Related papers: On singular limits of relative entropies
Certain duality of relative entropy can fail for chiral conformal net with nontrivial representations. In this paper we quantify such statement by defining a quantity which measures the failure of such duality, and identify this quantity…
Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…
We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite…
By using Araki's relative entropy, Lieb's convexity and the theory of singular integrals, we compute the mutual information associated with free fermions, and we deduce many results about entropies for chiral CFT's which are embedded into…
Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory…
A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was…
We study the entanglement entropies in one-dimensional open critical systems, whose effective description is given by a conformal field theory with boundaries. We show that for pure-state systems formed by the ground state or by the excited…
Recently, Zou obtained the generalized results on the bounds for Tsallis relative operator entropy. In this short paper, we give precise bounds for Tsallis relative operator entropy. We also give precise bounds of relative operator entropy.
We show that under natural growth conditions on the entropy function, convergence in relative entropy is equivalent to $L_p$-convergence. The main tool is the theory of Young measures, in a form that accounts for the formation of…
General hyperbolic systems of balance laws with inhomogeneity in space and time in all constitutive functions are studied in the context of relative entropy. A framework is developed in this setting that contributes to a measure-valued weak…
Various properties of relative entropy have led to its widespread use in information theory. These properties suggest that relative entropy has a role to play in systems that attempt to perform inference in terms of probability…
We derive a relative entropy inequality for capillary compressible fluids with density dependent viscosity. Applications in the context of weak-strong uniqueness analysis, pressureless fluids and high-Mach number flows are presented.
We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test…
In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the notion of measure-valued entropy solutions. Further we survey…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.
The limits of scaled relative entropies between probability distributions associated with N-particle weakly interacting Markov processes are considered. The convergence of such scaled relative entropies is established in various settings.…
We consider a conformal field theory in two dimensions in which an external perturbation is placed. We study the energy flux and entanglement entropy for one, two and multiple intervals and give a suggestion relating the two in some cases.…