Building Multiple Access Channels with a Single Particle

TL;DR

This paper explores how single particles, classical or quantum, can be used to build multiple access channels, revealing quantum advantages and characterizing the capabilities of such channels through an operational framework.

Contribution

It introduces a framework for analyzing single-particle multiple access channels and characterizes the classical set, demonstrating quantum particles can generate non-classical channels and violate certain inequalities.

Findings

Quantum particles can generate MACs outside the classical set.

A generalized fingerprinting inequality is identified as a facet of the classical MAC polytope.

Quantum particles can violate this inequality even with partial joint encoding.

Abstract

A multiple access channel describes a situation in which multiple senders are trying to forward messages to a single receiver using some physical medium. In this paper we consider scenarios in which this medium consists of just a single classical or quantum particle. In the quantum case, the particle can be prepared in a superposition state thereby allowing for a richer family of encoding strategies. To make the comparison between quantum and classical channels precise, we introduce an operational framework in which all possible encoding strategies consume no more than a single particle. We apply this framework to an N-port interferometer experiment in which each party controls a path the particle can traverse. When used for the purpose of communication, this setup embodies a multiple access channel (MAC) built with a single particle. We provide a full characterization of the N-party classical MACs that can be built from a single particle, and we show that every non-classical particle can generate a MAC outside the classical set. To further distinguish the capabilities of a single classical and quantum particle, we relax the locality constraint and allow for joint encodings by subsets of 1<K<= N parties. This generates a richer family of classical MACs whose polytope dimension we compute. We identify a "generalized fingerprinting inequality" as a valid facet for this polytope, and we verify that a quantum particle distributed among N separated parties can violate this inequality even when K=N-1. Connections are drawn between the single-particle framework and multi-level coherence theory. We show that every pure state with K-level coherence can be detected in a semi-device independent manner, with the only assumption being conservation of particle number.