Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems

TL;DR

This paper derives new bounds on the minimum output entropies of random quantum channels using free probability, revisits additivity violations for Re9nyi entropies, and analyzes norms of random channels.

Contribution

It provides novel bounds for quantum channel entropies, demonstrates violations of additivity for specific random channels, and computes asymptotic norms, advancing understanding of quantum information theory.

Findings

Random channels violate additivity of p-Re9nyi entropy.

New bounds for minimum output entropies are established.

Asymptotic limits of Schatten norms for certain channels are computed.

Abstract

In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and Winter to get violations of the additivity equalities for minimum output R\'enyi entropies. We show that random channels obtained by randomly coupling the input to a qubit violate the additivity of the $p$-R\'enyi entropy. For some sequences of random quantum channels, we compute almost surely the limit of their Schatten $S_1 \to S_p$ norms.