Hilbert's projective metric in quantum information theory

We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical distinguishability of quantum states and on the decrease of entanglement under LOCC protocols or other cone-preserving operations. The results are formulated in terms of general cones and base norms and lead to contractivity bounds for quantum channels, for instance improving Ruskai's trace-norm contraction inequality. A new duality between distinguishability measures and base norms is provided. For two given pairs of quantum states we show that the contraction of Hilbert's projective metric is necessary and sufficient for the existence of a probabilistic quantum operation that maps one pair onto the other. Inequalities between Hilbert's projective metric and the Chernoff bound, the fidelity and various norms are proven.Comment: 32 pages including 3 appendices and 3 figures; v2: minor changes, published versio

Monsters, black holes and the statistical mechanics of gravity

We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From the curved space perspective they are objects with large proper volume that can be glued on to an asymptotically flat space. At no point is the curvature or energy density required to be large in Planck units, and quantum gravitational effects are, in the conventional effective field theory framework, small everywhere. Since they can have more entropy than a black hole of equal mass, monsters are problematic for certain interpretations of black hole entropy and the AdS/CFT duality. In the second part of the paper we review recent developments in the foundations of statistical mechanics which make use of properties of high-dimensional (Hilbert) spaces. These results primarily depend on kinematics -- essentially, the geometry of Hilbert space -- and are relatively insensitive to dynamics. We discuss how this approach might be adopted as a basis for the statistical mechanics of gravity. Interestingly, monsters and other highly entropic configurations play an important role.Comment: 9 pages, 4 figures, revtex; invited Brief Review to be published in Modern Physics Letters

Unitarity and the Hilbert space of quantum gravity

Under the premises that physics is unitary and black hole evaporation is complete (no remnants, no topology change), there must exist a one-to-one correspondence between states on future null and timelike infinity and on any earlier spacelike Cauchy surface (e.g., slices preceding the formation of the hole). We show that these requirements exclude a large set of semiclassical spacetime configurations from the Hilbert space of quantum gravity. In particular, the highest entropy configurations, which account for almost all of the volume of semiclassical phase space, would not have quantum counterparts, i.e. would not correspond to allowed states in a quantum theory of gravity.Comment: 7 pages, 3 figures, revtex; minor changes in v2 (version published in Class. Quant. Grav.

Molecular and morphometric variation in European populations of the articulate brachiopod <i>Terebeatulina retusa</i>

Molecular and morphometric variation within and between population samples of the articulate brachiopod &lt;i&gt;Terebratulina&lt;/i&gt; spp., collected in 1985-1987 from a Norwegian fjord, sea lochs and costal sites in western Scotland, the southern English Channel (Brittany) and the western Mediterranean, were measured by the analysis of variation in the lengths of mitochondrial DNA (mtDNA) fragments produced by digestion with nine restriction endonucleases and by multivariate statistical analysis of six selected morphometric parameters. Nucleotide difference within each population sample was high. Nucleotide difference between population samples from the Scottish sites, both those that are tidally contiguous and those that appear to be geographically isolated, were not significantly different from zero. Nucleotide differences between the populations samples from Norway, Brittany, Scotland and the western Mediterranean were also very low. Morphometric analysis confirmed the absence of substantial differentiation

Self-Spin-Controlled Rotation of Spatial States of a Dirac Electron in a Cylindrical Potential via Spin-Orbit Interaction

Solution of the Dirac equation predicts that when an electron with non-zero orbital angular momentum propagates in a cylindrically symmetric potential, its spin and orbital degrees of freedom interact, causing the electron's phase velocity to depend on whether its spin and orbital angular momenta vectors are oriented parallel or anti-parallel with respect to each other. This spin-orbit splitting of the electronic dispersion curves can result in a rotation of the electron's spatial state in a manner controlled by the electron's own spin z-component value. These effects persist at non-relativistic velocities. To clarify the physical origin of this effect, we compare solutions of the Dirac equation to perturbative predictions of the Schrodinger-Pauli equation with a spin-orbit term, using the standard Foldy-Wouthuysen Hamiltonian. This clearly shows that the origin of the effect is the familiar relativistic spin-orbit interaction.Comment: 14 pages, 5 figures, 2 appendices, final versio

Quantum Fluctuation Theorems

Recent advances in experimental techniques allow one to measure and control systems at the level of single molecules and atoms. Here gaining information about fluctuating thermodynamic quantities is crucial for understanding nonequilibrium thermodynamic behavior of small systems. To achieve this aim, stochastic thermodynamics offers a theoretical framework, and nonequilibrium equalities such as Jarzynski equality and fluctuation theorems provide key information about the fluctuating thermodynamic quantities. We review the recent progress in quantum fluctuation theorems, including the studies of Maxwell's demon which plays a crucial role in connecting thermodynamics with information.Comment: As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Fundamental Aspects and New Directions", (Springer International Publishing, 2018

Promoting Essential Laminations

We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation respectively of an Anosov flow. Otherwise, F admits a pair of transverse very full genuine laminations. In the second case, M satisfies the weak geometrization conjecture - either its fundamental group contains Z+Z or it is word-hyperbolic. Moreover, if M is atoroidal, the mapping class group of M is finite, and any automorphism homotopic to the identity is isotopic to the identity.Comment: 56 pages, 11 figures; version 3: final version, incorporates referee's suggestion

Airborne Isocyanate Exposures in the Collision Repair Industry and a Comparison to Occupational Exposure Limits

Isocyanate exposure was evaluated in 33 spray painters from 25 Washington State autobody shops. Personal breathing zone samples (n = 228) were analyzed for isophorone diisocyanate (IPDI) monomer, 1,6-hexamethylene diisocyanate (HDI) monomer, IPDI polyisocyanate, and three polyisocyanate forms of HDI. The objective was to describe exposures to isocyanates while spray painting, compare them with short-term exposure limits (STELs), and describe the isocyanate composition in the samples. The composition of polyisocyanates (IPDI and HDI) in the samples varied greatly, with maximum amounts ranging from up to 58% for HDI biuret to 96% for HDI isocyanurate. There was a significant inverse relationship between the percentage composition of HDI isocyanurate to IPDI and to HDI uretdione. Two 15-min STELs were compared: (1) Oregon's Occupational Safety and Health Administration (OR-OSHA) STEL of 1000 μg/m3 for HDI polyisocyanate, and (2) the United Kingdom's Health and Safety Executive (UK-HSE) STEL of 70 μg NCO/m3 for all isocyanates. Eighty percent of samples containing HDI polyisocyanate exceeded the OR-OSHA STEL while 98% of samples exceeded the UKHSE STEL. The majority of painters (67%) wore half-face air-purifying respirators while spray painting. Using the OROSHA and the UK-HSE STELs as benchmarks, 21% and 67% of painters, respectively, had at least one exposure that exceeded the respirator's OSHA-assigned protection factor. A critical review of the STELs revealed the following limitations: (1) the OR-OSHA STEL does not include all polyisocyanates, and (2) the UK-HSE STEL is derived from monomeric isocyanates, whereas the species present in typical spray coatings are polyisocyanates. In conclusion, the variable mixtures of isocyanates used by autobody painters suggest that an occupational exposure limit is required that includes all polyisocyanates. Despite the limitations of the STELs, we determined that a respirator with an assigned protection factor of 25 or greater is required to protect against isocyanate exposures during spray painting. Consequently, half-face air-purifying respirators, which are most commonly used and have an assigned protection factor of 10, do not afford adequate respiratory protection

New national and regional bryophyte records, 72

ABSTRACT: New record of Sphagnum palustre L. to Graciosa Island (Azores).info:eu-repo/semantics/publishedVersio