Distilling Non-Locality

Two parts of an entangled quantum state can have a correlation in their joint behavior under measurements that is unexplainable by shared classical information. Such correlations are called non-local and have proven to be an interesting resource for information processing. Since non-local correlations are more useful if they are stronger, it is natural to ask whether weak non-locality can be amplified. We give an affirmative answer by presenting the first protocol for distilling non-locality in the framework of generalized non-signaling theories. Our protocol works for both quantum and non-quantum correlations. This shows that in many contexts, the extent to which a single instance of a correlation can violate a CHSH inequality is not a good measure for the usefulness of non-locality. A more meaningful measure follows from our results.Comment: Revised abstract, introduction and conclusion. Accepted by PR

Sensors for detecting analytes in fluids

Chemical sensors for detecting analytes in fluids comprise first and second conductive elements (e.g., electrical leads) electrically coupled to and separated by a chemically sensitive resistor which provides an electrical path between the conductive elements. The resistor comprises a plurality of alternating nonconductive regions (comprising a nonconductive organic polymer) and conductive regions (comprising a conductive material) transverse to the electrical path. The resistor provides a difference in resistance between the conductive elements when contacted with a fluid comprising a chemical analyte at a first concentration, than when contacted with a fluid comprising the chemical analyte at a second different concentration. Arrays of such sensors are constructed with at least two sensors having different chemically sensitive resistors providing dissimilar such differences in resistance. Variability in chemical sensitivity from sensor to sensor is provided by qualitatively or quantitatively varying the composition of the conductive and/or nonconductive regions. An electronic nose for detecting an analyte in a fluid may be constructed by using such arrays in conjunction with an electrical measuring device electrically connected to the conductive elements of each sensor

Sensors for detecting analytes in fluids

Chemical sensors for detecting analytes in fluids comprise first and second conductive elements (e.g., electrical leads) electrically coupled to and separated by a chemically sensitive resistor which provides an electrical path between the conductive elements. The resistor comprises a plurality of alternating nonconductive regions (comprising a nonconductive organic polymer) and conductive regions (comprising a conductive material) transverse to the electrical path. The resistor provides a difference in resistance between the conductive elements when contacted with a fluid comprising a chemical analyte at a first concentration, than when contacted with a fluid comprising the chemical analyte at a second different concentration. Arrays of such sensors are constructed with at least two sensors having different chemically sensitive resistors providing dissimilar such differences in resistance. Variability in chemical sensitivity from sensor to sensor is provided by qualitatively or quantitatively varying the composition of the conductive and/or nonconductive regions. An electronic nose for detecting an analyte in a fluid may be constructed by using such arrays in conjunction with an electrical measuring device electrically connected to the conductive elements of each sensor

Higher Geometric Structures on Manifolds and the Gauge Theory of Deligne Cohomology

We study smooth higher symmetry groups and moduli $\infty$-stacks of generic higher geometric structures on manifolds. Symmetries are automorphisms which cover non-trivial diffeomorphisms of the base manifold. We construct the smooth higher symmetry group of any geometric structure on $M$ and show that this completely classifies, via a universal property, equivariant structures on the higher geometry. We construct moduli stacks of higher geometric data as $\infty$-categorical quotients by the action of the higher symmetries, extract information about the homotopy types of these moduli $\infty$-stacks, and prove a helpful sufficient criterion for when two such higher moduli stacks are equivalent. In the second part of the paper we study higher $\mathrm{U}(1)$-connections. First, we observe that higher connections come organised into higher groupoids, which further carry affine actions by Baez-Crans-type higher vector spaces. We compute a presentation of the higher gauge actions for $n$-gerbes with $k$-connection, comment on the relation to higher-form symmetries, and present a new String group model. We construct smooth moduli $\infty$-stacks of higher Maxwell and Einstein-Maxwell solutions, correcting previous such considerations in the literature, and compute the homotopy groups of several moduli $\infty$-stacks of higher $\mathrm{U}(1)$- connections. Finally, we show that a discrepancy between two approaches to the differential geometry of NSNS supergravity (via generalised and higher geometry, respectively) vanishes at the level of moduli $\infty$-stacks of NSNS supergravity solutions.Comment: 102 pages; comments welcom

Temperature induced phase averaging in one-dimensional mesoscopic systems

We analyse phase averaging in one-dimensional interacting mesoscopic systems with several barriers and show that for incommensurate positions an independent average over several phases can be induced by finite temperature. For three strong barriers with conductances G_i and mutual distances larger than the thermal length, we obtain G ~ sqrt{G_1 G_2 G_3} for the total conductance G. For an interacting wire, this implies power laws in G(T) with novel exponents, which we propose as an experimental fingerprint to distinguish temperature induced phase averaging from dephasing.Comment: 6 pages, 5 figures; added one figure; slightly extende