Koashi-Winter relation for {\alpha}-Renyi entropies

TL;DR

This paper generalizes the Koashi-Winter relation using lpha-Renyi entropies, introducing a new classical correlation measure and analyzing its implications for quantum channel capacity and entanglement.

Contribution

It extends the Koashi-Winter relation to lpha-Renyi entropies and proposes a new classical correlation quantifier based on quantum Jensen Shannon divergence.

Findings

Derived analytical expressions for classical correlations.

Analyzed the relation between channel capacity and state discrimination.

Connected generalized robustness with classical correlations.

Abstract

This work presents a generalization of the Koashi-Winter relation for $\alpha$-Renyi entropies. This result is based on the Renyi\apos s entropy version of quantum Jensen Shannon divergence. By means of this definition, a classical correlations quantifier $C_{\alpha}(\rho_{AB}) = \sup_{\xi_{AB}^{M_B}} Q_{\alpha}(\xi_{AB}^{M_B})$ is proposed, where the optimization is taken over the ensembles $\xi_{AB}^{M_B}$ created by the outputs of the local measurement process. The main result is applied to the capacity of a quantum classical channel over a tripartite pure state $\psi_{ABE}$, that is rated above in function of the probability of success to discriminate the states in the ensemble $\xi_{AE}^{M_E}$, created by the local dephasing over partition $E$, and the asymptotic log generalized robustness of partition $AB$. Some analytical results are calculated for classical correlations and entanglement of formation.