Atemporal diagrams for quantum circuits

A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical properties to those of entangled states (map-state duality), and suggests useful analogies, such as the inverse of an entangled ket. Diagrams clarify the role of channel kets, transition operators, dynamical operators (matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite) operators are represented by diagrams with a symmetry that aids in understanding their connection with completely positive maps. The diagrams are used to analyze standard teleportation and dense coding, and for a careful study of unambiguous (conclusive) teleportation. A simple diagrammatic argument shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled using a one-qubit environment in a mixed state.Comment: Minor changes in references. Latex 32 pages, 13 figures in text using PSTrick

Deterministic and Unambiguous Dense Coding

Optimal dense coding using a partially-entangled pure state of Schmidt rank $\bar D$ and a noiseless quantum channel of dimension $D$ is studied both in the deterministic case where at most $L_d$ messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probability $\tau_x$) Bob knows for sure that Alice sent message $x$, and when it fails (probability $1-\tau_x$) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For $\bar D\leq D$ a bound is obtained for $L_d$ in terms of the largest Schmidt coefficient of the entangled state, and is compared with published results by Mozes et al. For $\bar D > D$ it is shown that $L_d$ is strictly less than $D^2$ unless $\bar D$ is an integer multiple of $D$, in which case uniform (maximal) entanglement is not needed to achieve the optimal protocol. The unambiguous case is studied for $\bar D \leq D$, assuming $\tau_x>0$ for a set of $\bar D D$ messages, and a bound is obtained for the average \lgl1/\tau\rgl. A bound on the average \lgl\tau\rgl requires an additional assumption of encoding by isometries (unitaries when $\bar D=D$) that are orthogonal for different messages. Both bounds are saturated when $\tau_x$ is a constant independent of $x$, by a protocol based on one-shot entanglement concentration. For $\bar D > D$ it is shown that (at least) $D^2$ messages can be sent unambiguously. Whether unitary (isometric) encoding suffices for optimal protocols remains a major unanswered question, both for our work and for previous studies of dense coding using partially-entangled states, including noisy (mixed) states.Comment: Short new section VII added. Latex 23 pages, 1 PSTricks figure in tex

Fast protocols for local implementation of bipartite nonlocal unitaries

In certain cases the communication time required to deterministically implement a nonlocal bipartite unitary using prior entanglement and LOCC (local operations and classical communication) can be reduced by a factor of two. We introduce two such "fast" protocols and illustrate them with various examples. For some simple unitaries, the entanglement resource is used quite efficiently. The problem of exactly which unitaries can be implemented by these two protocols remains unsolved, though there is some evidence that the set of implementable unitaries may expand at the cost of using more entanglement.Comment: Updated to published versio

The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice

We study completely integrable Hamiltonian systems whose monodromy matrices are related to the representatives for the set of gauge equivalence classes $\boldsymbol{\mathcal{M}}_F$ of polynomial matrices. Let $X$ be the algebraic curve given by the common characteristic equation for $\boldsymbol{\mathcal{M}}_F$. We construct the isomorphism from the set of representatives to an affine part of the Jacobi variety of $X$. This variety corresponds to the invariant manifold of the system, where the Hamiltonian flow is linearized. As the application, we discuss the algebraic completely integrability of the extended Lotka-Volterra lattice with a periodic boundary condition.Comment: Revised version, 26 page

Validation of the factor structure of the Eating Pathology Symptoms Inventory in an international sample of sexual minority men

Sexual minority individuals are at greater risk for the development of eating-disorder (ED) psychopathology. Despite the importance of understanding ED symptoms in sexual minority men, most ED measures were developed and validated in heterosexual, young adult, white women. The psychometric properties of ED measures in diverse populations remain largely unknown. The purpose of this study was to test: 1) whether the eight-factor structure of the Eating Pathology Symptoms Inventory (EPSI) replicated in sexual minority men and 2) group-level mean differences between gay and bisexual men on the eight EPSI scales. International participants (N = 722 sexual minority men from 20 countries) were recruited via the Grindr smartphone application. Confirmatory factor analysis (CFA) was completed using a weighted least square mean and variance adjusted estimator. Group differences in eating pathology between gay and bisexual men were tested using independent samples t-tests. The CFA model fit was good on all fit indices (CFI/TLI > 0.90, RMSEA < 0.06). Gay and bisexual men only differed on the EPSI Binge Eating scale. The results of this investigation suggest that the EPSI may be a useful tool for understanding eating pathology in this population. Using psychometrically sound assessment tools for sexual minority men is a vital piece of treatment planning and clinical decision making. The current study fills an important gap in the clinical and research literature by testing the validity and psychometric properties of a commonly used ED measure in sexual minority men

The classical limit for a class of quantum baker's maps

We show that the class of quantum baker's maps defined by Schack and Caves have the proper classical limit provided the number of momentum bits approaches infinity. This is done by deriving a semi-classical approximation to the coherent-state propagator.Comment: 18 pages, 5 figure

Connecting does not necessarily mean learning: Course handbooks as mediating tools in school-university partnerships

This is the author's accepted manuscript (titled "Course handbooks as mediating tools in learning to teach"). The final published article is available from the link below. Copyright @ 2011 American Association of Colleges for Teacher Education.Partnerships between schools and universities in England use course handbooks to guide student teacher learning during long field experiences. Using data from a yearlong ethnographic study of a postgraduate certificate of education programme in one English university, the function of course handbooks in mediating learning in two high school subject departments (history and modern foreign languages) is analyzed. Informed by Cultural Historical Activity Theory, the analysis focuses on the handbooks as mediating tools in the school-based teacher education activity systems. Qualitative differences in the mediating functions of the handbooks-in-use are examined and this leads to a consideration of the potential of such tools for teacher learning in school–university partnerships. Following Zeichner’s call for rethinking the relationships between schools and universities, the article argues that strong structural connections between different institutional sites do not necessarily enhance student teacher learning

Binge flying: Behavioural addiction and climate change

Recent popular press suggests that ‘binge flying’ constitutes a new site of behavioural addiction. We theoretically appraise and empirically support this proposition through interviews with consumers in Norway and the United Kingdom conducted in 2009. Consistent findings from across two national contexts evidence a growing negative discourse towards frequent short-haul tourist air travel and illustrate strategies of guilt suppression and denial used to span a cognitive dissonance between the short-term personal benefits of tourism and the air travel’s associated long-term consequences for climate change. Tensions between tourism consumption and changing social norms towards acceptable flying practice exemplify how this social group is beginning to (re)frame what constitutes ‘excessive’ holiday flying, despite concomitantly continuing their own frequent air travels