Related papers: Approximate tensorization of the relative entropy …

Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality…

Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…

We develop a quantum relative entropy method for the mean-field limit of quantum many-body systems. For closed systems governed by the von Neumann equation, we prove a quantitative stability estimate between the $N$-body density matrix and…

We study the relations between (tight) logarithmic Sobolev inequalities, entropy decay and spectral gap inequalities for Markov evolutions on von Neumann algebras. We prove that log-Sobolev inequalities (in the non-commutative form defined…

Given any half-sided modular inclusion of standard subspaces, we show that the entropy function associated with the decreasing one-parameter family of translated standard subspaces is convex for any given (not necessarily smooth) vector in…

The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term…

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…

Carrying the insights of conditional probability to the quantum realm is notoriously difficult due to the non-commutative nature of quantum observables. Nevertheless, conditional expectations on von Neumann algebras have played a…

We consider entanglement across a planar boundary in flat space. Entanglement entropy is usually thought of as the von Neumann entropy of a reduced density matrix, but it can also be thought of as half the von Neumann entropy of a product…

Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…

We study the von Neumann entropy of the partial trace of a system of two two-level atoms (qubits) in a dispersive cavity where the atoms are interacting collectively with a single mode electromagnetic field in the cavity. We make a contrast…

Von Neumann entropy has a natural extension to the case of an arbitrary semifinite von Neumann algebra, as was considered by I. E. Segal. We relate this entropy to the relative entropy and show that the entropy increase for an inclusion of…

We investigate the universal linear inequalities that hold for the von Neumann entropies in a multi-party system, prepared in a stabiliser state. We demonstrate here that entropy vectors for stabiliser states satisfy, in addition to the…

The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT)…

Taking only the characteristics as absolute, in the spirit of Arnold's "Geometrical Methods in the Theory of Ordinary Differential Equations" (Springer, 1988), we give an independent of coordinates formulation of general variational entropy…

Renyi entropy associated with spin tomograms of quantum states is shown to obey to new inequalities containing the dependence on quantum Fourier transform. The limiting inequality for the von Neumann entropy of spin quantum states and a new…

Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…

Based on the recently introduced averaging procedure in phase space, a new type of entropy is defined on the von Neumann lattice. This quantity can be interpreted as a measure of uncertainty associated with simultaneous measurement of the…

We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure two-fermion state, based on the Slater rank concept. It represents the natural generalization of the…

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…