This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels. A pure entangled state is prepared of a pair of systems R and Q, after which Q is subjected to a dynamical evolution given by the superoperator ${\mathit{E}}^{\mathit{Q}}$. Two interesting quantities can be defined for this process: the entanglement fidelity ${\mathit{F}}_{\mathit{e}}$ and the entropy exchange ${\mathit{S}}_{\mathit{e}}$. It turns out that neither of these quantities depends in any way on the system R, but only on the initial state and dynamical evolution of Q. ${\mathit{F}}_{\mathit{e}}$ and ${\mathit{S}}_{\mathit{e}}$ are related to various other fidelities and entropies and are connected by an inequality reminiscent of the Fano inequality of classical information theory. Some insight can be gained from these techniques into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes. © 1996 The American Physical Society.

This paper investigates properties of noisy quantum information channels. We define a quantity called coherent information, which measures the amount of quantum information conveyed in the noisy channel. This quantity can never be increased by quantum information processing, and it yields a simple necessary and sufficient condition for the existence of perfect quantum error correction. © 1996 The American Physical Society.

An explicit algorithm for performing Schumacher’s noiseless compression of quantum bits is given. This algorithm is based on a combinatorial expression for a particular bijection among binary strings. The algorithm, which adheres to the rules of reversible programming, is expressed in a high-level pseudocode language. It is implemented using O(${\mathit{n}}^3$) two- and three-bit primitive reversible operations, where n is the length of the qubit strings to be compressed. Also, the algorithm makes use of O(n) auxiliary qubits. Space-saving techniques based on those proposed by Bennett are developed which reduce this workspace to O(√n) while maintaining a running time of O(${\mathit{n}}^3$) (albeit with a larger constant). This latter algorithm is of interest because it has a slightly smaller time-space product, which is considered to be the relevant figure of merit for efficiency in some physical models. © 1996 The American Physical Society.

Quantum correlations between two particles show nonclassical properties that can be used for providing secure transmission of information. We present a quantum cryptographic system in which users store particles in a transmission center, where their quantum states are preserved using quantum memories. Correlations between the particles stored by two users are created upon request by projecting their product state onto a fully entangled state. Our system allows for secure communication between any pair of users who have particles in the same center. Unlike other quantum cryptographic systems, it can work without quantum channels and it is suitable for building a quantum cryptographic network. We also present a modified system with many centers. © 1996 The American Physical Society.

The dynamical problem of particle rotation in the classical and quantum cases is considered. The effect of a rotating potential on a quantum particle in a ring is analyzed. We find that in the quantum case the particle will be fully rotated only at discrete values of frequency. For large energies a particle generally does not rotate at all, aside from a neighborhood around the frequencies of full rotation whose width depends on the energy of the initial wave packet and the potential strength. The analogies with the classical case are discussed. We also discuss the relationship to flux problems and thermodynamic equilibrium. © 1996 The American Physical Society.

The general theory of path integral propagators for the solution of linear quantum state diffusion (LQSD) stochastic Schrödinger equations describing open quantum systems is developed. Both Hamiltonian and, where possible, Lagrangian path integrals are derived and their connection established. The Hamiltonian version turns out to be more suitable. The results also show how the stochastic terms in the LQSD equation introduce a weight functional under the path integral, thus restricting the set of contributing paths. The center of this weight functional is determined by the stochastic processes governing the LQSD equation. In general, this picture holds in a semiclassical limit only. Some peculiarities of stochastic path integrals are pointed out. We evaluate the stochastic path integral in closed form for soluble models, gaining further insight into the behavior of the solutions of the LQSD equation. © 1996 The American Physical Society.

An n-bit string is encoded as a sequence of nonorthogonal quantum states. The parity bit of that n-bit string is described by one of two density matrices, ${\mathrm{\rho }}_0^{\left(\mathit{n}\right)}$ and ${\mathrm{\rho }}_1^{\left(\mathit{n}\right)}$, both in a Hilbert space of dimension $2^{\mathit{n}}$. In order to derive the parity bit the receiver must distinguish between the two density matrices, e.g., in terms of optimal mutual information. In this paper we find the measurement which provides the optimal mutual information about the parity bit and calculate that information. We prove that this information decreases exponentially with the length of the string in the case where the single bit states are almost fully overlapping. We believe this result will be useful in proving the ultimate security of quantum cryptography in the presence of noise. © 1996 The American Physical Society.

Pairs of spin-1/2 particles are prepared in a Werner state (namely, a mixture of singlet and random components). If the random component is large enough, the statistical results of spin measurements that may be performed on each pair separately can be reproduced by an algorithm involving local ‘‘hidden’’ variables. However, if several such pairs are tested simultaneously, a violation of the Clauser-Horne-Shimony-Holt inequality may occur, and no local hidden variable model is compatible with the results. © 1996 The American Physical Society.

We investigate the resonant interaction of a dipolar j=0⇆j=1 angular-momentum transition with the quantized field in a dielectric sphere. New features arise on account of the degeneracy of atomic levels and field modes with low azimuthal angular momentum, in slightly deformed spheres (oblate spheroids). For TE-mode excitation we obtain the dynamics of a degenerate Λ or V configuration with the usual coherent-state collapse and revivals. For TM-mode excitation new behavior is found: due to interference between σ- and π-polarized transitions, which can be controlled by the atomic position and/or dipole orientation, coherent-state revivals and the corresponding atom-field energy exchange may be suppressed or delayed. © 1996 The American Physical Society.

Recently it has been shown by several authors that quantum states can be stabilized against decoherence by periodically performing measurements and unitary transformations. We extend their decay model to a more realistic one in the framework of quantum optics conforming to the Markov approximation. It is shown that all quantum error correcting codes are able to cope with this decay model too. © 1996 The American Physical Society.

To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wave function, but the entire density matrix, whose phases carry information about momentum and how pure the state is. An experimental setup is presented that can measure the density matrix (or equivalently, the Wigner function) of a beam of identically prepared charged particles to an arbitrary accuracy, limited only by count statistics and detector resolution. The particles enter into an electric field, causing simple harmonic oscillation in the transverse direction. This corresponds to rotating the Wigner function in phase space. With a slidable detector, the marginal distribution of the Wigner function can be measured from all angles. Thus the phase-space tomography formalism can be used to recover the Wigner function by the standard inversion of the radon transform. By applying this technique to, for instance, double-slit experiments with various degrees of environment-induced decoherence, it should be possible to make our understanding of decoherence and apparent wave-function collapse less qualitative and more quantitative. © 1996 The American Physical Society.

Using the invariant operator method, we have analytically obtained the exact wave function, propagator, and uncertainty relations for the quantum damped harmonic oscillator governed by a time-dependent external force with a tail characterizing the influence of the past. From these quantities, the frequency-dependent susceptibility, the index of refraction, and the extinction coefficient for N identical atoms in a volume V are evaluated. The susceptibility satisfies the common properties, known as Kramers-Kronig relations, and as a given parameter that determines the nature of the tail goes to infinity, the behaviors of these results are exactly reduced to the ones for a classical case. © 1996 The American Physical Society.

The vacuum-polarization contribution to the two-loop ground-state self-energy of hydrogenic ions is calculated with an exact Dirac-Coulomb propagator. Agreement at low Z with previous calculations is found and predictions for the effect at high Z are presented. © 1996 The American Physical Society.

Upper bound of the accessible information and lower bound of the Bayes cost in quantum detection processes for Gaussian state signals under the influence of thermal noise are derived by means of the superoperator representation of quantum states. It is shown that the upper and lower bounds are obtained by replacing the parameters of the signal quantum state with the renormalized parameters including the thermal noise effects in the accessible information and the minimum value of the Bayes cost in quantum detection processes in the absence of thermal noise. Analytic expressions of the upper and lower bounds are given for several quantum state signals. © 1996 The American Physical Society.

A scheme for distinguishing between binary signals of nonorthogonal coherent states with the minimum average error is proposed. In contrast to the well-known Dolinar scheme, it does not use a feedback process. Instead, it achieves the same minimum error bound by only unitary transformations and photon number counting. It is shown that the required transformation should produce the appropriate Schrödinger-cat states. An example of the Hamiltonian generating such a process is derived from a multiphoton nonlinear optical process. © 1996 The American Physical Society.

A classical electromagnetic zero-point field (ZPF) analog of the vacuum of quantum field theory has formed the basis for theoretical investigations in the discipline known as random or stochastic electrodynamics (SED). In SED the statistical character of quantum measurements is imitated by the introduction of a stochastic classical background electromagnetic field. Random electromagnetic fluctuations are assumed to provide perturbations which can mimic certain quantum phenomena while retaining a purely classical basis, e.g., the Casimir force, the van der Waals force, the Lamb shift, spontaneous emission, the rms radius of a quantum-mechanical harmonic oscillator, and the radius of the Bohr atom. This classical ZPF is represented as a homogeneous, isotropic ensemble of plane electromagnetic waves whose amplitude is exactly equivalent to an excitation energy of hν/2 of the corresponding quantized harmonic oscillator, this being the state of zero excitation of such an oscillator. There is thus no randomness in the classical electric-field amplitudes: Randomness is introduced entirely in the phases of the waves, which are normally distributed. Averaging over the random phases is assumed to be equivalent to taking the ground-state expectation values of the corresponding quantum operator. We demonstrate that this is not precisely correct by examining the statistics of the classical ZPF in contrast to that of the electromagnetic quantum vacuum. Starting with a general technique for the calculation of classical probability distributions for quantum state operators, we derive the distribution for the individual modes of the electric-field amplitude in the ground state as predicted by quantum field theory. We carry out the same calculation for the classical ZPF analog, and show that the distributions are only in approximate agreement, diverging as the density of k states decreases. We then introduce an alternative classical ZPF with a different stochastic character, and demonstrate that it can exactly reproduce the statistics of the electromagnetic vacuum of quantum electrodynamics (QED). Incorporating this field into SED, it is shown that the full probability distribution for the amplitude of the ground state of a quantum-mechanical harmonic oscillator can be derived within a classical framework. This should lead to the possibility of developing further successful correspondences between SED and QED. © 1996 The American Physical Society.

We investigate the scattering off three nonoverlapping disks equidistantly spaced along a line in the two-dimensional plane with the radii of the outer disks equal and the radius of the inner disk varied. This system is a two-dimensional scattering analog to the double-well-potential (bound state) problem in one dimension. In both systems the symmetry splittings between symmetric and antisymmetric states or resonances, respectively, have to be traced back to tunneling effects, as semiclassically the geometrical periodic orbits have no contact with the vertical symmetry axis. We construct the leading semiclassical ‘‘creeping’’ orbits that are responsible for the symmetry splitting of the resonances in this system. The collinear three-disk system is not only one of the simplest but also one of the most effective systems for detecting creeping phenomena. While in symmetrically placed n-disk systems creeping corrections affect the subleading resonances, they here alone determine the symmetry splitting of the three-disk resonances in the semiclassical calculation. It should therefore be considered as a paradigm for the study of creeping effects. © 1996 The American Physical Society.

A family of geometric phases associated with the evolution of a quantum system is introduced. These phases share the property of depending on the curve determined by the Schrödinger equation as well as on the choice of an orthonormal basis in the Hilbert space of states. Their role in the expansion of the wave function is examined, and a comparison with previous results about Berry phases is made. © 1996 The American Physical Society.

A system of quantum reasoning for a closed system is developed by treating nonrelativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity operator on a Hilbert space of histories. Provided a consistency condition is satisfied, the corresponding Boolean algebra of histories, called a framework, can be assigned probabilities in the usual way, and within a single framework quantum reasoning is identical to ordinary probabilistic reasoning. A refinement rule, which allows a probability distribution to be extended from one framework to a larger (refined) framework, incorporates the dynamical laws of quantum theory. Two or more frameworks which are incompatible because they possess no common refinement cannot be simultaneously employed to describe a single physical system. Logical reasoning is a special case of probabilistic reasoning in which (conditional) probabilities are 1 (true) or 0 (false). As probabilities are only meaningful relative to some framework, the same is true of the truth or falsity of a quantum description. The formalism is illustrated using simple examples, and the physical considerations which determine the choice of a framework are discussed. © 1996 The American Physical Society.

Broadening and shift rates by rare gases have been measured for the Tl transitions 6${\mathit{P}}_{1/2}$-${\mathit{nP}}_{1/2,3/2}$ (n=9-14) applying Doppler-free two-photon spectroscopy. The rates show a clearly significant dependence on the total angular momentum of the upper nP states and also a distinct behavior over the most interesting range of intermediate effective principle quantum numbers. Calculations using a van der Waals potential and a combination of polarization and Fermi pseudopotential describe these dependences well. © 1996 The American Physical Society.