Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels

TL;DR

This paper studies the asymptotic behavior of output states for tensor powers of conjugate pairs of random quantum channels, showing that certain well-behaved inputs do not violate additivity and identifying tensor products of Bell states as optimal.

Contribution

It provides the first analysis of asymptotic output states for well-behaved inputs of conjugate quantum channel pairs, supporting additivity conjectures.

Findings

Limit output states computed for well-behaved inputs.

Tensor products of Bell states asymptotically minimize output entropy.

Evidence supporting additivity for conjugate channel pairs.

Abstract

It is now well-known that, with high probability, the additivity of minimum output entropy does not hold for a pair of a random quantum channel and its complex conjugate. We investigate asymptotic behavior of output states of $r$-tensor powers of such pairs, as the dimension of inputs grows. We compute the limit output states for any sequence of well-behaved inputs, which consist of a large class of input states having a nice set of parameters. Then, we show that among these input states tensor products of Bell states give asymptotically the least output entropy, giving positive mathematical evidence towards additivity of above pairs of channels.