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

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-

Preparation of Mgo-ceo2 Mixed Oxide with Ionic Liquid as Catalyst for Dimethyl Carbonate Synthesis Via Transesterification

The synthesis and application of dimethyl carbonate (DMC) are achieving increasing importance due to its low toxicity and versatile reactivity. The phosgenation-route has been losing attraction recently due to the use of virulent phosgene. In transesterification process, DMC is co-generated with ethylene glycol (EG). In this study, various ionic liquids were used as template in coprecipitation methods to prepare mesoporous MgO-CeO2 mixed oxides particles. Among the ionic liquids, [Bmim][BF6] displayed the best performance in terms of activity, while [Omim][PF6] obtained the best selectivity for this reaction. The addition of IL's in the coprecipitation method increased the surface areaand pore volume of the catalysts. Meanwhile, the crystallite size of the catalysts was reduced many times. However, there is no effect of the surface areaand particle size as well on the catalytic activity of the catalyst in this reaction. The activity and selectivity of the catalyst depend on the base strength distribution. The moderate basic site is responsible for the catalytic activity, while the selectivity is more dependableon the strong basic site

The Normal State Resistivity of Grain Boundaries in YBa2Cu3O7-delta

Using an optimized bridge geometry we have been able to make accurate measurements of the properties of YBa2Cu3O7-delta grain boundaries above Tc. The results show a strong dependence of the change of resistance with temperature on grain boundary angle. Analysis of our results in the context of band-bending allows us to estimate the height of the potential barrier present at the grain boundary interface.Comment: 11 pages, 3 figure

Separability problem for multipartite states of rank at most four

One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial transposes are positive semidefinite). We show that any PPT state of rank two or three is separable and has length at most four. For separable states of rank four, we show that they have length at most six. It is six only for some qubit-qutrit or multiqubit states. It turns out that any PPT entangled state of rank four is necessarily supported on a 3x3 or a 2x2x2 subsystem. We obtain a very simple criterion for the separability problem of the PPT states of rank at most four: such a state is entangled if and only if its range contains no product vectors. This criterion can be easily applied since a four-dimensional subspace in the 3x3 or 2x2x2 system contains a product vector if and only if its Pluecker coordinates satisfy a homogeneous polynomial equation (the Chow form of the corresponding Segre variety). We have computed an explicit determinantal expression for the Chow form in the former case, while such expression was already known in the latter case.Comment: 19 page

Gastric Osteoma in a Dog

An eight year old female dog was referred with anorexia, nervousness and emaciation. At the point of time, severe lifelessness was the only symptom. Then euthanasia was done according to the owner’s decision. As a result of postmortem examination, thin white matters were found on the gastric mucosa of the greater curvature and there were no other significant gross findings. Tissue specimens were collected from the gastric wall, esophagus, gall bladder, aorta, heart, kidneys, liver, mesenteric lymph node, lungs, urinary bladder and spleen and processed for histopathology. Microscopically, the masses of stomach were consisted of well-differentiated osteoid tissues, the compact bone-osteocytes and the matured lamellated bone with Haversian system. It was diagnosed as osteoma of the stomach. Other organs were free on such histological findings

Construction of 3⊗33\otimes 3 entangled edge states with positive partial transposes

We construct a class of $3\otimes 3$ entangled edge states with positive partial transposes using indecomposable positive linear maps. This class contains several new types of entangled edge states with respect to the range dimensions of themselves and their partial transposes.Comment: 14 page