Abelian varieties isogenous to a power of an elliptic curve

Let $E$ be an elliptic curve over a field $k$. Let $R:= \text{End}\, E$. There is a functor $\mathscr{H}\!\!\mathit{om}_R(-,E)$ from the category of finitely presented torsion-free left $R$-modules to the category of abelian varieties isogenous to a power of $E$, and a functor $\text{Hom}(-,E)$ in the opposite direction. We prove necessary and sufficient conditions on $E$ for these functors to be equivalences of categories.Comment: 21 pages, comments welcom

Nonadditivity of Bipartite Distillable Entanglement follows from Conjecture on Bound Entangled Werner States

Assuming the validity of a conjecture in quant-ph/9910026 and quant-ph/9910022 we show that the distillable entanglement for two bipartite states, each of which individually has zero distillable entanglement, can be nonzero. We show that this also implies that the distillable entanglement is not a convex function. Our example consists of the tensor product of a bound entangled state based on an unextendible product basis with a Werner state which lies in the class of conjectured undistillable states.Comment: 4 pages RevTex, 1 figure, to appear in Phys. Rev. Lett. Title changed and small paragraph adde

Quantum Channel Capacity of Very Noisy Channels

We present a family of additive quantum error-correcting codes whose capacities exceeds that of quantum random coding (hashing) for very noisy channels. These codes provide non-zero capacity in a depolarizing channel for fidelity parameters $f$ when $f> .80944$. Random coding has non-zero capacity only for $f>.81071$; by analogy to the classical Shannon coding limit, this value had previously been conjectured to be a lower bound. We use the method introduced by Shor and Smolin of concatenating a non-random (cat) code within a random code to obtain good codes. The cat code with block size five is shown to be optimal for single concatenation. The best known multiple-concatenated code we found has a block size of 25. We derive a general relation between the capacity attainable by these concatenation schemes and the coherent information of the inner code states.Comment: 31 pages including epsf postscript figures. Replaced to correct important typographical errors in equations 36, 37 and in tex

Quantum Nonlocality without Entanglement

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles which also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.Comment: 27 pages, Latex, 6 ps figures. To be submitted to Phys. Rev. A. Version 2: 30 pages, many small revisions and extensions, author added. Version 3: Proof in Appendix D corrected, many small changes; final version for Phys. Rev. A Version 4: Report of Popescu conjecture modifie

Enhancing Protection for Vulnerable Waters

Governments worldwide do not adequately protect their limited freshwater systems and therefore place freshwater functions and attendant ecosystem services at risk. The best available scientific evidence compels enhanced protections for freshwater systems, especially for impermanent streams and wetlands outside of floodplains that are particularly vulnerable to alteration or destruction. New approaches to freshwater sustainability — implemented through scientifically informed adaptive management — are required to protect freshwater systems through periods of changing societal needs. One such approach introduced in the US in 2015 is the Clean Water Rule, which clarified the jurisdictional scope for federally protected waters. However, within hours of its implementation litigants convinced the US Court of Appeals for the Sixth Circuit to stay the rule, and the subsequently elected administration has now placed it under review for potential revision or rescission. Regardless of its outcome at the federal level, policy and management discussions initiated by the propagation of this rare rulemaking event have potential far-reaching implications at all levels of government across the US and worldwide. At this timely juncture, we provide a scientific rationale and three policy options for all levels of government to meaningfully enhance protection of these vulnerable waters. A fourth option, a \u27do-nothing\u27 approach, is wholly inconsistent with the well-established scientific evidence of the importance of these vulnerable waters

Discovery of a Potent and Selective Sphingosine Kinase 1 Inhibitor through the Molecular Combination of Chemotype-Distinct Screening Hits

Sphingosine kinase (SphK) is the major source of the lipid mediator and G protein-coupled receptor agonist sphingosine-1-phosphate (S1P). S1P promotes cell growth, survival, and migration and is a key regulator of lymphocyte trafficking. Inhibition of S1P signaling has been proposed as a strategy for treatment of inflammatory diseases and cancer. Two different formats of an enzyme-based high-throughput screen yielded two attractive chemotypes capable of inhibiting S1P formation in cells. The molecular combination of these screening hits led to compound <b>22a</b> (PF-543) with 2 orders of magnitude improved potency. Compound <b>22a</b> inhibited SphK1 with an IC₅₀ of 2 nM and was more than 100-fold selective for SphK1 over the SphK2 isoform. Through the modification of tail-region substituents, the specificity of inhibition for SphK1 and SphK2 could be modulated, yielding SphK1-selective, potent SphK1/2 dual, or SphK2-preferential inhibitors