The logic of entanglement

TL;DR

This paper formalizes the information flow in bipartite entanglement, re-analyzes existing quantum protocols, introduces new protocol designs, and proposes an automated scheme for protocol development based on entanglement's information capabilities.

Contribution

It presents a theorem characterizing entanglement's information flow, enabling protocol analysis, design, and extension to multipartite systems, with an automated design scheme.

Findings

Entanglement's information flow can be precisely characterized.

Existing protocols like teleportation are re-analyzed using the theorem.

New protocols, such as parallel logic gate composition, are proposed.

Abstract

We expose the information flow capabilities of pure bipartite entanglement as a theorem -- which embodies the exact statement on the `seemingly acausal flow of information' in protocols such as teleportation. We use this theorem to re-design and analyze known protocols (e.g. logic gate teleportation and entanglement swapping) and show how to produce some new ones (e.g. parallel composition of logic gates). We also show how our results extend to the multipartite case and how they indicate that entanglement can be measured in terms of `information flow capabilities'. Ultimately, we propose a scheme for automated design of protocols involving measurements, local unitary transformations and classical communication.