Related papers: Inequalities for Quantum Entropy: A Review with Co…
We consider some questions concerning the monotonicity properties of entropy and mean entropy of states on translationally invariant systems (classical lattice, quantum lattice and quantum continuous). By taking the property of strong…
Although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic (EE) states in the asymptotic limit, for the finite quantum systems, the relation is not so linear and requires detail…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…
Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
Given an arbitrary measurement over a system of interest, the outcome of a posterior measurement can be used for improving the statistical estimation of the system state after the former measurement. Here, we realize an…
Based on the proofs of the continuity of the conditional entropy by Alicki, Fannes, and Winter, we introduce in this work the almost locally affine (ALAFF) method. This method allows us to prove a great variety of continuity bounds for the…
Loschmidt's paradox asks why macroscopic irreversibility is universal despite the time-reversal symmetry of microscopic dynamics. We argue that irreversibility is not a property of the dynamics but of accessibility: chaotic evolution drives…
In quantum information theory, communication capacities are mostly given in terms of entropic formulas. Continuity of such entropic quantities are significant, as they ensure uniformity of measures against perturbations of quantum states.…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and…
It is well known that the von Neumann entropy is continuous on a subset of quantum states with bounded energy provided the Hamiltonian $H$ of the system satisfies the condition $\Tr\exp(-cH)<+\infty$ for any $c>0$. In this note we consider…
Information inequalities govern the ultimate limitations in information theory and as such play an pivotal role in characterizing what values the entropy of multipartite states can take. Proving an information inequality, however, quickly…
We prove number of quantitative stability bounds for the cases of equality in Petz's monotonicity theorem for quasi-relative entropies defined in terms of an operator monotone decreasing functions. Included in our results is a bound in…
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…
We derive a monogamy inequality for any local quantum resource and entanglement. It results from the fact that there is always a convex measure for a quantum resource, as shown here, and from the relation between entanglement and local…
We study a phenomenon occuring in various areas of quantum physics, in which an observable density (such as an energy density) which is classically pointwise nonnegative may assume arbitrarily negative expectation values after quantisation,…
We establish a tight upper bound for the difference in von Neumann entropies between two quantum states, $\rho_1$ and $\rho_2$. This bound is expressed in terms of the von Neumann entropies of the mutually orthogonal states derived from the…
Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…