Related papers: On the structure of optimal sets for tensor produc…
Recently Shor proved equivalence of several open (sub)additivity problems related to the Holevo capacity and the entanglement of formation [15]. In our previous note [6] equivalence of these to the additivity of the Holevo capacity for…
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 show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In…
In this paper, we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive trace-preserving (or stochastic) map. We provide strong support…
The notion of the Holevo capacity for arbitrarily constrained infinite dimensional quantum channels is introduced. It is shown that despite nonexistence of an optimal ensemble in this case it is possible to define the notion of the output…
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…
We introduce an infinite sequence of quantum channels for which the Holevo capacity is additive. The channel series is closely related to the quantum channels arising from universal quantum cloning machines. The additivity proof is…
The purpose of these notes is to discuss the relation between the additivity questions regarding the quantities (Holevo) capacity of a quantum channel T and entanglement of formation of a given bipartite state. In particular, using the…
We consider the image of some classes of bipartite quantum states under a tensor product of random quantum channels. Depending on natural assumptions that we make on the states, the eigenvalues of their outputs have new properties which we…
A conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel, as measured by the p-norm, should be multiplicative…
The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Re'nyi entropies at the output of a channel. The conjecture is proven true for all Re'nyi entropies of integer order greater than two in a class of Gaussian bosonic…
In this paper we give several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity. To this end a characteristic property of the optimal…
This paper is devoted to systematic study of properties of the quantum entropy and of the Holevo capacity considered as a function of a set of quantum states. The properties of restriction of the quantum entropy to arbitrary set of states…
We consider a nontrivial class of infinite dimensional quantum channels characterized by finiteness of the Holevo capacity. Some general properties of channels of this class are described. In particular, a special sufficient condition of…
It is now well-known that, with high probability, the additivity of minimum output entropy does not hold for a pair of a random quantum channel and its complex conjugate. We investigate asymptotic behavior of output states of $r$-tensor…
Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is in a certain class of unital qubit channels, with the other completely arbitrary. This qubit class includes the depolarizing…
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.
It is conjectured that the Holevo capacity of a product channel \Omega \otimes \Phi is achieved when product states are used as input. Amosov, Holevo and Werner have also conjectured that the maximal p-norm of a product channel is achieved…
We investigate spectral properties of the tensor products of two quantum channels defined on matrix algebras. This leads to the important question of when an arbitrary subalgebra can split into the tensor product of two subalgebras. We show…
The information carrying capacity of the d-dimensional depolarizing channel is computed. It is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space,…