Universal proofs of entropic continuity bounds via majorization flow

We introduce a notion of majorization flow, and demonstrate it to be a powerful tool for deriving simple and universal proofs of continuity bounds for entropic functions relevant in information theory. In particular, for the case of the alpha-R\'enyi entropy, whose connections to thermodynamics are discussed in this article, majorization flow yields a Lipschitz continuity bound for the case alpha > 1, thus resolving an open problem and providing a substantial improvement over previously known bounds.Comment: 29 pages; v2: added Cor. 3.2, Section 7, shortened some proofs, minor fixes; v3: added Section 6.2, minor fixe

Guesswork with Quantum Side Information

What is the minimum number of guesses needed on average to guess a realization of a random variable correctly The answer to this question led to the introduction of a quantity called guesswork by Massey in 1994, which can be viewed as an alternate security criterion to entropy. In this paper, we consider the guesswork in the presence of quantum side information, and show that a general sequential guessing strategy is equivalent to performing a single quantum measurement and choosing a guessing strategy based on the outcome. We use this result to deduce entropic one-shot and asymptotic bounds on the guesswork in the presence of quantum side information, and to formulate a semi-definite program (SDP) to calculate the quantity. We evaluate the guesswork for a simple example involving the BB84 states, both numerically and analytically, and we prove a continuity result that certifies the security of slightly imperfect key states when the guesswork is used as the security criterion

The Role of Eolian-Fluvial Interactions and Dune Dams in Landscape Change, Late Pleistocene-Holocene, Mojave Desert, USA

The formation of the Kelso Dunes in the eastern Mojave Desert, California, was a landscape-changing event triggered by an increase in sediment supply that followed the incision of Afton Canyon by the Mojave River ca. 25 ka. Eastward migration of sand dunes occurred along a well-defined eolian trans­port corridor. Dunes temporarily blocked washes resulting in substantial aggradation of eolian and fluvial sediments. Stratigraphic exposures reveal numerous fining-up sequences with interbedded eolian sands that provide evidence of dune dams and subsequent aggradation. Luminescence ages reveal that dune blocking and aggradation correspond to a regional pulse of alluvial fan sedimentation that occurred ca. 14–9 ka. Meanwhile, relative landscape stability occurred downstream of dune dams, resulting in the formation of a moderately developed soil on abandoned fluvial deposits. The next pulse of alluvial fan activity ca. 6–3 ka likely resulted in the breaching of the dune dams, followed by incision. Eolian system sediment state theory suggests that eolian activity in the Mojave Desert is closely tied to enhanced sediment supply, primarily related to the Mojave River–Lake Mo­jave system. Our data suggests that Intermittent Lake Mojave I, ca. 26–22 ka, triggered a large dune-building event that impounded massive amounts of sediment derived from alluvial fans deposited during the Pleistocene-Holocene transition. Breaching of dune dams and sediment recycling may have also increased sediment supply that contributed to late Holocene eolian activity. This profound impact on the regional geomorphology highlights the critical importance of eolian-fluvial interactions in desert environments

Eventually entanglement breaking Markovian dynamics: structure and characteristic times

Funder: Cantab Capital Institute for the Mathematics of InformationWe investigate entanglement breaking times of Markovian evolutions in discrete and continuous time. In continuous time, we characterize which Markovian evolutions are eventually entanglement breaking, that is, evolutions for which there is a finite time after which any entanglement initially present has been destroyed by the noisy evolution. In the discrete time framework, we consider the entanglement breaking index, that is, the number of times a quantum channel has to be composed with itself before it becomes entanglement breaking. The PPT-square conjecture is that every PPT quantum channel has an entanglement breaking index of at most 2; we prove that every faithful PPT quantum channel has a finite entanglement breaking index, and more generally, any faithful PPT CP map whose Hilbert-Schmidt adjoint is also faithful is eventually entanglement breaking. We also provide a method to obtain concrete bounds on this index for any faithful quantum channel. To obtain these estimates, we use a notion of robustness of separability to obtain bounds on the radius of the largest separable ball around faithful product states. We also extend the framework of Poincar\'e inequalities for nonprimitive semigroups to the discrete setting to quantify the convergence of quantum semigroups in discrete time, which is of independent interest

Eventually Entanglement Breaking Markovian Dynamics: Structure and Characteristic Times

Funder: Cantab Capital Institute for the Mathematics of InformationAbstract: We investigate entanglement breaking times of Markovian evolutions in discrete and continuous time. In continuous time, we characterize which Markovian evolutions are eventually entanglement breaking, that is, evolutions for which there is a finite time after which any entanglement initially present has been destroyed by the noisy evolution. In the discrete-time framework, we consider the entanglement breaking index, that is, the number of times a quantum channel has to be composed with itself before it becomes entanglement breaking. The PPT2 conjecture is that every PPT quantum channel has an entanglement breaking index of at most 2; we prove that every faithful PPT quantum channel has a finite entanglement breaking index, and more generally, any faithful PPT CP map whose Hilbert–Schmidt adjoint is also faithful is eventually entanglement breaking. We also provide a method to obtain concrete bounds on this index for any faithful quantum channel. To obtain these estimates, we use a notion of robustness of separability to obtain bounds on the radius of the largest separable ball around faithful product states. We also extend the framework of Poincaré inequalities for non-primitive semigroups to the discrete setting to quantify the convergence of quantum semigroups in discrete time, which is of independent interest

Reconstruction of the joint state of a two-mode Bose-Einstein condensate

We propose a scheme to reconstruct the state of a two-mode Bose-Einstein condensate, with a given total number of atoms, using an atom interferometer that requires beam splitter, phase shift and non-ideal atom counting operations. The density matrix in the number-state basis can be computed directly from the probabilities of different counts for various phase shifts between the original modes, unless the beamsplitter is exactly balanced. Simulated noisy data from a two-mode coherent state is produced and the state is reconstructed, for 49 atoms. The error can be estimated from the singular values of the transformation matrix between state and probability data.Comment: 4 pages (REVTeX), 5 figures (PostScript

Acute myopathy secondary to oral steroid therapy in a 49-year-old man: a case report

<p>Abstract</p> <p>Introduction</p> <p>Acute myopathy caused by oral corticosteroids is rare. We present a case of myopathy occurring after two doses of methylprednisolone. Typically, acute steroid myopathy occurs with therapy using intravenous corticosteroids at high doses. Acute myopathy developing very early in the course of treatment with oral corticosteroids has been reported only once in the literature. Corticosteroid therapy may be complicated by myopathy, usually chronic, after prolonged high-dose therapy. Acute myopathy caused by exogenous corticosteroids is rare, usually with intravenous corticosteroids at high doses.</p> <p>Case presentation</p> <p>A 49-year-old Caucasian man developed acute myopathy after taking oral methylprednisolone for only two days, 24 mg on day 1 and 20 mg on day 2. He discontinued the medication because of new-onset myalgias and lethargy on day 3 and was seen in our clinic four days after beginning therapy. He completely recovered in four weeks by discontinuing the corticosteroids.</p> <p>Conclusion</p> <p>Among the many complications of corticosteroid therapy, acute myopathy is very rare. It requires prompt recognition and adjustment of therapy.</p