A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal

Two quantum information processing protocols are said to be dual under resource reversal if the resources consumed (generated) in one protocol are generated (consumed) in the other. Previously known examples include the duality between entanglement concentration and dilution, and the duality between coherent versions of teleportation and super-dense coding. A quantum feedback channel is an isometry from a system belonging to Alice to a system shared between Alice and Bob. We show that such a resource may be reversibly decomposed into a perfect quantum channel and pure entanglement, generalizing both of the above examples. The dual protocols responsible for this decomposition are the ``feedback father'' (FF) protocol and the ``fully quantum reverse Shannon'' (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf'' protocol (FQSW), a generalization of the recently discovered ``quantum state merging'', is related to FF by source-channel duality, and to FQRS by time reversal duality, thus forming a triangle of dualities. The source-channel duality is identified as the origin of the previously poorly understood ``mother-father'' duality. Due to a symmetry breaking, the dualities extend only partially to classical information theory.Comment: 5 pages, 5 figure

Properties of Intersecting p-branes in Various Dimensions

General properties of intersecting extremal p-brane solutions of gravity coupled with dilatons and several different d-form fields in arbitrary space-time dimensions are considered. It is show that heuristically expected properties of the intersecting p-branes follow from the explicit formulae for solutions. In particular, harmonic superposition and S-duality hold for all p-brane solutions. Generalized T-duality takes place under additional restrictions on the initial theory parameters .Comment: 14 pages, RevTeX, misprints are corrected and more Comments are added, information about one of the authors (M.G.I.) available at http://www.geocities.com/CapeCanaveral/Lab/419

The coalescing-branching random walk on expanders and the dual epidemic process

Information propagation on graphs is a fundamental topic in distributed computing. One of the simplest models of information propagation is the push protocol in which at each round each agent independently pushes the current knowledge to a random neighbour. In this paper we study the so-called coalescing-branching random walk (COBRA), in which each vertex pushes the information to $k$ randomly selected neighbours and then stops passing information until it receives the information again. The aim of COBRA is to propagate information fast but with a limited number of transmissions per vertex per step. In this paper we study the cover time of the COBRA process defined as the minimum time until each vertex has received the information at least once. Our main result says that if $G$ is an $n$-vertex $r$-regular graph whose transition matrix has second eigenvalue $\lambda$, then the COBRA cover time of $G$ is $\mathcal O(\log n )$, if $1-\lambda$ is greater than a positive constant, and $\mathcal O((\log n)/(1-\lambda)^3))$, if $1-\lambda \gg \sqrt{\log( n)/n}$. These bounds are independent of $r$ and hold for $3 \le r \le n-1$. They improve the previous bound of $O(\log^2 n)$ for expander graphs. Our main tool in analysing the COBRA process is a novel duality relation between this process and a discrete epidemic process, which we call a biased infection with persistent source (BIPS). A fixed vertex $v$ is the source of an infection and remains permanently infected. At each step each vertex $u$ other than $v$ selects $k$ neighbours, independently and uniformly, and $u$ is infected in this step if and only if at least one of the selected neighbours has been infected in the previous step. We show the duality between COBRA and BIPS which says that the time to infect the whole graph in the BIPS process is of the same order as the cover time of the COBRA proces

Building flat space-time from information exchange between quantum fluctuations

We consider a hypothesis in which classical space-time emerges from information exchange (interactions) between quantum fluctuations in the gravity theory. In this picture, a line element would arise as a statistical average of how frequently particles interact, through an individual rate $dt\sim 1/f_t$ and spatially interconnecting rates $dl\sim c/f$. The question is if space-time can be modelled consistently in this way. The ansatz would be opposite to the standard treatment of space-time as insensitive to altered physics at event horizons (disrupted propagation of information) but by extension relate to the connection of space-time to entanglement (interactions) through the gauge/gravity duality. We make a first, rough analysis of the implications this type of quantization would have on the classical structure of flat space-time, and of what would be required of the interactions. Seeing no obvious reason for why the origin would be unrealistic, we comment on expected effects in the presence of curvature.Comment: 22 pages. v3: extended introductio

On the relationship between matched filter theory as applied to gust loads and phased design loads analysis

A theoretical basis and example calculations are given that demonstrate the relationship between the Matched Filter Theory approach to the calculation of time-correlated gust loads and Phased Design Load Analysis in common use in the aerospace industry. The relationship depends upon the duality between Matched Filter Theory and Random Process Theory and upon the fact that Random Process Theory is used in Phased Design Loads Analysis in determining an equiprobable loads design ellipse. Extensive background information describing the relevant points of Phased Design Loads Analysis, calculating time-correlated gust loads with Matched Filter Theory, and the duality between Matched Filter Theory and Random Process Theory is given. It is then shown that the time histories of two time-correlated gust load responses, determined using the Matched Filter Theory approach, can be plotted as parametric functions of time and that the resulting plot, when superposed upon the design ellipse corresponding to the two loads, is tangent to the ellipse. The question is raised of whether or not it is possible for a parametric load plot to extend outside the associated design ellipse. If it is possible, then the use of the equiprobable loads design ellipse will not be a conservative design practice in some circumstances