Classical communication through quantum causal structures

TL;DR

This paper investigates the limits of classical communication capacities in quantum processes with indefinite causal order, showing that exotic causal structures do not surpass traditional causally separable processes in communication efficiency.

Contribution

It formulates classical capacities for bipartite quantum processes using the process matrix formalism and establishes bounds on communication protocols in indefinite causal structures.

Findings

One-way communication cannot outperform causally separable processes.

Bi-directional communication does not exceed one-way communication limits.

Multi-party broadcast communication is bounded by definite ordered process limits.

Abstract

Quantum mechanics allows operations to be in indefinite causal order. Recently there have been active discussions on enhanced communication strategies through exotic causal structures. In light of this, through the process matrix formalism, we formulate different classical capacities for a bi-partite quantum process. We find that a one-way communication protocol through an arbitrary process cannot outperform a causally separable process, i.e., we can send at most one bit per qubit. Next, we study bi-directional communication through a causally separable process. Our result shows, a bi-directional protocol cannot exceed the limit of one way communication protocol. Finally, we generalise this result to multi-party broadcast communication protocol through a definite ordered process.