# On the minimum output entropy of random orthogonal quantum channels

## TL;DR

This paper investigates the asymptotic behavior of output entropy in sequences of random orthogonal quantum channels, revealing that maximally entangled states minimize output entropy for even tensor powers, contrasting with unitary-based channels.

## Contribution

It demonstrates that maximally entangled states minimize output entropy in random orthogonal channels for even tensor powers, a novel finding differing from unitary channel behavior.

## Key findings

- Maximally entangled states minimize output entropy for even tensor powers.
- Distinct behavior from Haar-random unitary channels.
- Formulation of conjectures on regularized minimum output entropy.

## Abstract

We consider sequences of random quantum channels defined using the Stinespring formula with Haar-distributed random orthogonal matrices. For any fixed sequence of input states, we study the asymptotic eigenvalue distribution of the outputs through tensor powers of random channels. We show that the input states achieving minimum output entropy are tensor products of maximally entangled states (Bell states) when the tensor power is even. This phenomenon is completely different from the one for random quantum channels constructed from Haar-distributed random unitary matrices, which leads us to formulate some conjectures about the regularized minimum output entropy.