The Power of LOCCq State Transformations

Reversible state transformations under entanglement non-increasing operations give rise to entanglement measures. It is well known that asymptotic local operations and classical communication (LOCC) are required to get a simple operational measure of bipartite pure state entanglement. For bipartite mixed states and multipartite pure states it is likely that a more powerful class of operations will be needed. To this end \cite{BPRST01} have defined more powerful versions of state transformations (or reducibilities), namely LOCCq (asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC (asymptotic LOCC with catalysis). In this paper we show that {\em LOCCq state transformations are only as powerful as asymptotic LOCC state transformations} for multipartite pure states. We first generalize the concept of entanglement gambling from two parties to multiple parties: any pure multipartite entangled state can be transformed to an EPR pair shared by some pair of parties and that any irreducible $m$ $(m\ge 2)$ party pure state can be used to create any other state (pure or mixed), using only local operations and classical communication (LOCC). We then use this tool to prove the result. We mention some applications of multipartite entanglement gambling to multipartite distillability and to characterizations of multipartite minimal entanglement generating sets. Finally we discuss generalizations of this result to mixed states by defining the class of {\em cat distillable states}

Wing flutter calculations with the CAP-TSD unsteady transonic small disturbance program

The application and assessment is described of CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code for flutter prediction. The CAP-TSD program was developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures. Flutter calculations are presented for two thin, swept-and-tapered wing planforms with well defined modal properties. The calculations are for Mach numbers from low subsonic to low supersonic values, including the transonic range, and are compared with subsonic linear theory and experimental flutter data. The CAP-TSD flutter results are generally in good agreement with the experimental values and are in good agreement with subsonic linear theory when wing thickness is neglected

QIP = PSPACE

We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update method to a class of semidefinite programs that captures the computational power of quantum interactive proofs. As the containment of PSPACE in QIP follows immediately from the well-known equality IP = PSPACE, the equality QIP = PSPACE follows.Comment: 21 pages; v2 includes corrections and minor revision

Predictors of Vitamin D Supplementation Amongst Infants in Ireland Throughout The First Year of Life

A prospective observational study was conducted. Self-complete questionnaires recorded socio-demographic characteristics, health behaviours and supplementation practices for 158 mother-infant dyads at 4, 9 and 12 months post-partum. A 2-day food diary was also obtained on 12-month-old infants to examine the contribution of diet to vitamin D intakes