  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.
