4 research outputs found
Entropy in general physical theories
Information plays an important role in our understanding of the physical
world. We hence propose an entropic measure of information for any physical
theory that admits systems, states and measurements. In the quantum and
classical world, our measure reduces to the von Neumann and Shannon entropy
respectively. It can even be used in a quantum or classical setting where we
are only allowed to perform a limited set of operations. In a world that admits
superstrong correlations in the form of non-local boxes, our measure can be
used to analyze protocols such as superstrong random access encodings and the
violation of `information causality'. However, we also show that in such a
world no entropic measure can exhibit all properties we commonly accept in a
quantum setting. For example, there exists no`reasonable' measure of
conditional entropy that is subadditive. Finally, we prove a coding theorem for
some theories that is analogous to the quantum and classical setting, providing
us with an appealing operational interpretation.Comment: 20 pages, revtex, 7 figures, v2: Coding theorem revised, published
versio
Random graph states, maximal flow and Fuss-Catalan distributions
For any graph consisting of vertices and edges we construct an
ensemble of random pure quantum states which describe a system composed of
subsystems. Each edge of the graph represents a bi-partite, maximally entangled
state. Each vertex represents a random unitary matrix generated according to
the Haar measure, which describes the coupling between subsystems. Dividing all
subsystems into two parts, one may study entanglement with respect to this
partition. A general technique to derive an expression for the average
entanglement entropy of random pure states associated to a given graph is
presented. Our technique relies on Weingarten calculus and flow problems. We
analyze statistical properties of spectra of such random density matrices and
show for which cases they are described by the free Poissonian
(Marchenko-Pastur) distribution. We derive a discrete family of generalized,
Fuss-Catalan distributions and explicitly construct graphs which lead to
ensembles of random states characterized by these novel distributions of
eigenvalues.Comment: 37 pages, 24 figure