相关论文: Monotonicity of the Quantum Relative Entropy Under…

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 show that a recent definition of relative R\'enyi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of M\"uller-Lennert et al.

This article presents in a self-contained way A. Uhlmann's celebrated Theorem of monotonicity of the relative entropy under completely positive and trace preserving maps. The Theorem is presented in its more general form and meaningful…

The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when…

Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…

A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum…

This is an outline of work in progress. We study the conjecture that the topological entropy of a real cubic map depends ``monotonely'' on its parameters, in the sense that each locus of constant entropy in parameter space is a connected…

Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…

We derive the monotonicity of the quantum relative entropy by an elementary operational argument based on Stein's lemma in quantum hypothesis testing. For the latter we present an elementary and short proof that requires the law of large…

We investigate the situation when a normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change fixed quantum Renyi's entropy of the density of a normal state. It is also shown that such…

It is common to assess the "memory strength" of a stationary process looking at how fast the normalized log-determinant of its covariance submatrices (i.e., entropy rate) decreases. In this work, we propose an alternative characterization…

We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of the space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for…

Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences such as the strong…

The monotonicity of entropy is investigated for real quadratic rational maps on the real circle $\mathbb{R}\cup\{\infty\}$ based on the natural partition of the corresponding moduli space $\mathcal{M}_2(\mathbb{R})$ into its monotonic,…

We show that a positive linear map preserves local continuity (convergence) of the entropy if and only if it preserves finiteness of the entropy, i.e. transforms operators with finite entropy to operators with finite entropy. The last…

We show that the topological entropy is monotonic for unimodal interval maps which are obtained from the restriction of quadratic rational maps with real coefficients. This is done by ruling out the existence of certain post-critical curves…

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…

We prove that the entropy function on the moduli space of real quadratic rational maps is not monotonic by exhibiting a continuum of disconnected level sets. This entropy behavior is in stark contrast with the case of polynomial maps, and…

The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor's Monotonicity Conjecture. In contrast, the existing proofs rely in one…

We revisit the monotonicity of relative entropy under the action of quantum channels, a foundational result in quantum information theory. Among the several available proofs, we focus on those by Petz and Uhlmann, which we reformulate…