Related papers: On the structure of optimal sets for tensor produc…
We study whether the entanglement of formation is additive over tensor products and derive a necessary and sufficient condition for optimality of vector states that enables us to show additivity in two special cases.
The thermodynamic resourcefulness of quantum channels primarily depends on their underlying causal structure and their ability to generate quantum correlations. We quantify this interplay within the resource theory of athermality for…
This paper considers a class of qubit channels for which three states are always sufficient to achieve the Holevo capacity. For these channels it is known that there are cases where two orthogonal states are sufficient, two non-orthogonal…
Recently, the projective robustness of quantum states has been introduced in [arXiv:2109.04481(2021)]. It shows that the projective robustness is a useful resource monotone and can comprehensively characterize capabilities and limitations…
A simple criterion for local equality between the constrained Holevo capacity and the quantum mutual information of a quantum channel is obtained. It implies that the set of all states for which this equality holds is determined by the…
We consider sequences of random quantum channels defined using the Stinespring formula with Haar-distributed random orthogonal matrices. For any fixed sequence of input states, we study the asymptotic eigenvalue distribution of the outputs…
Recently there has been considerable activity on the subject of additivity of various quantum channel capacities. Here, we construct a family of channels with sharply bounded classical, hence private capacity. On the other hand, their…
Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact…
Werner states have a host of interesting properties, which often serve to illuminate the unusual properties of quantum information. Starting from these states, one may define a family of quantum channels, known as the Holevo-Werner…
We study quantum channels that are close to another channel with weakly additive Holevo information and derive upper bounds on their classical capacity. Examples of channels with weakly additive Holevo information are entanglement-breaking…
We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which…
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…
It is shown that for real finite dimensional Hilbert spaces the additivity property of the minimum output entropy for quantum channels is always true.
The continuity properties of the convex closure of the output entropy of infinite dimensional channels and their applications to the additivity problem are considered. The main result of this paper is the statement that the superadditivity…
We introduce quotient maps in the category of operator systems and show that the maximal tensor product is projective with respect to them. Whereas, the maximal tensor product is not injective, which makes the $({\rm el},\max)-nuclearity…
A condition for reversibility (sufficiency) of a channel with respect to a given countable family of states with bounded rank is obtained. This condition shows that a quantum channel preserving the Holevo quantity of at least one (discrete…
The minimum entropy output is computed for rotationally invariant quantum channels acting on spin-1/2 and spin-1 systems. For the case of two parallel such channels and initial entangled (singlet) state the entropy of the output is higher…
The problem of additivity of the Minimum Output Entropy is of fundamental importance in Quantum Information Theory (QIT). It was solved by Hastings in the one-shot case, by exhibiting a pair of random quantum channels. However, the initial…
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…
The entropy H_T(rho) of a state rho with respect to a channel T and the Holevo capacity of the channel require the solution of difficult variational problems. For a class of 1-qubit channels, which contains all the extremal ones, the…