Related papers: Lower semicontinuity of the relative entropy distu…

It is proved that the local discontinuity jumps of the quantum relative entropy do not increase under action of quantum channels and operations.

We prove that for any infinite-dimensional quantum channel the entropic disturbance (defined as difference between the $\chi$-quantity of a generalized ensemble and that of the image of the ensemble under the channel) is lower…

It is well known that the quantum mutual information and its conditional version do not increase under local channels. I this paper we show that the recently established lower semicontinuity of the quantum conditional mutual information…

It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…

Quantitative analysis of discontinuity of basic characteristics of quantum states and channels is presented. First we consider general estimates for discontinuity jump (loss) of the von Neumann entropy for a given converging sequence of…

By using relative entropy of coherence, we characterize the coherence gain induced by some quantum evolutions, including the cohering power of unitary operations and the decohering power of quantum operations. We find that the cohering…

A criterion of local continuity of the relative entropy of resource -- the relative entropy distance to the set of free states -- is obtained. Several basic corollaries of this criterion are presented. Applications to the relative entropy…

We introduce the notion of reduced relative quantum entropy and prove that it is convex. This result is then used to give a simplified proof of a theorem of Lieb and Seiringer.

This paper introduces the concepts of correlation entropy and local correlation entropy for free semigroup actions on compact metric space, and explores their fundamental properties. Thereafter, we generalize some classical results on…

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…

The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any…

Quantum networks play a key role in many scenarios of quantum information theory. Here we consider the quantum causal networks in the manner of entropy. First we present a revised smooth max-relative entropy of quantum combs, then we…

For a subalgebra of a generic CCR algebra, we consider the relative entropy between a general (not necessarily pure) quasifree state and a coherent excitation thereof. We give a unified formula for this entropy in terms of single-particle…

Quantum coherence profoundly alters classical thermodynamic expectations by modifying the structure and accessibility of probability distributions. Classically, transitions to lower-entropy states (local second-law violations) are…

Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…

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…

We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channel this is…

Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite…

The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this…

We propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is…