced density matrix of a multilevel quantum‐mechanical system interacting with a thermal bath. The method is based on a new decomposition of the Redfield relaxation tensor that makes possible its direct application to the density matrix without explicit construction of the full tensor. In the resulting expressions, only ordinary matrices are involved and so any quantum system whose Hamiltonian can be diagonalized can be treated with the full Redfield theory. To efficiently solve the equation of motion for the density matrix, we introduce a generalization of the short‐iterative‐Lanczos propagator. Together, these contributions allow the complete Redfield theory to be applied to significantly larger systems than was previously possible. Several model calculations are presented to illustrate the methodology, including one example with 172 quantum states.

273 citations


Journal ArticleDOI
TL;DR: In this article, the authors apply simultaneously the principles of quantum mechanics and general relativity to find an intrinsic limitation to quantum measurements of space-time distances and show that the intrinsic uncertainty of a length is proportional to the one third power of the length itself.
Abstract: Applying simultaneously the principles of quantum mechanics and general relativity we find an intrinsic limitation to quantum measurements of space-time distances. The intrinsic uncertainty of a length is shown to be proportional to the one third power of the length itself. This uncertainty in space-time measurements implies an intrinsic uncertainty of the space-time metric and yields quantum decoherence for particles heavier than the Planck mass.

227 citations


Journal ArticleDOI
TL;DR: Two schemes employing cavity QED phenomena to realize the teleportation of quantum states following the principle outlined by Bennett are presented.
Abstract: We present two schemes employing cavity QED phenomena to realize the teleportation of quantum states following the principle outlined by Bennett et al [Phys Rev Lett 70, 1895 (1993)]

158 citations


Journal ArticleDOI
TL;DR: The classical limit of quantum mechanics is usually discussed in terms of Ehrenfest's theorem, which states that, for a sufficiently narrow wave packet, the mean position in the quantum state will follow a classical trajectory.
Abstract: The classical limit of quantum mechanics is usually discussed in terms of Ehrenfest's theorem, which states that, for a sufficiently narrow wave packet, the mean position in the quantum state will follow a classical trajectory. We show, however, that that criterion is neither necessary nor sufficient to identify the classical regime. Generally speaking, the classical limit of a quantum state is not a single classical orbit, but an ensemble of orbits. The failure of the mean position in the quantum state to follow a classical orbit often merely reflects the fact that the centroid of a classical ensemble need not follow a classical orbit. A quantum state may behave essentially classically, even when Ehrenfest's theorem does not apply, if it yields agreement with the results calculated from the Liouville equation for a classical ensemble. We illustrate this fact with examples that include both regular and chaotic classical motions.

Journal ArticleDOI
TL;DR: In this article, the quantum gravitational scale of inflation is calculated by finding a sharp probability peak in the distribution function of chaotic inflationary cosmologies driven by a scalar field with large negative constant Ξ of nonminimal interaction.

Journal ArticleDOI
TL;DR: The primary quantum state diffusion (PSD) theory as mentioned in this paper is an alternative quantum theory from which classical dynamics, quantum dynamics and localization dynamics are derived, based on four principles, that a system is represented by an operator, its state by a normalized state vector, the state vector satisfies a Langevin-Ito state diffusion equation, and the resultant density operator for an ensemble must satisfy an equation of elementary Lindblad form.
Abstract: Primary quantum state diffusion (PSD) theory is an alternative quantum theory from which classical dynamics, quantum dynamics and localization dynamics are derived. It is based on four principles, that a system is represented by an operator, its state by a normalized state vector, the state vector satisfies a Langevin-Ito state diffusion equation, and the resultant density operator for an ensemble must satisfy an equation of elementary Lindblad form. There are three conditions. The ז 0 first determines the operator, to within an undetermined universal time constant ז 0 . The second and third conditions put opposing bounds on ז 0 . Dissipation of coherence is distinguished from destruction of coherence. The state diffusion destroys coherence and produces the localization or reduction that makes classical dynamics possible. PSD theory is a development of the environmental quantum state diffusion theory of Gisin and Percival and particularly resembles earlier proposals by Gisin and by Milburn. It is also related to the spontaneous localization theories of Ghirardi, Rimini and Weber, of Diosi and of Pearle. The non-relativistic PSD theory is of value only for systems which occupy small regions of space. Special relativity is needed for more extended systems even when they contain only slowly moving massive particles. Experiments on coherence lifetimes and matter interferometry are proposed which either measure ז 0 or put bounds on it, and which might distinguish between PSD and ordinary quantum mechanics.

Journal ArticleDOI
TL;DR: In this article, generalized statistical distributions for identical particles are introduced for the case where filling a single-particle quantum state by particles depends on filling states of different momenta, and an equation determining the statistical distribution for these statistics is derived.
Abstract: Generalized statistical distributions for identical particles are introduced for the case where filling a single-particle quantum state by particles depends on filling states of different momenta. The system of one-dimensional bosons with a two-body potential that can be solved by means of the thermodynamic Bethe ansatz is shown to be equivalent thermodynamically to a system of free particles obeying statistical distributions of the above class. The quantum statistics arising in this way are completely determined by the two-particle scattering phases of the corresponding interacting systems. An equation determining the statistical distributions for these statistics is derived.

Journal ArticleDOI
TL;DR: In this paper, the authors examine a system in which both coherent driving and dissipative damping involve the simultaneous creation and annihilation of pairs of photons, and compare the results of the simulation methods with each other and with density-matrix calculations.
Abstract: Recent work on the dynamics of open systems has shown how the density operator may be unraveled into component state-vector trajectories using quantum-state diffusion or the quantum-jump model. In traditional dissipative environments the coherent evolution is stochastically perturbed by the action of the reservoir or environment, so that superposition states are dephased. We examine a system in which both coherent driving and dissipative damping involve the simultaneous creation and annihilation of pairs of photons. This has unusual consequences for the creation and decay of coherences. We analyze this problem using the two recently proposed simulation methods and compare the results of the simulation methods with each other and with density-matrix calculations. We also demonstrate the formation of Schr\"odinger ``cat'' states of the field through the action of dissipation and depict them using the Wigner and Husimi quasiprobability functions.

Journal ArticleDOI
TL;DR: In this article, the decay of coherence when a quantum system interacts with a much larger environment is usually described by a master equation for the system reduced density matrix and emphasizes the evolution of an entire ensemble.
Abstract: The decay of coherence when a quantum system interacts with a much larger environment is usually described by a master equation for the system reduced density matrix and emphasizes the evolution of an entire ensemble. We consider two methods that have been developed recently to simulate the evolution of single realizations. Quantum-state diffusion involves both diffusion, where the individual quantum trajectory fluctuates through a Wiener process deriving from the environment, and localization to a coherent state, an eigenstate of the relevant Lindblad operator describing the coupling of the system to the environment. We demonstrate the localization process for different initial states and utilize the Wigner function to depict this localization in phase space. We concentrate on quantum states that can be expressed as a superposition of appropriate coherent states. For an initial superposition of two coherent states (a Schr\"odinger ``cat''), one of the two components will dominate the evolution. For initial Fock states, which can be described as a continuous superposition of coherent states on a ring, localization takes place when one coherent state is selected from that ring where each component has nearly the same energy as the original Fock state. We also consider the localization from a nonclassical squeezed ground state, which can be expressed as a superposition of coherent states along a line in phase space. The second simulation method considered is the state vector Monte Carlo, or ``quantum jump,'' approach, which relates to the direct counting of decay quanta. In the case of an initial Schr\"odinger ``cat,'' we find that when no quantum is detected the ``cat'' shrinks, but when a quantum is detected, the Schr\"odinger ``cat'' ``jumps'' from one type of ``cat'' to another with different internal phase. For an initial squeezed state we show how quantum jumps lead to individual realizations which are superpositions of two squeezed states.

Journal ArticleDOI
TL;DR: A fundamental bound upon the measurability of finite-dimensional quantum states is proved using the Shannon information theory and the Bayesian methodology for inverting quantum data.
Abstract: Using the Shannon information theory and the Bayesian methodology for inverting quantum data [K. R. W. Jones, Ann. Phys. (N.Y.) 207, 140 (1991)] we prove a fundamental bound upon the measurability of finite-dimensional quantum states. To do so we imagine a thought experiment for the quantum communication of a pure state , known to one experimenter, to his colleague via the transmission of N identical copies of it in the limit of zero temperature. Initial information available to the second experimenter is merely that of the allowed manifold of superpositions upon which the chosen may lie. Her efforts to determine it, in an optimal way, subject to the fundamental constraints imposed by quantum noise, define a statistical uncertainty principle. This limits the accuracy with which can be measured according to the number N of transmitted copies. The general result is illustrated in the physically realizable case of polarized photons.

01 Jan 1994
TL;DR: A review of quantum effects in cosmology is given in this article, where the main emphasis is made on physical interpretations and possible observational consequences of the effects, and the main points of interest are: 1. The present state of the universe. 2. What can we expect from a complete cosmological theory.
Abstract: A review of quantum effects in cosmology is given. The main emphasis is made on physical interpretations and possible observational consequences of the effects. The paper includes the following sections: 1. Introduction. The present state of the Universe. 2. What can we expect from a complete cosmological theory? 3. An overview of quantum effects in cosmology. 4. Parametric (superadiabatic) amplification of classical waves. 5. Graviton creation in the inflationary universe. 6. Quantum states of a harmonic oscillator. 7. Squeezed quantum states of relic gravitons and primordial density perturbations. 8. Quantum cosmology, minisuperspace models and inflation. 9. From the space of classical solutions to the space of wavefunctions. 10. On the probability of quantum tunneling from 'nothing'. 11. Duration of inflation and possible remnants of the preinflationary Universe. 12. Relic gravitons and the birth of the Universe.



Journal ArticleDOI
TL;DR: Numerically the distribution of Hilbert-space vectors evolving in the presence of a small random perturbation is studied, thereby providing additional support for a characterization of quantum chaos that uses concepts from information theory.
Abstract: For the quantum kicked top we study numerically the distribution of Hilbert-space vectors evolving in the presence of a small random perturbation. For an initial coherent state centered in a chaotic region of the classical dynamics, the evolved perturbed vectors are distributed essentially like random vectors in Hilbert space. In contrast, for an initial coherent state centered near an elliptic (regular) fixed point of the classical dynamics, the evolved perturbed vectors remain close together, explore only a few dimensions of Hilbert space, and do not explore them randomly. These results support and extend the results of earlier studies, thereby providing additional support for a characterization of quantum chaos that uses concepts from information theory.


Journal ArticleDOI
TL;DR: The quantum state diffusion model provides equations for the localization or reduction of quantum states of wide-open systems as discussed by the authors, and it is proved that the rate of selflocalization of a selfadjoint environment operator towards one of its eigenstates is no less than 2.
Abstract: In a wide-open quantum system, the effect of the Hamiltonian is negligible by comparison with the effect of the environment. For open systems, this is the opposite limit to closed or isolated systems. The quantum state diffusion model provides equations for the localization or reduction of quantum states of wide-open systems. The ensemble localization of an operator is defined, and it is proved that the rate of selflocalization of a selfadjoint environment operator towards one of its eigenstates is no less than 2. A bound is also obtained for the rate of selflocalization of some non-selfadjoint operators, which localize to minimum indeterminacy wave packets. The theory is presented for quasiclassical systems. For a sufficient number of independent environment operators, the states localize asymptotically to wave packets with Heisenberg indeterminacy products close to the minimum, which look to classical eyes like phase space points. To zeroth order in h(cross), the time-dependent WKB theory of quantum state diffusion due to a single operator shows localization or reduction within and between fixed classical sheets or Lagrangian manifolds. To first order, the sheets themselves diffuse. The rate of localization in an ensemble is determined by commutation terms with either sign and by correlation terms which always increase the localization. For the quasiclassical case the latter dominate, and this leads to a purely classical theory of localization, with a picture based on the diffusion of phase space densities. This means that state diffusion dynamics, like Hamiltonian dynamics, has a purely classical form, in which Planck's constant plays no role.

Journal ArticleDOI
TL;DR: In this article, a measurement setup based on the deflection of atoms from a quantized electromagnetic field and a strategy which leads to the knowledge of the complete quantum state of this field is presented.
Abstract: We present a measurement setup based on the deflection of atoms from a quantized electromagnetic field and a strategy which leads to the knowledge of the complete quantum state of this field. The same setup reveals the expectation value of the phase operator ${e}^{i\ensuremath{\varphi}}$.

Journal ArticleDOI
TL;DR: A simple, essentially topological analysis reveals an interplay between the Aharonov-Bohm phase and Berry's phase in the phase accumulated by a charged particle in an extended quantum state as it encircles one or more magnetic fluxons.
Abstract: We investigate the phase accumulated by a charged particle in an extended quantum state as it encircles one or more magnetic fluxons, each carrying half a flux unit. A simple, essentially topological analysis reveals an interplay between the Aharonov-Bohm phase and Berry's phase.

Posted Content
TL;DR: In this paper, the analysis of the protection measurements is presented and it is argued, contrary to recent claims, that they measure the quantum state and not the potential of the system itself.
Abstract: Protective measurements, which we have introduced recently, allow to measure properties of the state of a single quantum system and even the Schr\"odinger wave itself. These measurements require a protection, sometimes due to an additional procedure and sometimes due to the potential of the system itself. The analysis of the protective measurements is presented and it is argued, contrary to recent claims, that they measure the quantum state and not the protective potential. Some other misunderstandings concerning our proposal are clarified.

Journal ArticleDOI
TL;DR: In this article, a single light beam, generated by type-II down-conversion, is split by a beam splitter, and when a set of quartz plates is inserted into the single beam, the coincidence counting rate between the split beams exhibits a 100% frequency-beating modulation.
Abstract: A single light beam, generated by type-II down-conversion, is split by a beam splitter. When a set of quartz plates is inserted into the single beam, the coincidence counting rate between the split beams exhibits a 100% frequency-beating modulation. This nonclassical phenomena is a manifestation of a two-photon entangled state in which the two-particle state is entangled simultaneously in spin and space-time.

Journal ArticleDOI
TL;DR: In this paper, an atomic interference method is presented that can be used to construct arbitrary superpositions of coherent states with equal mean photon number in a single-mode cavity by sending only one atom through the apparatus.
Abstract: An atomic interference method is presented that can be used to construct arbitrary superpositions of coherent states with equal mean photon number in a single-mode cavity by sending only one atom through the apparatus. The method is suitable to generate any quantum state that has a one-dimensional coherent state representation on a circle in phase space. This method is demonstrated in the case of generating Fock states.

Journal ArticleDOI
TL;DR: For the class of potentials V = −|γ|/rν, where r = −∞ 2, these solutions are normalizable and correspond to bound states, if the angular momentum quantum number l > 0.

Journal ArticleDOI
TL;DR: It is shown, by imposing the supersymmetry and Lorentz quantum constraints, that there are no physical quantum states in the diagonal Bianchi type-IX model of supergravity with a non-zero cosmological constant.
Abstract: Diagonal Bianchi type-IX models are studied in the quantum theory of $N=1$ supergravity with a cosmological constant. It is shown, by imposing the supersymmetry and Lorentz quantum constraints, that there are no physical quantum states in this model. The $k=+1$ Friedmann model in supergravity with a cosmological constant does admit quantum states. However, the Bianchi type-IX model provides a better guide to the behavior of a generic state, since more gravitino modes are available to be excited. These results indicate that there may be no physical quantum states in the full theory of $N=1$ supergravity with a nonzero cosmological constant.