Two qubit copying machine for economical quantum eavesdropping

We study the mapping which occurs when a single qubit in an arbitrary state interacts with another qubit in a given, fixed state resulting in some unitary transformation on the two qubit system which, in effect, makes two copies of the first qubit. The general problem of the quality of the resulting copies is discussed using a special representation, a generalization of the usual Schmidt decomposition, of an arbitrary two-dimensional subspace of a tensor product of two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can reproduce the results of any two qubit copying machine of this type. A simple stochastic generalization (using a ``classical'' random signal) of the copying machine is also considered. These copying machines provide simple embodiments of previously proposed optimal eavesdropping schemes for the BB84 and B92 quantum cryptography protocols.Comment: Minor changes. 26 pages RevTex including 7 PS figure

A cross sectional study investigating the association between exposure to food outlets and childhood obesity in Leeds, UK.

Background: Current UK policy in relation to the influence of the ‘food environment’ on childhood obesity appears to be driven largely on assumptions or speculations because empirical evidence is lacking and findings from studies are inconsistent. The aim of this study was to investigate the number of food outlets and the proximity of food outlets in the same sample of children, without solely focusing on fast food. Methods: Cross sectional study over 3 years (n = 13,291 data aggregated). Body mass index (BMI) was calculated for each participant, overweight and obesity were defined as having a BMI >85th (sBMI 1.04) and 95th (sBMI 1.64) percentiles respectively (UK90 growth charts). Home and school neighbourhoods were defined as circular buffers with a 2 km Euclidean radius, centred on these locations. Commuting routes were calculated using the shortest straight line distance, with a 2 km buffer to capture varying routes. Data on food outlet locations was sourced from Leeds City Council covering the study area and mapped against postcode. Food outlets were categorised into three groups, supermarkets, takeaway and retail. Proximity to the nearest food outlet in the home and school environmental domain was also investigated. Age, gender, ethnicity and deprivation (IDACI) were included as covariates in all models. Results: There is no evidence of an association between the number of food outlets and childhood obesity in any of these environments; Home Q4 vs. Q1 OR = 1.11 (95% CI = 0.95-1.30); School Q4 vs. Q1 OR = 1.00 (95% CI 0.87 – 1.16); commute Q4 vs. Q1 OR = 0.1.00 (95% CI 0.83 – 1.20). Similarly there is no evidence of an association between the proximity to the nearest food outlet and childhood obesity in the home (OR = 0.77 [95% CI = 0.61 – 0.98]) or the school (OR = 1.01 [95% CI 0.84 – 1.23]) environment. Conclusions: This study provides little support for the notion that exposure to food outlets in the home, school and commuting neighbourhoods increase the risk of obesity in children. It seems that the evidence is not well placed to support Governmental interventions/recommendations currently being proposed and that policy makers should approach policies designed to limit food outlets with caution

Energy of gravitational radiation in plane-symmetric space-times

Gravitational radiation in plane-symmetric space-times can be encoded in a complex potential, satisfying a non-linear wave equation. An effective energy tensor for the radiation is given, taking a scalar-field form in terms of the potential, entering the field equations in the same way as the matter energy tensor. It reduces to the Isaacson energy tensor in the linearized, high-frequency approximation. An energy conservation equation is derived for a quasi-local energy, essentially the Hawking energy. A transverse pressure exerted by interacting low-frequency gravitational radiation is predicted.Comment: 7 REVTeX4 page

Optimal Eavesdropping in Quantum Cryptography. II. Quantum Circuit

It is shown that the optimum strategy of the eavesdropper, as described in the preceding paper, can be expressed in terms of a quantum circuit in a way which makes it obvious why certain parameters take on particular values, and why obtaining information in one basis gives rise to noise in the conjugate basis.Comment: 7 pages, 1 figure, Latex, the second part of quant-ph/970103

P,T-Violating Nuclear Matrix Elements in the One-Meson Exchange Approximation

Expressions for the P,T-violating NN potentials are derived for $\pi$, $\rho$ and $\omega$ exchange. The nuclear matrix elements for $\rho$ and $\omega$ exchange are shown to be greatly suppressed, so that, under the assumption of comparable coupling constants, $\pi$ exchange would dominate by two orders of magnitude. The ratio of P,T-violating to P-violating matrix elements is found to remain approximately constant across the nuclear mass table, thus establishing the proportionality between time-reversal-violation and parity-violation matrix elements. The calculated values of this ratio suggest a need to obtain an accuracy of order $5 \times 10^{-4}$ for the ratio of the PT-violating to P-violating asymmetries in neutron transmission experiments in order to improve on the present limits on the isovector pion coupling constant.Comment: 17 pages, LaTeX, no figure

Correlation inequalities for noninteracting Bose gases

For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0 independent of the number of particles we derive the inequalities _N < _{N+1}, _N _N _N for i\neq j, \partial _N/\partial \beta >0 and ^+_N _N. Here N_i is the occupation number of the ith eigenstate of H^0, \beta is the inverse temperature and the superscript + refers to adding an extra level to those of H^0. The results follow from the convexity of the N-particle free energy as a function of N.Comment: a further inequality adde

Geometry of Universal Magnification Invariants

Recent work in gravitational lensing and catastrophe theory has shown that the sum of the signed magnifications of images near folds, cusps and also higher catastrophes is zero. Here, it is discussed how Lefschetz fixed point theory can be used to interpret this result geometrically. It is shown for the generic case as well as for elliptic and hyperbolic umbilics in gravitational lensing.Comment: RevTEX4, 13 pages, submitted to J. Math. Phy