Classical information capacity of a class of quantum channels

We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. For this class of channels the norm of the output is maximized for the output being a normalized projection. We prove the additivity of the minimal output Renyi entropies with entropic parameters contained in [0, 2], generalizing an argument by Alicki and Fannes, and present a number of examples in detail. In order to relate these results to the classical information capacity, we introduce a weak form of covariance of a channel. We then identify several instances of weakly covariant channels for which we can infer the additivity of the classical information capacity. Both additivity results apply to the case of an arbitrary number of different channels. Finally, we relate the obtained results to instances of bi-partite quantum states for which the entanglement cost can be calculated.Comment: 14 pages, RevTeX (replaced with published version

Irrigation management in Pakistan: four papers

Irrigation management / Financing / Case studies / Sociological analysis / Policy / Agricultural development / Pakistan

Milwaukee Longitudinal School Choice Evaluation: Annual School Testing Summary Report 2010-11

Effective at the start of the 2010-11 school year, 2009 Wisconsin Act 28 requires private schools participating in the Milwaukee Parental Choice Program (MPCP) to administer the state test, the Wisconsin Knowledge and Concepts Examinations (WKCE) in reading, mathematics and science to all MPCP pupils in the same grades as public school students tested under Title 1 of the federal No Child Left Behind Act. Prior to the 2010-11 school year, 2005 Wisconsin Act 125 required private schools participating in the MPCP to administer a nationally normed standardized test of their choosing annually in reading, mathematics, and science to the MPCP students enrolled in the 4th, 8th, and 10th grades. Schools are currently given the option to continue to administer other nationally normed tests if they wish, in addition to the WKCE. The law further directs MPCP schools to submit copies of the test scores from all tests and examinations administered to their pupils in 2010-11 to the School Choice Demonstration Project (SCDP) for processing and reporting to the Legislative Audit Bureau. During the 2010-11 school year, all 102 MPCP schools that were required to administer tests did so and provided the results to the SCDP. Specifically, the SCDP received 10,657 WKCE test scores. Sixty-three schools submitted only the WKCE test scores and the remaining 39 schools submitted both nationally normed tests, such as the Iowa Test of Basic Skills and the WKCE. Five MPCP schools were not required to send in scores as they enrolled no MPCP students in mandatory testing grades

Entanglement and Frustration in Ordered Systems

This article reviews and extends recent results concerning entanglement and frustration in multipartite systems which have some symmetry with respect to the ordering of the particles. Starting point of the discussion are Bell inequalities: their relation to frustration in classical systems and their satisfaction for quantum states which have a symmetric extension. It is then discussed how more general global symmetries of multipartite systems constrain the entanglement between two neighboring particles. We prove that maximal entanglement (measured in terms of the entanglement of formation) is always attained for the ground state of a certain nearest neighbor interaction Hamiltonian having the considered symmetry with the achievable amount of entanglement being a function of the ground state energy. Systems of Gaussian states, i.e. quantum harmonic oscillators, are investigated in more detail and the results are compared to what is known about ordered qubit systems.Comment: 13 pages, for the Proceedings of QIT-EQIS'0