Table of contents

Journal of Physics A: Mathematical and General invites manuscript submissions on topics in quantum information and computation, for publication in a Special Issue in late Spring 2001.

In the past five years the new field of quantum information and computation has emerged, not only offering the potential of immense practical computing power but also suggesting deep links between the well-established disciplines of quantum theory, information theory and computer science.

As Guest Editors of this Special Issue, we encourage submissions in all aspects of the general area of quantum information and computation. Particular subjects will include: quantum entanglement, non-locality, quantum communication, quantum algorithms and quantum cryptography.

Manuscripts submitted to this Special Issue of Journal of Physics A will be refereed according to the normal criteria and procedures of the journal, in accordance with the following schedule:

• Deadline for receipt of contributed papers: 15 November 2000

• Deadline for acceptance of articles: 15 March 2001

• Publication of Special Issue: Late Spring 2001

This Special Issue will appear in both the paper and online editions of Journal of Physics A. Contributors of papers published in the issue will receive a complimentary copy, in addition to the usual 25 free offprints.

If you would like more information about this Special Issue, please contact us at jphysa@ioppublishing.co.uk. If you wish to submit an article, please see the author guidelines at www.iop.org/Journals/nfa.

A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to a hierarchy of identities for q-binomial coefficients.

We have developed an improved algorithm that allows us to enumerate the number of site animals (polyominoes) on the square lattice up to size 46. Analysis of the resulting series yields an improved estimate, τ = 4.062 570(8), for the growth constant of lattice animals and confirms, to a very high degree of certainty, that the generating function has a logarithmic divergence. We prove the bound τ>3.903 18. We also calculate the radius of gyration of both lattice animals and polygons enumerated by area. The analysis of the radius of gyration series yields the estimate ν = 0.641 15(5), for both animals and polygons enumerated by area. The mean perimeter of polygons of area n is also calculated. A number of new amplitude estimates are given.

The Wehrl phase distribution is defined as a phase density of the Wehrl classical information entropy. The new measure is applied to describe the quantum phase properties of some optical fields including Fock states, coherent and squeezed states, and superposition of chaotic and coherent fields. The Wehrl phase distribution is compared with both the conventional Wehrl entropy and Husimi phase distribution (the marginal Husimi Q-function). It is shown that the Wehrl phase distribution is a good measure of the phase-space uncertainty (noise), phase locking and phase bifurcation effects. It is also demonstrated that the Wehrl phase distribution properly describes phase randomization processes, and thus can be used in a description of the quantum optical phase.

The asymptotic expansion of the eigenvalues of the cubic anharmonic oscillator is studied in a region of the coupling constant plane in which there is a sequence of exponentially small subseries beyond the standard Rayleigh-Schrödinger perturbation theory (RSPT) power series. We give a simple algorithm for the calculation of these subseries (to any desired order) in terms of the RSPT coefficients expressed as polynomials in the quantum number, and illustrate our results with numerical Borel-Padé summations of the expansion up to third exponentially small order.

Operator quantization of the WZNW theory for the affine Lie algebra ĝ with the constrained (1)^d subalgebra is performed using a modification of the generalized canonical quantization method. The constrained theory is equivalent to the g/u(1)^d coset conformal field theory. Realizations of the g/u(1)^d parafermions for arbitrary d are found.

The problem of a non-relativistic electron in the presence of a uniform electromagnetic field and of one impurity, described by means of an Aharonov-Bohm point-like vortex, is studied. The exact solution is found and the quantum Hall conductance turns out to be the same as in the impurity-free case. This exactly solvable model seems to give indications, concerning the possible microscopic mechanisms underlying the integer quantum Hall effect, which sensibly deviate from some proposals available in the literature.

The pseudoperturbative shifted-l expansion technique (PSLET) is generalized for states with an arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between the angular momentum and the dimensionality of the central force Schrödinger equation, are used to construct part of the D-dimensional spiked harmonic oscillator bound-state spectra. PSLET results are found to compare excellently with those from direct numerical integration and generalized variational methods.

We consider a set of operators = (₁,...,_N) with diagonal representatives P(n) in the space of generalized coherent states |n⟩:  = ∫dµ(n) P(n)|n⟩⟨n|. We regularize the coherent-state path integral as a limit of a sequence of averages ⟨ ⟩_L over polygonal paths with L vertices n_1,...,L. The distribution of the path centroid = (1/L)∑_{l = 1}^LP(n_l) tends to the Wigner function W(x), the joint distribution for the operators: W(x) = lim _L→∞⟨δ_N(x-)⟩_L. This result is proved in the case where the Hamiltonian commutes with . The Wigner function is non-positive if the dominant paths with path centroid in a certain region have Berry phases close to odd multiples of π. For finite L the path centroid distribution is a Wigner function convolved with a Gaussian of variance inversely proportional to L. The results are illustrated by numerical calculations of the spin Wigner function from SU(2) coherent states. The relevance to the quantum Monte Carlo sign problem is also discussed.

Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular, the relation between on-shell crossing symmetry and off-shell Einstein causality. Among the collateral results of this new non-perturbative approach are profound relations between crossing symmetry of particle physics and Hawking-Unruh-like thermal aspects (KMS property, entropy attached to horizons) of quantum matter behind causal horizons, aspects which hitherto were exclusively related to Killing horizons in curved spacetime rather than with localization aspects in Minkowski space particle physics. The scope of this modular framework is amazingly wide and ranges from providing a conceptual basis for the d = 1 + 1 bootstrap-formfactor programme for factorizable d = 1 + 1 models to a decomposition theory of quantum field theories in terms of a finite collection of unitarily equivalent chiral conformal theories placed a specified relative position within a common Hilbert space (in d = 1 + 1 a holographic relation and in higher dimensions more like a scanning). The new framework gives a spacetime interpretation to the Zamolodchikov algebra and explains its thermal aspects.