Complete Separability and Fourier representations of n-qubit states

Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these two bases and to emphasize its interpretation as a Fourier transform. We then prove a general sufficient condition for complete separability in terms of the spin coefficients and give necessary and sufficient conditions for the complete separability of a class of generalized Werner densities. As a further application of the theory, we give necessary and sufficient conditions for full separability for a particular set of $n$-qubit states whose densities all satisfy the Peres condition

Mutually Unbiased Bases, Generalized Spin Matrices and Separability

A collection of orthonormal bases for a complex dXd Hilbert space is called mutually unbiased (MUB) if for any two vectors v and w from different bases the square of the inner product equals 1/d: || ^{2}=1/d. The MUB problem is to prove or disprove the the existence of a maximal set of d+1 bases. It has been shown in [W. K. Wootters, B. D. Fields, Annals of Physics, 191, no. 2, 363-381, (1989)] that such a collection exists if d is a power of a prime number p. We revisit this problem and use dX d generalizations of the Pauli spin matrices to give a constructive proof of this result. Specifically we give explicit representations of commuting families of unitary matrices whose eigenvectors solve the MUB problem. Additionally we give formulas from which the orthogonal bases can be readily computed. We show how the techniques developed here provide a natural way to analyze the separability of the bases. The techniques used require properties of algebraic field extensions, and the relevant part of that theory is included in an Appendix

A religious program for a Christian arts college

Thesis (Ed.M.)--Boston Universit

A Cross-Cultural Perspective on Selected Mental Health Systems

The information provided from authors around the world on their respective mental health systems is analyzed and compared. Several key dimensions are utilized, including the relationship of mental health services to other services, institutional care, community care, staffing, prevention and mental health promotion services, and accessibility. Resources and governmental priorities are identified as being essential to the provision of effective services. It is clear that the general trends identified by the experts for mental health in both developing and developed countries are by no means universal in applicability

What is the best macrolide for atypical pneumonia?

Erythromycin, clarithromycin, and azithromycin are equally effective in treating pneumonia caused by Mycoplasma pneumoniae or Chlamydophila (formerly Chlamydia) pneumoniae (strength of recommendation [SOR]: B, small head-to-head trials). Macrolide choice can be based on other considerations--cost, side effects, and effectiveness against other suspected pathogens (SOR: C, expert opinion)

Economically viable forest restoration in shifting cultivation landscapes

Shifting cultivation is a predominant land use across the tropics, feeding hundreds of millions of marginalised people, causing significant deforestation, and encompassing a combined area of land ten-fold greater than that used for oil palm and rubber. A key question is whether carbon-based payment for ecosystem services (PES) schemes can cost-effectively bring novel restoration and carbon-sensitive management practices to shifting agriculture. Using economic models that uniquely consider the substantial area of fallow land needed to support a single cultivated plot, we calculated the break-even carbon prices required for PES to match the opportunity cost of intervention in shifting agriculture. We do so in the North-east Indian biodiversity hotspot, where 35.4% of land is managed under shifting agriculture. We found net revenues of US$829.53–2581.95 per 30 ha when fallow area is included, which are an order of magnitude lower than previous estimates. Abandoning shifting agriculture entirely is highly feasible with break-even prices as low as US$1.33 t−1 CO2, but may conflict with food security. The oldest fallow plots could be fully restored for US$0.89 t−1 CO2 and the expansion of shifting agriculture into primary forest halted for US$0.51 t−1 CO2, whereas abandoning short-fallow systems would cost US$12.60 t−1 CO2. A precautionary reanalysis accounting for extreme economic uncertainty and leakage costs suggests that all interventions, excluding abandoning short-fallow systems, remain economically viable with prices less than US$4.00 t−1 CO2. Even with poorly formed voluntary carbon markets, shifting agriculture represents a critical opportunity for low-cost forest restoration whilst diversifying income streams of marginalised communities across a vast area