One parameter family of indecomposable optimal entanglement witnesses arising from generalized Choi maps

In the recent paper [Chru\'{s}ci\'{n}ski and Wudarski, arXiv:1105.4821], it was conjectured that the entanglement witnesses arising from some generalized Choi maps are optimal. We show that this conjecture is true. Furthermore, we show that they provide a one parameter family of indecomposable optimal entanglement witnesses.Comment: 3 page

Facial structures for various notions of positivity and applications to the theory of entanglement

In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied to study the notions of entangled edge states with positive partial transposes and optimality of entanglement witnesses.Comment: An expository note. Section 7 and Section 8 have been enlarge

Entanglement witnesses arising from Choi type positive linear maps

We construct optimal PPTES witnesses to detect $3\otimes 3$ PPT entangled edge states of type $(6,8)$ constructed recently \cite{kye_osaka}. To do this, we consider positive linear maps which are variants of the Choi type map involving complex numbers, and examine several notions related to optimality for those entanglement witnesses. Through the discussion, we suggest a method to check the optimality of entanglement witnesses without the spanning property.Comment: 18 pages, 4 figures, 1 tabl

ASEAN-EU university network programme on EMC and SI education

This paper reports about a project for the creation of an innovative university course devoted to the preparation of future electronic designers to the challenges imposed by the assurance of the electrical performance of high-speed electronic systems. The target groups are future university teaching staff and future electronic systems designers. Activities are developed by means of sharing research results, seminars, experience exchange and the development of demonstrators to be used for teaching. The partnership is composed by Technical University of Turin (Italy), University of Hannover (Germany), University of Nottingham (UK), Nanyang Technological University (Singapore) and King Monguts Institute of Technology Lad-krabang, Bangkok (Thailand). The program is partially funded by the European Commission under the ASEAN-EU University Network Programme (AUNP) and its duration is 24 months

Public geographies II: being organic

This second report on ‘public geographies' considers the diverse, emergent and shifting spaces of engaging with and in public/s. Taking as its focus the more ‘organic’ rather than ‘traditional’ approach to doing public geography, as discussed in the first report, it explores the multiple and unorthodox ways in which engagements across academic-public spheres play out, and what such engagements may mean for geography/ers. The report first explores the role of the internet in ‘enabling conversations', generating a range of opportunities for public geography through websites, wikis, blogs, file-sharing sites, discussion forums and more, thinking critically about how technologies may enable/disable certain kinds of publically engaged activities. It then considers issues of process and praxis: how collaborations with groups/communities/organizations beyond academia are often unplanned, serendipitous encounters that evolve organically into research/learning/teaching endeavours; but also that personal politics/positionality bring an agency to bear upon whether we, as academics, follow the leads we may stumble upon. The report concludes with a provocative question – given that many non-academics appear to be doing some amazing and inspiring projects and activities, thoughtful, critical and (arguably) examples of organic public geographies, what then is academia’s role

Extremal extensions of entanglement witnesses: Unearthing new bound entangled states

In this paper, we discuss extremal extensions of entanglement witnesses based on Choi's map. The constructions are based on a generalization of the Choi map due to Osaka, from which we construct entanglement witnesses. These extremal extensions are powerful in terms of their capacity to detect entanglement of positive under partial transpose (PPT) entangled states and lead to unearthing of entanglement of new PPT states. We also use the Cholesky-like decomposition to construct entangled states which are revealed by these extremal entanglement witnesses.Comment: 8 pages 6 figures revtex4-

Optimality for indecomposable entanglement witnesses

We examine various notions related with the optimality for entanglement witnesses arising from Choi type positive linear maps. We found examples of optimal entanglement witnesses which are non-decomposable, but which are not `non-decomposable optimal entanglement witnesses' in the sense of [M. Lewenstein, B. Kraus, J. Cirac, and P. Horodecki, Phys. Rev. A 62, 052310 (2000)]. We suggest to use the term `PPTES witness' and `optimal PPTES witness' in the places of `non-decomposable entanglement witness' and `non-decomposable optimal entanglement witnesses' in order to avoid possible confusion. We also found examples of non-extremal optimal entanglement witnesses which are indecomposable.Comment: 5 pages, 1 figure, 1 tabl