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 .)

Creatine kinase-deficient hearts exhibit increased susceptibility to ischemia-reperfusion injury and impaired calcium homeostasis.

The creatine kinase (CK) system is involved in the rapid transport of high-energy phosphates from the mitochondria to the sites of maximal energy requirements such as myofibrils and sarcolemmal ion pumps. Hearts of mice with a combined knockout of cytosolic M-CK and mitochondrial CK (M/Mito-CK(-/-)) show unchanged basal left ventricular (LV) performance but reduced myocardial high-energy phosphate concentrations. Moreover, skeletal muscle from M/Mito-CK(-/-) mice demonstrates altered Ca2+ homeostasis. Our hypothesis was that in CK-deficient hearts, a cardiac phenotype can be unmasked during acute stress conditions and that susceptibility to ischemia-reperfusion injury is increased because of altered Ca2+ homeostasis. We simultaneously studied LV performance and myocardial Ca2+ metabolism in isolated, perfused hearts of M/Mito-CK(-/-) (n = 6) and wild-type (WT, n = 8) mice during baseline, 20 min of no-flow ischemia, and recovery. Whereas LV performance was not different during baseline conditions, LV contracture during ischemia developed significantly earlier (408 +/- 72 vs. 678 +/- 54 s) and to a greater extent (50 +/- 2 vs. 36 +/- 3 mmHg) in M/Mito-CK(-/-) mice. During reperfusion, recovery of diastolic function was impaired (LV end-diastolic pressure: 22 +/- 3 vs. 10 +/- 2 mmHg), whereas recovery of systolic performance was delayed, in M/Mito-CK(-/-) mice. In parallel, Ca2+ transients were similar during baseline conditions; however, M/Mito-CK(-/-) mice showed a greater increase in diastolic Ca2+ concentration ([Ca2+]) during ischemia (237 +/- 54% vs. 167 +/- 25% of basal [Ca2+]) compared with WT mice. In conclusion, CK-deficient hearts show an increased susceptibility of LV performance and Ca2+ homeostasis to ischemic injury, associated with a blunted postischemic recovery. This demonstrates a key function of an intact CK system for maintenance of Ca2+ homeostasis and LV mechanics under metabolic stress conditions

Creatine kinase-deficient hearts exhibit increased susceptibility to ischemia-reperfusion injury and impaired calcium homeostasis.

The creatine kinase (CK) system is involved in the rapid transport of high-energy phosphates from the mitochondria to the sites of maximal energy requirements such as myofibrils and sarcolemmal ion pumps. Hearts of mice with a combined knockout of cytosolic M-CK and mitochondrial CK (M/Mito-CK(-/-)) show unchanged basal left ventricular (LV) performance but reduced myocardial high-energy phosphate concentrations. Moreover, skeletal muscle from M/Mito-CK(-/-) mice demonstrates altered Ca2+ homeostasis. Our hypothesis was that in CK-deficient hearts, a cardiac phenotype can be unmasked during acute stress conditions and that susceptibility to ischemia-reperfusion injury is increased because of altered Ca2+ homeostasis. We simultaneously studied LV performance and myocardial Ca2+ metabolism in isolated, perfused hearts of M/Mito-CK(-/-) (n = 6) and wild-type (WT, n = 8) mice during baseline, 20 min of no-flow ischemia, and recovery. Whereas LV performance was not different during baseline conditions, LV contracture during ischemia developed significantly earlier (408 +/- 72 vs. 678 +/- 54 s) and to a greater extent (50 +/- 2 vs. 36 +/- 3 mmHg) in M/Mito-CK(-/-) mice. During reperfusion, recovery of diastolic function was impaired (LV end-diastolic pressure: 22 +/- 3 vs. 10 +/- 2 mmHg), whereas recovery of systolic performance was delayed, in M/Mito-CK(-/-) mice. In parallel, Ca2+ transients were similar during baseline conditions; however, M/Mito-CK(-/-) mice showed a greater increase in diastolic Ca2+ concentration ([Ca2+]) during ischemia (237 +/- 54% vs. 167 +/- 25% of basal [Ca2+]) compared with WT mice. In conclusion, CK-deficient hearts show an increased susceptibility of LV performance and Ca2+ homeostasis to ischemic injury, associated with a blunted postischemic recovery. This demonstrates a key function of an intact CK system for maintenance of Ca2+ homeostasis and LV mechanics under metabolic stress conditions

Look After Yourself: Students Consistently Showing High Resilience Engaged in More Self-Care and Proved More Resilient During the COVID-19 Pandemic

The COVID-19 pandemic has prompted severe restrictions on everyday life to curb the spread of infections. For example, teaching at universities has been switched to an online format, reducing students' opportunities for exchange, and social interaction. Consequently, their self-reported mental health has significantly decreased and there is a pressing need to elucidate the underlying mechanisms—ideally considering not only data collected during the pandemic, but also before. One hundred seventeen German university students aged 18-27 were assessed for known resilience factors (optimism, self-care, social support, generalized self-efficacy) and subsequently completed surveys on stress experiences and mental health every 3 months over a period of 9 months before the outbreak of the pandemic and once during the first lockdown in Germany. For each timepoint before the pandemic, we regressed participants' mental health against the reported stressor load, such that the resulting residuals denote better or worse than expected outcomes, i.e., the degree of resilient functioning. We then tested whether different expressions in the resilience factors were predictive of distinct resilient functioning trajectories, which were identified through latent class growth analysis. Finally, we investigated whether trajectory class, resilience factors, and perceived stress predicted resilience during the pandemic. Results show rather stable resilient functioning trajectories, with classes differing mainly according to degree rather than change over time. More self-care was associated with a higher resilient functioning trajectory, which in turn was linked with the most favorable pandemic response (i.e., lower perceived stress and more self-care). Although findings should be interpreted with caution given the rather small sample size, they represent a rare examination of established resilience factors in relation to resilience over an extended period and highlight the relevance of self-care in coping with real-life stressors such as the pandemic