Emulation Capacity between Idempotent Channels

TL;DR

This paper investigates the limits of emulating quantum channels, specifically idempotent ones, providing a formula for zero-error capacity and revealing non-reversibility in general cases.

Contribution

It offers a single-letter formula for zero-error emulation capacity between idempotent quantum channels and analyzes conditions for reversibility and strong converse rates.

Findings

Zero-error emulation capacity expressed via channel structure.

Emulation is generally not reversible for idempotent channels.

Strong converse rate matches capacity when channels are identity or dephasing.

Abstract

We study the optimal rates of emulation (also called interconversion) between quantum channels. When the source and the target channels are idempotent, we give a single-letter expression for the zero-error emulation capacity in terms of structural properties of the range of the two channels. This expression shows that channel emulation is not reversible for general idempotent channels. Furthermore, we establish a strong converse rate that matches with the zero-error emulation capacity when the source or the target channel is either an identity or a completely dephasing channel.