Related papers: On some entropy inequalities
Using the monotonity of relative entropy of composite quantum systems we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Example of qutrit state inequalities and the "qubit portrait" bound for the…
Talagrand's fundamental result on the entropy numbers is slightly improved. Our proof uses different ideas based on results from greedy approximation.
We derive a universal inequality that provides a lower bound on the ensemble-averaged von Neumann entropy change in a quantum system subject to continuous measurement and dissipation. Our result clarifies how entropy production is…
Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…
This short note contains a list of new results concerning the R\'{e}nyi entropy, the Tsallis entropy, and the Heun functions associated with positive linear operators.
We define and study a relative free entropy quantity, analogous in its properties to Voiculescu's relative free entropy Chi^*(...:B). Our definition uses matricial microstates, unlike his definition, which involves non-commutative Hilbert…
In this article we study relationship between three measures of distinguishability of quantum states called as divergence, relative entropy and the substate property.
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
We establish a general class of entropy inequalities that take the concise form of Gaussian comparisons. The main result unifies many classical and recent results, including the Shannon-Stam inequality, the Brunn-Minkowski inequality, the…
R\'enyi entropy is a one-parameter generalization of Shannon entropy, which has been used in various fields of physics. Despite its wide applicability, the physical interpretations of the R\'enyi entropy are not widely known. In this paper,…
This paper presents self-contained proofs of the strong subadditivity inequality for quantum entropy and some related inequalities for the quantum relative entropy, most notably its convexity and its monotonicity under stochastic maps.…
By generalizing the density matrix to a transition matrix between two states, represented as $|\phi\rangle$ and $|\psi\rangle$, one can define the pseudoentropy analogous to the entanglement entropy. In this paper, we establish an operator…
We prove conjectures on the relative entropy of entanglement (REE) for two families of multipartite qubit states. Thus, analytic expressions of REE for these families of states can be given. The first family of states are composed of…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
In this paper, we introduce two notions of a relative operator $(\alpha, \beta)$-entropy and a Tsallis relative operator $(\alpha, \beta)$-entropy as two parameter extensions of the relative operator entropy and the Tsallis relative…
Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…
In this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. The latter inequality, which we call…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
An observer increases in relative entropy as it receives information from what it is observing. In a system of only an observer and the observed, an increase in the relative entropy of the observer is a decrease in the relative entropy of…