Orthogonal polynomial kernels and canonical correlations for Dirichlet measures

We consider a multivariate version of the so-called Lancaster problem of characterizing canonical correlation coefficients of symmetric bivariate distributions with identical marginals and orthogonal polynomial expansions. The marginal distributions examined in this paper are the Dirichlet and the Dirichlet multinomial distribution, respectively, on the continuous and the N-discrete d-dimensional simplex. Their infinite-dimensional limit distributions, respectively, the Poisson-Dirichlet distribution and Ewens's sampling formula, are considered as well. We study, in particular, the possibility of mapping canonical correlations on the d-dimensional continuous simplex (i) to canonical correlation sequences on the d+1-dimensional simplex and/or (ii) to canonical correlations on the discrete simplex, and vice versa. Driven by this motivation, the first half of the paper is devoted to providing a full characterization and probabilistic interpretation of n-orthogonal polynomial kernels (i.e., sums of products of orthogonal polynomials of the same degree n) with respect to the mentioned marginal distributions. We establish several identities and some integral representations which are multivariate extensions of important results known for the case d=2 since the 1970s. These results, along with a common interpretation of the mentioned kernels in terms of dependent Polya urns, are shown to be key features leading to several non-trivial solutions to Lancaster's problem, many of which can be extended naturally to the limit as $d\rightarrow\infty$.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ403 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

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

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

Collaborative working within UK NHS secondary care and across sectors for COPD and the impact of peer review : qualitative findings from the UK National COPD Resources and Outcomes Project

Introduction: We investigated the effects on collaborative work within the UK National Health Service (NHS) of an intervention for service quality improvement: informal, structured, reciprocated, multidisciplinary peer review with feedback and action plans. The setting was care for chronic obstructive pulmonary disease (COPD). Theory and methods: We analysed semi-structured interviews with 43 hospital respiratory consultants, nurses and general managers at 24 intervention and 11 control sites, as part of a UK randomised controlled study, the National COPD Resources and Outcomes Project (NCROP), using Scott’s conceptual framework for action (inter-organisational, intra-organisational, inter-professional and inter-individual). Three areas of care targeted by NCROP involved collaboration across primary and secondary care. Results: Hospital respiratory department collaborations with commissioners and hospital managers varied. Analysis suggested that this is related to team responses to barriers. Clinicians in unsuccessful collaborations told ‘atrocity stories’ of organisational, structural and professional barriers to service improvement. The others removed barriers by working with government and commissioner agendas to ensure continued involvement in patients’ care. Multidisciplinary peer review facilitated collaboration between participants, enabling them to meet, reconcile differences and exchange ideas across boundaries. Conclusions: The data come from the first randomised controlled trial of organisational peer review, adding to research into UK health service collaborative work, which has had a more restricted focus on inter-professional relations. NCROP peer review may only modestly improve collaboration but these data suggest it might be more effective than top-down exhortations to change when collaboration both across and within organisations is required