Multiplicativity properties of entrywise positive maps

Multiplicativity of certain maximal p -> q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity (CP) is either augmented by, or replaced by, the requirement that the entries of a matrix representative of the map are non-negative (EP). In particular, for integer t, multiplicativity holds for the maximal 2 -> 2t norm of a product of two maps, whenever one of the pair is EP; for the maximal 1 -> t norm for pairs of CP maps when one of them is also EP; and for the maximal 1 -> 2t norm for the product of an EP and a 2-positive map. Similar results are shown in the infinite-dimensional setting of convolution operators on L^2(R), with the pointwise positivity of an integral kernel replacing entrywise positivity of a matrix. These results apply in particular to Gaussian bosonic channels.Comment: results extended to some infinite dimensional cases, including the Gaussian bosonic channe

The structure of degradable quantum channels

Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs of some known results. In the case of qubits, we provide a complete characterization of all degradable channels with two dimensional output, give a new proof that a qubit channel with two Kraus operators is either degradable or anti-degradable and present a complete description of anti-degradable unital qubit channels with a new proof. For higher output dimensions we explore the relationship between the output and environment dimensions ($d_B$ and $d_E$ respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with a environment that is "small" in the sense $d_E \leq d_B$. Perhaps surprisingly, we also present examples of degradable channels with ``large'' environments, in the sense that the minimal dimension $d_E > d_B$. Indeed, one can have $d_E > \tfrac{1}{4} d_B^2$. In the case of channels with diagonal Kraus operators, we describe the subclass which are complements of entanglement breaking channels. We also obtain a number of results for channels in the convex hull of conjugations with generalized Pauli matrices. However, a number of open questions remain about these channels and the more general case of random unitary channels.Comment: 42 pages, 3 figures, Web and paper abstract differ; (v2 contains only minor typo corrections

A Case Study Examining the Connections Between Student-Teacher Relationships and Student Motivation in the Upper Elementary Classroom

The purpose of this multiple case study was to develop an in-depth understanding of how student-teacher relationships are connected to student motivation within the upper elementary, fourth, fifth, and sixth grade, classroom for students at Small Rural Elementary School (SRES; pseudonym) in southeastern Pennsylvania. The theory guiding this study is Maslow’s hierarchy of need as it explains the effects human needs have on motivation, confirming the significance of students having their basic needs met in the classroom by their teacher in order to be motivated to achieve greater outcomes in the classroom. The study was guided by a central research question: how are student-teacher relationships connected to student motivation in the upper elementary classroom? The multiple case study utilized three data collection methods: surveys, interviews, and a focus group. Data were then coded to find common themes on how student-teacher relationships are created through the meeting of physical, physiological, mental, and emotional needs of students and examine the impact these relationships have on student motivation in the upper elementary classroom at SRES. The findings of this research suggested SRES upper elementary teachers are able to build authentic relationships with their students through simple acts in the classroom that meet the student physical, physiological, mental, and emotional needs, and in turn students are more motivated within the classrooms of teachers they have genuine relationships with, where trust has become the foundation

"It's not just about the patient, it's the families too.": End of life care in the home environment

Introduction: Most people when asked say they would prefer to die at home. However, ‘Death in Usual Place of Residence’ (DiUPR) does not give any real insight into the quality and experiences of care received. Additionally, DiUPR involves other family members resident in the home environment and their needs, preferences and experiences also need consideration. Aim(s) and Method(s): The aim of this work was to explore the experiences of patients and informal caregivers receiving at-home care from a specialist palliative care service. We undertook individual interviews with 11 patients and 10 significant others. We used the Pictor technique, a novel interview tool used to sensitively explore networks of support and experiences of palliative care. Interviews were analysed thematically. Results: Caring for a loved one at home was acknowledged as draining, but participants were effusive about the excellent at-home professional support they received from the specialist service. The care provided evidently recognised the needs of both patients and their families. Effective co-ordination of care, including liaison with other services was especially appreciated. Conclusion(s): With increasing trends towards DiUPR, it is vital that there are sufficient well-resourced palliative care services available in the community to support both patients and their families at the end of life. Pictor is a useful means to obtain detailed insight into individual experiences of end of life care. Care co-ordination emerged as key concern for patients receiving End of Life Care and their families

A Fall from Grace: United States v. W. R. Grace and the Need for Criminal Discovery Reform

This article examines several 2009 cases involving prosecutorial misconduct arising from the federal government\u27s failure to live up to its criminal discovery obligations. The article focuses specifically on U.S. v. W.R. Grace, a Clean Air Act criminal case in Montana. The authors\u27 analysis of Grace and other cases suggests that the absence of a clear, enforceable rule jeopardizes the government\u27s ability to fairly prosecute its cases and supports amending Rule 16 to eliminate the gap between prosecutors\u27 legal and ethical duties, and to require the pretrial disclosure of evidence favorable to the defendant

Exploring Perceived Usability and Interpretability of Aviation Weather Products Among GA Pilots

Introduction Results Discussion Current Investigation