Pancharatnam and Berry Phases in Three-Level Photonic Systems

A theoretical analysis of Pancharatnam and Berry phases is made for biphoton three-level systems, which are produced via frequency degenerate co-linear spontaneous parametric down conversion (SPDC). The general theory of Pancharatnam phases is discussed with a special emphasis on geodesic 'curves'in Hilbert space. Explicit expressions for Pancharatnam, dynamical and geometrical phases are derived for the transformations produced by linear phase-converters. The problem of gauge invariance is treated along all the article

Improperly obtained evidence in the Commonwealth: lessons for England and Wales?

English law's traditional approach to the admissibility of improperly obtained evidence is currently being rethought in response to a range of domestic and international pressures. With the position in England and Wales following the House of Lords' decision in A and Others (2005) firmly in mind, this article undertakes a selective review of comparative approaches to the admissibility of improperly obtained evidence in Australia, Canada and New Zealand. Having analysed relevant legislation and case law in each jurisdiction, general principles are derived to guide future developments in English law, in conformity with the European Convention on Human Rights

The twistor geometry of three-qubit entanglement

A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states can be represented by the points of the Klein quadric ${\cal Q}$ a space known from twistor theory. It is shown that three-qubit invariants are vanishing on special subspaces of ${\cal Q}$. An invariant vanishing for the $GHZ$ class is proposed. A geometric interpretation of the canonical decomposition and the inequality for distributed entanglement is also given.Comment: 4 pages RevTeX

Phase Dynamics of Two Entangled Qubits

We make a geometric study of the phases acquired by a general pure bipartite two level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a simple description of the dynamics of the entangled state's phase during the whole evolution. The global phase after a cyclic evolution is always an entire multiple of $\pi$ for all bipartite states, a result that does not depend on the degree of entanglement. There are three different types of phases combining themselves so as to result in the $n \pi$ global phase. They can be identified as dynamical, geometrical and topological. Each one of them can be easily identified using the presented geometric description. The interplay between them depends on the initial state and on its trajectory and the results obtained are shown to be in connection to those on mixed states phases.Comment: 9 figures, slightly different version from the accepted on

Gait Extraction and Description by Evidence-Gathering

Using gait as a biometric is of increasing interest, yet there are few model-based, parametric, approaches to extract and describe moving articulated objects. One new approach can detect moving parametric objects by evidence gathering, hence accruing known performance advantages in terms of performance and occlusion. Here we show how that the new technique can be extended not only to extract a moving person, but also to extract and concurrently provide a gait signature for use as a biometric. We show the natural relationship between the bases of these approaches, and the results they can provide. As such, these techniques allow for gait extraction and description for recognition purposes, and with known performance advantages of a well-established vision technique

Wiretapping a hidden network

We consider the problem of maximizing the probability of hitting a strategically chosen hidden virtual network by placing a wiretap on a single link of a communication network. This can be seen as a two-player win-lose (zero-sum) game that we call the wiretap game. The value of this game is the greatest probability that the wiretapper can secure for hitting the virtual network. The value is shown to equal the reciprocal of the strength of the underlying graph. We efficiently compute a unique partition of the edges of the graph, called the prime-partition, and find the set of pure strategies of the hider that are best responses against every maxmin strategy of the wiretapper. Using these special pure strategies of the hider, which we call omni-connected-spanning-subgraphs, we define a partial order on the elements of the prime-partition. From the partial order, we obtain a linear number of simple two-variable inequalities that define the maxmin-polytope, and a characterization of its extreme points. Our definition of the partial order allows us to find all equilibrium strategies of the wiretapper that minimize the number of pure best responses of the hider. Among these strategies, we efficiently compute the unique strategy that maximizes the least punishment that the hider incurs for playing a pure strategy that is not a best response. Finally, we show that this unique strategy is the nucleolus of the recently studied simple cooperative spanning connectivity game

Multi-particle Correlations in Quaternionic Quantum Systems

We investigate the outcomes of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multi-particle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements of particle spin components.Comment: REVTeX 3.0, 16 pages, no figures, UM-P-94/54, RCHEP-94/1

On non-L2L^2 solutions to the Seiberg-Witten equations

We show that a previous paper of Freund describing a solution to the Seiberg-Witten equations has a sign error rendering it a solution to a related but different set of equations. The non-$L^2$ nature of Freund's solution is discussed and clarified and we also construct a whole class of solutions to the Seiberg-Witten equations.Comment: 8 pages, Te