Quantum privacy and quantum coherence

We derive a simple relation between a quantum channel's capacity to convey coherent (quantum) information and its usefulness for quantum cryptography.Comment: 6 pages RevTex; two short comments added 7 October 199

Indeterminate-length quantum coding

The quantum analogues of classical variable-length codes are indeterminate-length quantum codes, in which codewords may exist in superpositions of different lengths. This paper explores some of their properties. The length observable for such codes is governed by a quantum version of the Kraft-McMillan inequality. Indeterminate-length quantum codes also provide an alternate approach to quantum data compression.Comment: 32 page

On asymptotic continuity of functions of quantum states

A useful kind of continuity of quantum states functions in asymptotic regime is so-called asymptotic continuity. In this paper we provide general tools for checking if a function possesses this property. First we prove equivalence of asymptotic continuity with so-called it robustness under admixture. This allows us to show that relative entropy distance from a convex set including maximally mixed state is asymptotically continuous. Subsequently, we consider it arrowing - a way of building a new function out of a given one. The procedure originates from constructions of intrinsic information and entanglement of formation. We show that arrowing preserves asymptotic continuity for a class of functions (so-called subextensive ones). The result is illustrated by means of several examples.Comment: Minor corrections, version submitted for publicatio

Entanglement on mixed stabilizer states: normal forms and reduction procedures

Published versio

Additivity and non-additivity of multipartite entanglement measures

We study the additivity property of three multipartite entanglement measures, i.e. the geometric measure of entanglement (GM), the relative entropy of entanglement and the logarithmic global robustness. First, we show the additivity of GM of multipartite states with real and non-negative entries in the computational basis. Many states of experimental and theoretical interests have this property, e.g. Bell diagonal states, maximally correlated generalized Bell diagonal states, generalized Dicke states, the Smolin state, and the generalization of D\"{u}r's multipartite bound entangled states. We also prove the additivity of other two measures for some of these examples. Second, we show the non-additivity of GM of all antisymmetric states of three or more parties, and provide a unified explanation of the non-additivity of the three measures of the antisymmetric projector states. In particular, we derive analytical formulae of the three measures of one copy and two copies of the antisymmetric projector states respectively. Third, we show, with a statistical approach, that almost all multipartite pure states with sufficiently large number of parties are nearly maximally entangled with respect to GM and relative entropy of entanglement. However, their GM is not strong additive; what's more surprising, for generic pure states with real entries in the computational basis, GM of one copy and two copies, respectively, are almost equal. Hence, more states may be suitable for universal quantum computation, if measurements can be performed on two copies of the resource states. We also show that almost all multipartite pure states cannot be produced reversibly with the combination multipartite GHZ states under asymptotic LOCC, unless relative entropy of entanglement is non-additive for generic multipartite pure states.Comment: 45 pages, 4 figures. Proposition 23 and Theorem 24 are revised by correcting a minor error from Eq. (A.2), (A.3) and (A.4) in the published version. The abstract, introduction, and summary are also revised. All other conclusions are unchange

Spin and Rotations in Galois Field Quantum Mechanics

We discuss the properties of Galois Field Quantum Mechanics constructed on a vector space over the finite Galois field GF(q). In particular, we look at 2-level systems analogous to spin, and discuss how SO(3) rotations could be embodied in such a system. We also consider two-particle `spin' correlations and show that the Clauser-Horne-Shimony-Holt (CHSH) inequality is nonetheless not violated in this model.Comment: 21 pages, 11 pdf figures, LaTeX. Uses iopart.cls. Revised introduction. Additional reference

Effects of fluoxetine on functional outcomes after acute stroke (FOCUS): a pragmatic, double-blind, randomised, controlled trial

Background Results of small trials indicate that fluoxetine might improve functional outcomes after stroke. The FOCUS trial aimed to provide a precise estimate of these effects. Methods FOCUS was a pragmatic, multicentre, parallel group, double-blind, randomised, placebo-controlled trial done at 103 hospitals in the UK. Patients were eligible if they were aged 18 years or older, had a clinical stroke diagnosis, were enrolled and randomly assigned between 2 days and 15 days after onset, and had focal neurological deficits. Patients were randomly allocated fluoxetine 20 mg or matching placebo orally once daily for 6 months via a web-based system by use of a minimisation algorithm. The primary outcome was functional status, measured with the modified Rankin Scale (mRS), at 6 months. Patients, carers, health-care staff, and the trial team were masked to treatment allocation. Functional status was assessed at 6 months and 12 months after randomisation. Patients were analysed according to their treatment allocation. This trial is registered with the ISRCTN registry, number ISRCTN83290762. Findings Between Sept 10, 2012, and March 31, 2017, 3127 patients were recruited. 1564 patients were allocated fluoxetine and 1563 allocated placebo. mRS data at 6 months were available for 1553 (99·3%) patients in each treatment group. The distribution across mRS categories at 6 months was similar in the fluoxetine and placebo groups (common odds ratio adjusted for minimisation variables 0·951 [95% CI 0·839–1·079]; p=0·439). Patients allocated fluoxetine were less likely than those allocated placebo to develop new depression by 6 months (210 [13·43%] patients vs 269 [17·21%]; difference 3·78% [95% CI 1·26–6·30]; p=0·0033), but they had more bone fractures (45 [2·88%] vs 23 [1·47%]; difference 1·41% [95% CI 0·38–2·43]; p=0·0070). There were no significant differences in any other event at 6 or 12 months. Interpretation Fluoxetine 20 mg given daily for 6 months after acute stroke does not seem to improve functional outcomes. Although the treatment reduced the occurrence of depression, it increased the frequency of bone fractures. These results do not support the routine use of fluoxetine either for the prevention of post-stroke depression or to promote recovery of function. Funding UK Stroke Association and NIHR Health Technology Assessment Programme