Related papers: Isotropic quantum spin channels and additivity que…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…
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,…
Some new examples of quantum channels for which the infimum of the output entropy is additive under taking a tensor product of channels are given.
Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models…
Entropic quantifiers of states lie at the cornerstone of the quantum information theory. While a quantum state can be abstracted as a device that only has outputs, the most general quantum device is a quantum channel that also has inputs.…
It is known that the minimal output entropy is additive for any product of entanglement breaking (EB) channels. The same is true for the Renyi entropy, where additivity is equivalent to multiplicativity of the $1 \rightarrow q$ norm for all…
We introduce a model of non-Gaussian quantum channel that stems from the combination of two physically relevant processes occurring in open quantum systems, namely amplitude damping and dephasing. For it we find input states approaching…
We study the asymptotic behavior of the output states of sequences of quantum channels. Under a natural assumption, we show that the output set converges to a compact convex set, clarifying and substantially generalizing results in [BCN13].…
The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often…
The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work…
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…
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…
We study mixed unitary channels generated by finite subgroups of the group of all unitary operators in a Hilbert space. Based on the majorization theory we introduce techniques allowing to calculate different characteristics of output…
The additivity of minimal output entropy is proved for the Weyl channel obtained by the deformation of a q-c Weyl channel. The classical capacity of channel is calculated.
We develop an approximation approach to infinite dimensional quantum channels based on detailed investigation of the continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely…
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…
This article provides an elementary introduction to Gaussian channels and their capacities. We review results on the classical, quantum, and entanglement assisted capacities and discuss related entropic quantities as well as additivity…
An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity. The example is one of a family of channels which are related to 3-state channels. The capacity of the product channel is studied and…
We study the additivity problems for the classical capacity of quantum channels, the minimal output entropy and its convex closure. We show for each of them that additivity for arbitrary pairs of channels holds iff it holds for arbitrary…
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…