2020/06/30 by Yujie Zhang, Xinan Chen, Eric Chitambar
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Constraint (computer-aided design) #Dimension (graph theory) #Discrete mathematics #Geometry #Mathematics #Particle (ecology) #Physics #Polytope #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum superposition #Set (abstract data type) #Superposition principle #Topology (electrical circuits) #Triangle inequality #math-ph #math.MP #quant-ph
paper · pdf · doi:10.22331/q-2022-02-16-653
published as Quantum 6, 653 (2022)
arxiv created 2022/02/09 · openalex publication_date 2022/02/16 · arxiv updated 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.