Building Multiple Access Channels with a Single Particle

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.

Information Carried by a Single Particle in Quantum Multiple-Access Channels

“…On the one hand, this is not surprising since our encoding strategy uses an initial state |ψ that places smaller and smaller weight on the paths of additional parties. However, on the other hand, we have not been able to find any superior coding method, and in fact, many coding schemes (such as the "fingerprinting" protocol [6,10]) have a rate sum that vanishes as N grows large. A significant open problem is to find upper bounds on the largest N -party rate sum using a single quantum particle, which we conjecture will not be too far from the lower bound depicted in Fig.…”

“…To compare how much classical information can be carried by a classical or quantum particle with none of its internal degrees of freedom being accessible, we utilize the framework of single-particle MACs developed in Ref. [10]. This framework, which we now briefly describe, was inspired by previous work [11,12] that captured the resource-theoretic features of quantum coherence in a multi-port interferometer setup.…”

“…where U preserves the overall particle number in the system A and the environment E. This set of operations was termed number-preserving extendible (NPE) operations in Ref. [10] and was fully characterized for an arbitrary number of particles. Here we focus only on the case where there is at most one particle.…”

“…Since this can be done for an arbitrary n, this result suggests, roughly speaking, that a single quantum particle can carry an arbitrarily large amount of information in point-to-point communication. Complementing the point-to-point communication results, it was recently discovered via convex polytope analysis that using a single quantum particle, one can generate multiple-access channels (MACs) that cannot be constructed with a classical particle [6,10]. However, these latter results pertain to the specific transition probabilities p(y|x 1 , • • • , x N ) of the generated N -party MACs.…”

“…In this paper, we provide a positive answer to this question. Specifically, we utilize the framework of single-particle multiple-access channels (MACs) developed in [10] to investigate the achievable rate regions of distributed communication using a single particle. While the communication rate sum of the different senders is always upper bounded by 1 bit if a single classical particle is used, in the quantum setting a rate sum of at least 1.10 bits is achievable for two senders.…”