Estimates for compression norms and additivity violation in quantum information

TL;DR

This paper provides estimates for the free contraction norm in quantum information, using free probability theory, and offers a new proof of the additivity violation of minimum output entropy in quantum channels.

Contribution

It introduces a method to estimate the free contraction norm and presents a novel, simplified proof of the additivity violation in quantum information theory.

Findings

Estimated the free contraction norm using super convergence techniques.

Provided a new proof of the violation of additivity of minimum output entropy.

Enhanced understanding of spectral properties of random quantum channels.

Abstract

The free contraction norm (or the (t)-norm) was introduced by Belinschi, Collins and Nechita as a tool to compute the typical location of the collection of singular values associated to a random subspace of the tensor product of two Hilbert spaces. In turn, it was used in by them in order to obtain sharp bounds for the violation of the additivity of the minimum output entropy for random quantum channels with Bell states. This free contraction norm, however, is difficult to compute explicitly. The purpose of this note is to give a good estimate for this norm. Our technique is based on results of super convergence in the context of free probability theory. As an application, we give a new, simple and conceptual proof of the violation of the additivity of the minimum output entropy.