Related papers: Relative Entropy for Quantum Channels
Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum…
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of…
We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state, characterizes the coupling of the principal system with the environment. For any quantum channel $\Phi$ acting on a…
We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…
We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum R\'enyi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only…
In this paper, we present new families of quantum channels for which corresponding minimum output R\'enyi $p$-entropy is not additive. Our manuscript is motivated by the results of Grudka et al., J. Phys. A: Math. Theor. 43 425304 and we…
By using the Choi-Jamio{\l}kowski isomorphism, we propose a well-defined coherence measure of quantum channels based on the generalized $\alpha$-$z$-relative R\'{e}nyi entropy. In addition, we present an alternative coherence measure of…
Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Renyi entropies of channels are not generally additive for p>1, we demonstrate here by a careful random selection…
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…
Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamio{\l}kowski-Choi representation,…
Using generalized bosons, we construct the fuzzy sphere $S_F^2$ and monopoles on $S_F^2$ in a reducible representation of $SU(2)$. The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an…
We investigate minimum output (R\'enyi) entropy of qubit channels and unital quantum channels. We obtain an exact formula for the minimum output entropy of qubit channels, and bounds for unital quantum channels. Interestingly, our bounds…
The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…
Most quantum divergences derive their structure from classical f-divergences or Renyi-type constructions, a dependence that obscures several quantum geometric effects. We introduce a quantum relative-alpha-entropy that extends Umegaki's…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
In this paper a notion of entropy transmission of quantum channels is introduced as a natural extension of Ohya's entropy. Here by quantum channel is meant unital completely positive mappings (ucp) of $B(H)$ into itself, where $H$ is an…
We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…
In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and…