Related papers: Local Additivity Revisited

We show that the minimum von-Neumann entropy output of a quantum channel is locally additive. Hasting's counterexample for the additivity conjecture, makes this result quite surprising. In particular, it indicates that the non-additivity of…

We show that the minimum Renyi entropy output of a quantum channel is locally additive for Renyi parameter alpha>1. While our work extends the results of [10] (in which local additivity was proven for alpha=1), it is based on several new…

We give a direct proof of the additivity of the minimum output entropy of a particular quantum channel which breaks the multiplicativity conjecture. This yields additivity of the classical capacity of this channel, a result obtained by a…

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 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…

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…

Additivity of minimal entropy output is proven for the class of quantum channels $\Lambda_t (A):=t A^{T}+(1-t)\tau (A)$ in the parameter range $-2/(d^2-2)\le t \le 1/(d+1)$.

We introduce two additive invariants of output quantum channels. If the value of one these invariants is less than 1 then the logarithm of the inverse of its value is a positive lower bound for the regularized minimum entropy of an output…

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 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…

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…

This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the…

We show that under a certain condition of local commutativity the minimum von-Neumann entropy output of a quantum channel is locally additive. We also show that local minima of the 2-norm entropy functions are closed under tensor products…

Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…

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…

In this paper, we compute the exact values of the minimum output entropy and the completely bounded minimal entropy of very large classes of quantum channels acting on matrix algebras $\mathrm{M}_n$. Our new and simple approach relies on…

We argue that a fundamental (conjectured) property of memoryless quantum channels, namely the strong superadditivity, is intimately related to the decreasing property of the quantum relative entropy. Using the latter we first give, for a…

We introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of…

We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove…

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…