On two-distillable Werner states

We consider bipartite mixed states in a $d\otimes d$ quantum system. We say that $\rho$ is PPT if its partial transpose $1 \otimes T (\rho)$ is positive semidefinite, and otherwise $\rho$ is NPT. The well-known Werner states are divided into three types: (a) the separable states (the same as the PPT states); (b) the one-distillable states (necessarily NPT); and (c) the NPT states which are not one-distillable. We give several different formulations and provide further evidence for validity of the conjecture that the Werner states of type (c) are not two-distillable.Comment: 19 pages, expanded version containing new result

D-optimal matrices of orders 118, 138, 150, 154 and 174

We construct supplementary difference sets (SDS) with parameters $(59;28,22;21)$, $(69;31,27;24)$, $(75;36,29;28)$, $(77;34,31;27)$ and $(87;38,36;31)$. These SDSs give D-optimal designs (DO-designs) of two-circulant type of orders 118,138,150,154 and 174. Until now, no DO-designs of orders 138,154 and 174 were known. While a DO-design (not of two-circulant type) of order 150 was constructed previously by Holzmann and Kharaghani, no such design of two-circulant type was known. The smallest undecided order for DO-designs is now 198. We use a novel property of the compression map to speed up some computations.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1409.596

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

Asymmetric Dimethylarginine Is a Marker of Endothelial Dysfunction in Thrombotic Antiphospholipid Syndrome Patients

Objective: The potential contribution of asymmetric dimethylarginine (ADMA) and high-sensitivity C reactive protein (hsCRP) to endothelial dysfunction in APS patients has not been studied in detail, until now. The study involved 105 APS patients (59 diagnosed with primary APS (PAPS) and 46 APS associated with systemic lupus erythematosus (SAPS)) who were compared to 40 controls. Endothelial dysfunction was assessed by measurement of flow-mediated dilatation (FMD) and glyceryl trinitrate dilatation (NMD) of the brachial artery. ADMA (micromol/L) was analyzed by ELISA. Results: FMD in patients with APS was significantly lower than that of the controls (p < 0.001), with no difference between the PAPS and the SAPS groups. ADMA and hsCRP concentrations were significantly higher in the patient cohort than in the control group (p < 0.001, p = 0.006, respectively), as was the case with the SAPS group as compared to the PAPS group (p < 0.001, p = 0.022, respectively). FMD impairment correlated to ADMA (ρ 0.472, p < 0.001) and to hsCRP (ρ 0.181, p = 0.033). In the regression model, the ADMA concentration confirmed the strength of its association (B 0.518, SE 0.183, Wald 8.041, p = 0.005, Exp(B) 1.679, 95% CI 1.174–2.402) to FMD impairment. The synergistic probability model of ADMA and hsCRP caused FMD impairment when the positivity of β2GPIIgG was added. ADMA may be used as a simple and low-cost tool for verifying the presence of endothelial dysfunction in APS patients. According to the results of the study, we could presume that hsCRP, together with aPL, has a preparatory effect on the endothelium in causing endothelial dysfunction