Related papers: Relative entropy for von Neumann subalgebras
Relative entropy serves as a cornerstone concept in quantum information theory. In this work, we study relative entropy of random states from major generic state models of Hilbert-Schmidt and Bures-Hall ensembles. In particular, we derive…
We derive exact relations between the Renyi entanglement entropies and the particle number fluctuations of spatial connected regions in systems of N noninteracting fermions in arbitrary dimension. We prove that the asymptotic large-N…
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and…
We make a systematic study of standard $f$-divergences in general von Neumann algebras. An important ingredient of our study is to extend Kosaki's variational expression of the relative entropy to an arbitary standard $f$-divergence, from…
We present an analytical formula for the asymptotic relative entropy of entanglement for Werner states of arbitrary dimension. We then demonstrate its validity using methods from convex optimization. To our knowledge, this is the first case…
In this paper we deal with two quantum relative entropy preserver problems on the cones of positive (either positive definite or positive semidefinite) operators. The first one is related to a quantum R\'enyi relative entropy like quantity…
We compute the quantum Renyi relative entropies in an infinite spinless fermionic chain with a defect. Doing a numerical analysis we will show that the resulting quantity depends non trivially on the effective central charge of the theory.…
We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the…
Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
We establish a discrete analog of the R\'enyi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within log e of the usual Shannon entropy. Additionally we investigate the entropic…
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…
We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we define a secret sharing scheme, storing information invisible…
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…
We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's…
The Renyi entropy coprises a group of data estimates that sums up the well-known Shannon entropy, acquiring a considerable lot of its properties. It appears as unqualified and restrictive entropy, relative entropy, or common data, and has…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…
Recently a new quantum generalization of the Renyi divergence and the corresponding conditional Renyi entropies was proposed. Here we report on a surprising relation between conditional Renyi entropies based on this new generalization and…
We obtain an estimate of free entropy of generators in a type ${II}_1$-factor $\mc{M}$ which has a subfactor $\mc{N}$ of finite index with a subalgebra $\mc{P}=\mc{P}_1\vee\mc{P}_2\subset\mc{N}$ where $\mc{P}_1=\mc{R}_1'\cap\mc{P}$,…