Entropy Production of Doubly Stochastic Quantum Channels

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly-stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.Comment: 24 page

Relative Entropy Convergence for Depolarizing Channels

We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the log-Sobolev-1 constant. Our main result is the computation of this constant. As an application we use the log-Sobolev-1 constant of the depolarizing channels to improve the concavity inequality of the von-Neumann entropy. This result is compared to similar bounds obtained recently by Kim et al. and we show a version of Pinsker's inequality, which is optimal and tight if we fix the second argument of the relative entropy. Finally, we consider the log-Sobolev-1 constant of tensor-powers of the completely depolarizing channel and use a quantum version of Shearer's inequality to prove a uniform lower bound.Comment: 21 pages, 3 figure

Sandwiched Rényi Convergence for Quantum Evolutions

We study the speed of convergence of a primitive quantum time evolution towards its fixed point in the distance of sandwiched R\'enyi divergences. For each of these distance measures the convergence is typically exponentially fast and the best exponent is given by a constant (similar to a logarithmic Sobolev constant) depending only on the generator of the time evolution. We establish relations between these constants and the logarithmic Sobolev constants as well as the spectral gap. An important consequence of these relations is the derivation of mixing time bounds for time evolutions directly from logarithmic Sobolev inequalities without relying on notions like lp-regularity. We also derive strong converse bounds for the classical capacity of a quantum time evolution and apply these to obtain bounds on the classical capacity of some examples, including stabilizer Hamiltonians under thermal noise.Comment: 35 pages, 4 figures. Version to be published in the Quantum Journa

Renal complications in chronic hypoparathyroidism – a systematic cross-sectional assessment

ContextAlthough renal long-term complications are acknowledged in chronic hypoparathyroidism (HPT), standardized investigations are scarce.ObjectiveTo systematically investigate renal complications and their predictors in hypoparathyroid patients compared to matched individuals.DesignProspective observational study in 161 patients with chronic HPT.MethodsPatients received renal ultrasound, clinical and laboratory assessments. An individual 1:3 matching with participants from the German population-based Study of Health in Pomerania was performed.ResultsOf 161 patients (92% postoperative HPT), prevalence of eGFR <60ml/min/1.73m2 was 21%, hypercalciuria 41%. Compared to healthy individuals, HPT patients had a significantly lower eGFR (74.2 vs. 95.7 ml/min/1.73m², p<0.01). Renal ultrasound revealed calcifications in 10% (nephrocalcinosis in 7% and calculi in 3%). Patients with renal calcifications had higher levels of 24-hour urine calcium excretion (8.34 vs. 5.08 mmol/d, p=0.02), spot urine calcium excretion (4.57 vs. 2.01 mmol/L, p=0.01) and urine calcium-to-creatinine ratio (0.25 vs. 0.16, p<0.01) than patients without calcifications. Albumin-corrected calcium, phosphate, calcium-phosphate product, 25-hydroxyvitamin D in serum, eGFR, daily calcium intake or disease duration were not significantly different between these two groups. Including patients receiving rhPTH therapy, a lower serum phosphate concentration (odds ratio 1.364 [95% confidence interval (CI) 1.049-1.776], p<0.05) and a longer disease duration of HPT (odds ratio 1.063 [95% CI 1.021-1.106], p<0.01) were significant predictors for renal calcifications. Excluding patients receiving rhPTH therapy, a higher 24-hour urine calcium excretion (odds ratio 1.215 [95% CI 1.058-1.396], p<0.01) was a significant predictor for renal calcifications but not serum magnesium or disease duration.ConclusionsPrevalence of impaired renal function among patients with chronic HPT is increased and independent from visible renal calcifications. Depending on exclusion of patients with rhPTH therapy, regression analysis revealed disease duration and serum phosphate or disease duration and 24-hour urinary calcium excretion as predictors for renal calcifications.Clin Trials IdentifierNCT0558559

Dismantling Brazil's science threatens global biodiversity heritage

In the middle of a political and fiscal crisis, the Brazilian government is applying successive budget cuts, including in science funding. Recent cuts radically affect research programs on biodiversity that are crucial components for the design and monitoring of public policies for nature conservation and sustainable development. We analyze the consequences of such cuts on the Research Program on Biodiversity (PPBio), the largest biodiversity research network in Brazil (626 researchers, nine networks in all Brazilian biomes). Brazil holds a substantial part of the world's biodiversity and of tropical forests that play a significant role for regional and global climate stability. If underfunding is maintained, the dismantling of the Brazilian PPBio will have consequences that go beyond biodiversity knowledge itself but affect society as a whole. Brazil will likely fail to reach the National Targets for Biodiversity 2011–2020, and it will be difficult to fulfill the restoration target of the Brazilian NDC and to advance with the sustainable development goals. © 2017 Associação Brasileira de Ciência Ecológica e Conservaçã