Additivity violation of quantum channels via strong convergence to semi-circular and circular elements

TL;DR

This paper demonstrates additivity violations in quantum channels constructed from Gaussian and Ginibre ensembles by leveraging free probability theory, specifically semi-circular and circular systems, and strong convergence techniques.

Contribution

It introduces a new class of random quantum channels and proves additivity violations using free probability and strong convergence, extending prior results beyond Haar-distributed unitaries.

Findings

Violations of additivity and multiplicativity in the asymptotic regime.

Use of free probability to analyze quantum channel properties.

New class of channels exhibiting non-classical behavior.

Abstract

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 investigate random completely positive maps made of Gaussian Unitary Ensembles and Ginibre Ensembles regarding this matter. Using semi-circular systems and circular systems of free probability, we not only show the multiplicativity violation of maximum output norms in the asymptotic regimes but also prove the additivity violation via Haagerup inequality for a new class of random quantum channels constructed by rectifying the above completely positive maps based on strong convergence.