481,779 research outputs found
On entropic quantities related to the classical capacity of infinite dimensional quantum channels
In this paper we consider the -function (the Holevo capacity of
constrained channel) and the convex closure of the output entropy for arbitrary
infinite dimensional channel.
It is shown that the -function of an arbitrary channel is a concave
lower semicontinuous function on the whole state space, having continuous
restriction to any set of continuity of the output entropy.
The explicit representation for the convex closure of the output entropy is
obtained and its properties are explored. It is shown that the convex closure
of the output entropy coincides with the convex hull of the output entropy on
the convex set of states with finite output entropy. Similarly to the case of
the -function, it is proved that the convex closure of the output entropy
has continuous restriction to any set of continuity of output entropy. Some
applications of these results to the theory of entanglement are discussed.
The obtained properties of the convex closure of the output entropy make it
possible to generalize to the infinite dimensional case the convex duality
approach to the additivity problem.Comment: 25 page
Wigner Function and Entanglement Entropy for Bosons from Non-Equilibrium Field Theory
We propose a new method of calculating entanglement entropy of a many-body
interacting Bosonic system (open or closed) in a field theoretic approach
without replica methods. The Wigner function and Renyi entropy of a Bosonic
system undergoing arbitrary non-equilibrium dynamics can be obtained from its
Wigner characteristic function, which we identify with the Schwinger Keldysh
partition function in presence of quantum sources turned on at the time of
measurement. For non-interacting many body systems, starting from arbitrary
density matrices, we provide exact analytic formulae for Wigner function and
entanglement entropy in terms of the single particle Green's functions. For
interacting systems, we relate the Wigner characteristic to the connected
multi-particle correlators of the system. We use this formalism to study the
evolution of an open quantum system from a Fock state with negative Wigner
function and zero entropy, to a thermal state with positive Wigner function and
finite entropy. The evolution of the Renyi entropy is non-monotonic in time for
both Markovian and non-Markovian dynamics. The entropy is also found to be
anti-correlated with negativity of the Wigner function of a -mode open
quantum system.Comment: 5+7 Pages, 2+2 Figure
An information theory for preferences
Recent literature in the last Maximum Entropy workshop introduced an analogy
between cumulative probability distributions and normalized utility functions.
Based on this analogy, a utility density function can de defined as the
derivative of a normalized utility function. A utility density function is
non-negative and integrates to unity. These two properties form the basis of a
correspondence between utility and probability. A natural application of this
analogy is a maximum entropy principle to assign maximum entropy utility
values. Maximum entropy utility interprets many of the common utility functions
based on the preference information needed for their assignment, and helps
assign utility values based on partial preference information. This paper
reviews maximum entropy utility and introduces further results that stem from
the duality between probability and utility
On the entropy of a function
AbstractA common statement made when discussing the efficiency of compression programs like JPEG is that the transformations used, the discrete cosine or wavelet transform, decorrelate the data. The standard measure used for the information content of the data is the probabilistic entropy. The data can, in this case, be considered as the sampled values of a function. However no sampling independent definition of the entropy of a function has been proposed. Such a definition is given and it is shown that the entropy so defined is the same as the entropy of the sampled data in the limit as the sample spacing goes to zero
Renyi Entropy of the XY Spin Chain
We consider the one-dimensional XY quantum spin chain in a transverse
magnetic field. We are interested in the Renyi entropy of a block of L
neighboring spins at zero temperature on an infinite lattice. The Renyi entropy
is essentially the trace of some power of the density matrix of the
block. We calculate the asymptotic for analytically in terms of
Klein's elliptic - function. We study the limiting entropy as a
function of its parameter . We show that up to the trivial addition
terms and multiplicative factors, and after a proper re-scaling, the Renyi
entropy is an automorphic function with respect to a certain subgroup of the
modular group; moreover, the subgroup depends on whether the magnetic field is
above or below its critical value. Using this fact, we derive the
transformation properties of the Renyi entropy under the map and show that the entropy becomes an elementary function of the
magnetic field and the anisotropy when is a integer power of 2, this
includes the purity . We also analyze the behavior of the entropy as
and and at the critical magnetic field and in the
isotropic limit [XX model].Comment: 28 Pages, 1 Figur
Supersymmetric Renyi Entropy
We consider 3d N>= 2 superconformal field theories on a branched covering of
a three-sphere. The Renyi entropy of a CFT is given by the partition function
on this space, but conical singularities break the supersymmetry preserved in
the bulk. We turn on a compensating R-symmetry gauge field and compute the
partition function using localization. We define a supersymmetric observable,
called the super Renyi entropy, parametrized by a real number q. We show that
the super Renyi entropy is duality invariant and reduces to entanglement
entropy in the q -> 1 limit. We provide some examples.Comment: 39 pages, 4 figure
Black hole entropy functions and attractor equations
The entropy and the attractor equations for static extremal black hole
solutions follow from a variational principle based on an entropy function. In
the general case such an entropy function can be derived from the reduced
action evaluated in a near-horizon geometry. BPS black holes constitute special
solutions of this variational principle, but they can also be derived directly
from a different entropy function based on supersymmetry enhancement at the
horizon. Both functions are consistent with electric/magnetic duality and for
BPS black holes their corresponding OSV-type integrals give identical results
at the semi-classical level. We clarify the relation between the two entropy
functions and the corresponding attractor equations for N=2 supergravity
theories with higher-derivative couplings in four space-time dimensions. We
discuss how non-holomorphic corrections will modify these entropy functions.Comment: 21 pages,LaTeX,minor change
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