Classical capacities of quantum channels with environment assistance

TL;DR

This paper investigates how a helper controlling the environment state can enhance the classical capacity of quantum channels, exploring various scenarios including separable states, entanglement, and conferencing between parties.

Contribution

It introduces and analyzes the classical capacities of quantum channels with environment assistance, considering multiple scenarios such as separable states, entanglement, and communication protocols.

Findings

Helper-controlled environment can increase channel capacity.

Entanglement and conferencing further enhance communication capabilities.

Different helper restrictions lead to varied capacity outcomes.

Abstract

A quantum channel physically is a unitary interaction between the information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the interaction, is assumed to be fixed and known to the sender and receiver. Here, following the model introduced by us earlier [Karumanchi et al., arXiv[quant-ph]:1407.8160], we consider a benevolent third party, i.e. a helper, controlling the environment state, and how the helper's presence changes the communication game. In particular, we define and study the classical capacity of a unitary interaction with helper, indeed two variants, one where the helper can only prepare separable states across many channel uses, and one without this restriction. Furthermore, the two even more powerful scenarios of pre-shared entanglement between helper and receiver, and of classical communication between sender and helper (making them conferencing encoders) are considered.