Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

TL;DR

This paper analyzes the statistical properties of outputs from products of random quantum channels with entangled inputs, revealing regimes where entropy is lower than basic bounds, thus advancing understanding of quantum information theory.

Contribution

It introduces a classification of regimes where von Neumann entropy is lower on average, generalizing models related to quantum entropy additivity counterexamples.

Findings

Identifies regimes with lower average von Neumann entropy

Revisits models relevant to entropy additivity counterexamples

Provides a classification of entropy behavior in quantum channels

Abstract

Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.