Signal or Noise? Information Theory and the Novel

In the context of a hostile funding environment, universities are increasingly asked to justify their output in narrowly defined economic terms, and this can be difficult in Humanities or Arts faculties where productivity is rarely reducible to a simple financial indicator. This can lead to a number of immediate consequences that I have no need to rehearse here, but can also result in some interesting tensions within the academic community itself. First is that which has become known as the ‘Science Wars’: the increasingly acrimonious exchanges between scientists and scientific academics and cultural critics or theorists about who has the right to describe the world. Much has already been said—and much remains to be said—about this issue, but it is not my intention to discuss it here. Rather, I will look at a second area of contestation: the incorporation of scientific theory into literary or cultural criticism. Much of this work comes from a genuine commitment to interdisciplinarity, and an appreciation of insights that a fresh perspective can bring to a familiar object. However, some can be seen as cynical attempts to lend literary studies the sort of empirical legitimacy of the sciences. In particular, I want to look at a number of critics who have applied information theory to the literary work. In this paper, I will examine several instances of this sort of criticism, and then, through an analysis of a novel by American author Richard Powers, Three Farmers on Their Way to a Dance, show how this sort of criticism merely reduces the meaningful analysis of a complex literary text.

One-dimensional quantum walk with unitary noise

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P-t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be Tsimilar toalpha(-2), where alpha is the standard deviation of the noise.

On the distributed compression of quantum information

The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian-Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction.

Bounds on integrals of the Wigner function

The integral of the Wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one. It is shown that for systems with 1 degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over an possible states, reduces to the problem of finding the greatest and least eigenvalues of a Hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Cultural information gathering by Australian students in France

Interviews with Australian university students returning from study in France indicate that problems in accessing crucial information are common experiences, and frequently lead to students reproducing stereotypes of French administrative inefficiency. Our paper argues that the issue is not one of information per se but of cultural differences in the dissemination of information. It analyses the ways in which students interpret their information-gathering difficulties, and the appropriateness of the strategies they devise for overcoming them. It then examines the pedagogical implications for preparing students for study abroad, suggesting means of both equipping students with alternative ways of understanding 'information skills' and intervening in the perpetuation of stereotypes. Cet article se base sur une quarantaine d'interviews avec des étudiants australiens ayant effectué des séjours d'études en France. La difficulté d'accéder aux renseignements jugés indispensables revient souvent au cours des entretiens, source de frustrations qui amène les Australiens à reproduire un stéréotype de l'inefficacité française. Nous posons qu'il s'agit moins d'un manque d'informations que d'une différence culturelle dans la diffusion des renseignements. Notre analyse porte sur les façons dont les étudiants interprètent leurs difficultés, ainsi que sur l'utilité de leurs stratégies pour réunir les données souhaitées. Ce travail a des conséquences pédagogiques pour la préparation de tels séjours : nous suggérons des moyens de conduire les étudiants à concevoir autrement la recherche de l'information et leurs expériences, intervenant ainsi dans la transmission des stéréotypes.

Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunnelling. The ene:rgy gap is never zero when the tunnelling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalized phase from a self-trapping phase that occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.

On entanglement and Lorentz transformations

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin 1/2 particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

Optimal quantum measurements for phase-shift estimation in optical interferometry

Quantum information theory, applied to optical interferometry, yields a 1/n scaling of phase uncertainty Delta phi independent of the applied phase shift phi, where n is the number of photons in the interferometer. This 1/n scaling is achieved provided that the output state is subjected to an optimal phase measurement. We establish this scaling law for both passive (linear) and active (nonlinear) interferometers and identify the coefficient of proportionality. Whereas a highly nonclassical state is required to achieve optimal scaling for passive interferometry, a classical input state yields a 1/n scaling of phase uncertainty for active interferometry.

Affective and evaluative descriptors of pain in the McGill Pain Questionnaire: reduction and reorganization

Recent reports indicate that several descriptors of pain sensations in the McGill Pain Questionnaire (MPQ) are difficult to classify within MPQ sensory subcategories because of incomprehension, underuse, or ambiguity of usage. Adopting the same methodology of recent studies, the present investigation focused on the affective and evaluative subcategories of the MPQ. A decision rule revealed that only 6 of 18 words met criteria for the affective category and 5 of 11 words met criteria for the evaluative category, thus warranting a reduced list of words in these categories. This reduction, however, led to negligible loss of information transmitted. Despite notable changes in classification, the intensity ratings of the retained words correlated very highly with those originally reported for the MPQ. In conclusion, although the intensity ratings of MPQ affective and evaluative descriptors need no revision, selective reduction and reorganization of these descriptors can enhance the efficiency of this approach to pain assessment. [copy ] 2001 by the American Pain Society

Reflection of structural waves at a solid/liquid interface

This paper investigates the reflection characteristics of structural or guided waves in rods at a solid/liquid interface. Structural waves, whose wavelengths are much larger than the diameter of the rod, are described in a first approximation by classical one-dimensional wave theory. The reflection characteristics of such waves at a solid/liquid (melting) interface has been reported by two different ultrasonic measurement techniques: first, measuring the fast regression rate of a melting interface during the burning of metal rod samples in an oxygen-enriched environment, and second, monitoring the propagation of the solid/liquid interface during the slow melting and solidification of a rod sample in a furnace. The second work clearly shows that the major reflection occurs from the solid/liquid interface and not the liquid/gas interface as predicted by plane longitudinal wave reflectivity theory. The present work confirms this observation by reporting on the results of some specially designed experiments to identify the main interface of reflection for structural waves in rods. Hence, it helps in explaining the fundamental discrepancy between the reflection characteristics at a solid/liquid interface between low frequency structural waves and high frequency bulk waves, and confirms that the detected echo within a burning metallic rod clearly represents a reflection from the solid/liquid interface. (C) 2003 Elsevier Science B.V. All rights reserved.

Pseudo memory effects, majorization and entropy in quantum random walks

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.

Quantum dynamics of a model for two Josephson-coupled Bose-Einstein condensates

In this work, we investigate the quantum dynamics of a model for two singlemode Bose-Einstein condensates which are coupled via Josephson tunnelling. Using direct numerical diagonalization of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalized and selftrapping phases. We show that these behaviours are dependent on both the initial state of the system and regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.