Asymmetric information capacities of reciprocal pairs of quantum channels

TL;DR

This paper investigates the asymmetric quantum communication capacities of reciprocal pairs of quantum channels, revealing differences from classical expectations and highlighting unique quantum behaviors.

Contribution

It introduces the concept of reciprocal pairs of quantum channels and demonstrates their asymmetric classical communication capacities, contrasting with classical symmetry.

Findings

Reciprocal quantum channels can have different classical capacities.

Explicit examples are provided with depolarizing and Weyl-covariant channels.

Quantum reciprocal pairs exhibit asymmetry not present in classical channels.

Abstract

Reciprocal pairs of quantum channels are defined as completely positive transformations which admit a rigid, distance-preserving, yet not completely-positive transformation that allows to reproduce the outcome of one from the corresponding outcome of the other. From a classical perspective these transmission lines should exhibit the same communication efficiency. This is no longer the case in the quantum setting: explicit asymmetric behaviours are reported studying the classical communication capacities of reciprocal pairs of depolarizing and Weyl-covariant channels.