Separable approximations of density matrices of composite quantum systems

We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)]. Such approximations allow to represent in an optimal way any density operator as a sum of a separable state and an entangled state of a certain form. For two qubit systems (M=N=2) the best separable approximation has a form of a mixture of a separable state and a projector onto a pure entangled state. We formulate a necessary condition that the pure state in the best separable approximation is not maximally entangled. We demonstrate that the weight of the entangled state in the best separable approximation in arbitrary dimensions provides a good entanglement measure. We prove in general for arbitrary M and N that the best separable approximation corresponds to a mixture of a separable and an entangled state which are both unique. We develop also a theory of optimal separable approximations for states with positive partial transpose (PPT states). Such approximations allow to decompose any density operator with positive partial transpose as a sum of a separable state and an entangled PPT state. We discuss procedures of constructing such decompositions.Comment: 12 pages, 2 figure

Effects of Anacetrapib in Patients with Atherosclerotic Vascular Disease

BACKGROUND: Patients with atherosclerotic vascular disease remain at high risk for cardiovascular events despite effective statin-based treatment of low-density lipoprotein (LDL) cholesterol levels. The inhibition of cholesteryl ester transfer protein (CETP) by anacetrapib reduces LDL cholesterol levels and increases high-density lipoprotein (HDL) cholesterol levels. However, trials of other CETP inhibitors have shown neutral or adverse effects on cardiovascular outcomes. METHODS: We conducted a randomized, double-blind, placebo-controlled trial involving 30,449 adults with atherosclerotic vascular disease who were receiving intensive atorvastatin therapy and who had a mean LDL cholesterol level of 61 mg per deciliter (1.58 mmol per liter), a mean non-HDL cholesterol level of 92 mg per deciliter (2.38 mmol per liter), and a mean HDL cholesterol level of 40 mg per deciliter (1.03 mmol per liter). The patients were assigned to receive either 100 mg of anacetrapib once daily (15,225 patients) or matching placebo (15,224 patients). The primary outcome was the first major coronary event, a composite of coronary death, myocardial infarction, or coronary revascularization. RESULTS: During the median follow-up period of 4.1 years, the primary outcome occurred in significantly fewer patients in the anacetrapib group than in the placebo group (1640 of 15,225 patients [10.8%] vs. 1803 of 15,224 patients [11.8%]; rate ratio, 0.91; 95% confidence interval, 0.85 to 0.97; P=0.004). The relative difference in risk was similar across multiple prespecified subgroups. At the trial midpoint, the mean level of HDL cholesterol was higher by 43 mg per deciliter (1.12 mmol per liter) in the anacetrapib group than in the placebo group (a relative difference of 104%), and the mean level of non-HDL cholesterol was lower by 17 mg per deciliter (0.44 mmol per liter), a relative difference of -18%. There were no significant between-group differences in the risk of death, cancer, or other serious adverse events. CONCLUSIONS: Among patients with atherosclerotic vascular disease who were receiving intensive statin therapy, the use of anacetrapib resulted in a lower incidence of major coronary events than the use of placebo. (Funded by Merck and others; Current Controlled Trials number, ISRCTN48678192 ; ClinicalTrials.gov number, NCT01252953 ; and EudraCT number, 2010-023467-18 .)

Chronic phosphocreatine depletion by the creatine analogue beta-guanidinopropionate is associated with increased mortality and loss of ATP in rats after myocardial infarction.

BACKGROUND: The failing myocardium is characterized by reductions of phosphocreatine (PCr) and free creatine content and by decreases of energy reserve via creatine kinase (CK), ie, CK reaction velocity (Flux(CK)). It has remained unclear whether these changes contribute directly to contractile dysfunction. In the present study, myocardial PCr stores in a heart failure model were further depleted by feeding of the PCr analogue beta-guanidinopropionate (GP). Functional and metabolic consequences were studied. METHODS AND RESULTS: Rats were subjected to sham operation or left coronary artery ligation (MI). Surviving rats were assigned to 4 groups and fed with 0% (n=7, Sham; n=5, MI) or 1% (n=7 Sham+GP, n=8 MI+GP) GP. Two additional groups were fed GP for 2 or 4 weeks before MI. After 8 weeks, hearts were isolated and perfused, and left ventricular pressure-volume curves were obtained. High-energy phosphate metabolism was determined with (31)P NMR spectroscopy. After GP feeding or MI, left ventricular pressure-volume curves were depressed by 33% and 32%, respectively, but GP feeding in MI hearts did not further impair mechanical function. Both MI and GP feeding reduced PCr content and Flux(CK), but here, effects were additive. In MI+GP rats, PCr levels and Flux(CK) were reduced by 87% and 94%, respectively. Although ATP levels were maintained in the GP and MI groups, ATP content was reduced by 18% in MI+GP hearts. Furthermore, 24-hour mortality in GP-prefed rats was 100%. CONCLUSIONS: Rats with an 87% predepletion of myocardial PCr content cannot survive an acute MI. Chronically infarcted hearts subjected to additional PCr depletion cannot maintain ATP homeostasis