Unitary conjugation channels with continuous random phases

TL;DR

This paper investigates the spectral properties and asymptotic behavior of unitary conjugation channels with continuous random phases, revealing that discrete phases can replicate the channel average in certain cases.

Contribution

It provides new insights into the spectral analysis of channels with continuous phases and demonstrates that discrete phases suffice for channel averaging.

Findings

Spectral properties of the channel average are characterized.

Asymptotic behaviors of repeated quantum interactions are derived.

Discrete phases can achieve the channel average with continuous uniform phases.

Abstract

We consider unitary conjugation channels with continuous random phases. The spectral properties of the channel average are examined, thereby the asymptotic behaviors of the repeated quantum interactions of the motion are derived. We then study the channels with uniformly distributed continuous phases on an interval. In this context, it is shown that discrete phases are sufficient to achieve the channel average.