Related papers: Additivity in Isotropic Quantum Spin Channels
For a given quantum channel we consider two optimal sets of states, related to the Holevo capacity and to the minimal output entropy of this channel. Some properties of these sets as well as the necessary and sufficient condition for their…
We describe analytical properties of the average output entropy of a quantum channel as a function of a pair (channel, input ensemble). In particular, tight semicontinuity bounds for this function with the rank/energy constraints are…
We study a natural generalization of the additivity problem in quantum information theory: given a pair of quantum channels, then what is the set of convex trace functions that attain their maximum on unentangled inputs, if they are applied…
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…
In this paper, we study the minimal output entropy of EPOSIC channels. We determine the cases where their minimal output entropy is zero, and obtain some partial results on the fulfillment of their entanglement breaking property.Our results…
We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. For this class of channels the norm of the output is maximized for the output being a normalized projection. We…
We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. We construct a unital channel…
Additivity of the minimal output entropy for the family of transpose depolarizing channels introduced by Fannes et al. [quant-ph/0410195] is considered. It is shown that using the method of our previous paper [quant-ph/0403072] allows us to…
It is easy to show coincidence of the entanglement-assisted classical capacity and the Holevo capacity for any c-q channel between finite dimensional quantum systems. In this paper we prove the converse assertion: coincidence of the…
Hastings recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy. In this paper we present an expanded version of Hastings' proof. In addition to a careful elucidation of the…
Inspired by Montanaro's work, we introduce the concept of additivity rates of a quantum channel $L$, which give the first order (linear) term of the minimum output $p$-R\'enyi entropies of $L^{\otimes r}$ as functions of $r$. We lower bound…
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…
We present explicit quantum channels with strictly sub-additive minimum output R\'enyi entropy for all $p>1$, improving upon prior constructions which handled $p>2$. Our example is provided by explicit constructions of linear subspaces with…
Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity. However, this cannot be achieved for a few quantities that have been established as…
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…
Additivity violation of minimum output entropy, which shows non-classical properties in quantum communication, had been proved in most cases for random quantum channels defined by Haar-distributed unitary matrices. In this paper, we…
In the present paper we study the entropy gain $H(\Phi [\rho])-H(\rho)$ for infinite-dimensional channels $\Phi$. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive \cite{al}, there is a plenty…
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…
There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty…
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…