Bounded Littlewood identities

We describe a method, based on the theory of Macdonald-Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald's partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R,S) in terms Macdonald polynomials of type A, are q,t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups, important in the theory of plane partitions. As applications of our results we obtain combinatorial formulas for characters of affine Lie algebras, Rogers-Ramanujan identities for such algebras complementing recent results of Griffin et al., and transformation formulas for Kaneko-Macdonald-type hypergeometric series

Mixture of multiple copies of maximally entangled states is quasi-pure

Employing the general BXOR operation and local state discrimination, the mixed state of the form \rho^{(k)}_{d}=\frac{1}{d^{2}}\sum_{m,n=0}^{d-1}(|\phi_{mn}><\phi_{mn}|)^{\otim es k} is proved to be quasi-pure, where $\{|\phi_{mn}>\}$ is the canonical set of mutually orthogonal maximally entangled states in $d\times d$. Therefore irreversibility does not occur in the process of distillation for this family of states. Also, the distillable entanglement is calculated explicitly.Comment: 6 pages, 1 figure. The paper is subtantially revised and the general proof is give

Rates of asymptotic entanglement transformations for bipartite mixed states: Maximally entangled states are not special

We investigate the asymptotic rates of entanglement transformations for bipartite mixed states by local operations and classical communication (LOCC). We analyse the relations between the rates for different transitions and obtain simple lower and upper bound for these transitions. In a transition from one mixed state to another and back, the amount of irreversibility can be different for different target states. Thus in a natural way, we get the concept of "amount" of irreversibility in asymptotic manipulations of entanglement. We investigate the behaviour of these transformation rates for different target states. We show that with respect to asymptotic transition rates under LOCC, the maximally entangled states do not have a special status. In the process, we obtain that the entanglement of formation is additive for all maximally correlated states. This allows us to show irreversibility in asymptotic entanglement manipulations for maximally correlated states in 2x2. We show that the possible nonequality of distillable entanglement under LOCC and that under operations preserving the positivity of partial transposition, is related to the behaviour of the transitions (under LOCC) to separable target states.Comment: 9 pages, 3 eps figures, REVTeX4; v2: presentation improved, new considerations added, title changed; v3: minor changes, published versio

Output state in multiple entanglement swapping

The technique of quantum repeaters is a promising candidate for sending quantum states over long distances through a lossy channel. The usual discussions of this technique deals with only a finite dimensional Hilbert space. However the qubits with which one implements this procedure will "ride" on continuous degrees of freedom of the carrier particles. Here we analyze the action of quantum repeaters using a model based on pulsed parametric down conversion entanglement swapping. Our model contains some basic traits of a real experiment. We show that the state created, after the use of any number of parametric down converters in a series of entanglement swappings, is always an entangled (actually distillable) state, although of a different form than the one that is usually assumed. Furthermore, the output state always violates a Bell inequality.Comment: 11 pages, 6 figures, RevTeX

Nonsymmetric interpolation macdonald polynomials and gl_n basic hypergeometric series

The Knop-Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type gl_n. Our main results include a new q-binomial theorem, a new q-Gauss sum, and several transformation formulae for gl_n series

Irreversibility in asymptotic manipulations of entanglement

We show that the process of entanglement distillation is irreversible by showing that the entanglement cost of a bound entangled state is finite. Such irreversibility remains even if extra pure entanglement is loaned to assist the distillation process.Comment: RevTex, 3 pages, no figures Result on indistillability of PPT states under pure entanglement catalytic LOCC adde

Modern Architecture in Dallas, Texas

The purpose of this study is to show that an awareness of modern architecture is developing in Dallas, Texas. This will be shown by an analysis of several recently constructed residential, civic, and commercial buildings. The contributions of American and European architects who have influenced our contemporary architecture are reviewed to in order to develop a background for this study. This will be shown by an analysis of several recently constructed residential, civic and commercial buildings

Distillable entanglement in d⊗dd\otimes d dimension

Distillable entanglement ($E_d$) is one of the acceptable measures of entanglement of mixed states. Based on discrimination through local operation and classical communication, this paper gives $E_d$ for two classes of orthogonal multipartite maximally entangled states.Comment: 6 page

The accuracy and accessibility of cited evidence: a study examining mental health policy documents

PURPOSE: Evidence-based policy making is increasingly being advocated by governments and scholars. To show that policies are informed by evidence, policy-related documents that cite external sources should ideally provide direct access to, and accurately represent, the referenced source and the evidence it provides. Our aim was to find a way to systematically assess the prevalence of referencing accuracy and accessibility issues in referenced statements selected from a sample of mental health-related policy documents. METHOD: 236 referenced statements were selected from 10 mental health-related policy documents published between 2013 and 2018. Policy documents were chosen as the focus of this investigation because of their relative accessibility and impact on clinical practice. Statements were rated against their referenced sources in terms of the (i) content accuracy in relation to the information provided by the referenced source and (ii) degree of accessibility of the source and the required evidence from the references provided. RESULTS: Of the 236 statements, 41 (59.7%) accurately represented the referenced source, 45 (19.1%) contained major errors and 50 (21.2%) contained minor errors in accuracy. For accessibility, 126 (53.4%) directly referenced primary sources of evidence that supported the claims made, 36 (15.3%) contained indirect references, 18 (7.6%) provided 'dead-end' references, and 11 (4.7%) references were completely inaccessible. CONCLUSIONS: With only slightly over half of all statements assessed providing fully accessible references and accurately representing the referenced source, these components of referencing quality deserve further attention if evidence-informed policy goals are to be achieved. The rating framework used in the current study proved to be a simple and straightforward method to assess these components and can provide a baseline against which interventions can be designed to improve referencing quality

Reversible transformations from pure to mixed states, and the unique measure of information

Transformations from pure to mixed states are usually associated with information loss and irreversibility. Here, a protocol is demonstrated allowing one to make these transformations reversible. The pure states are diluted with a random noise source. Using this protocol one can study optimal transformations between states, and from this derive the unique measure of information. This is compared to irreversible transformations where one does not have access to noise. The ideas presented here shed some light on attempts to understand entanglement manipulations and the inevitable irreversibility encountered there where one finds that mixed states can contain "bound entanglement".Comment: 10 pages, no figures, revtex4, table added, to appear in Phys. Rev.