Building Multiple Access Channels with a Single Particle

Yujie Zhang1, Xinan Chen2, and Eric Chitambar2

1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
2Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

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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 ${1\lt K\le N}$ 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.

A single quantum particle, unlike its classical counterpart, can be in different locations simultaneously. This property of quantum particles is known as superposition in quantum mechanics and has led to numerous genuine quantum phenomena. For example, in the celebrated double-slit experiment, if quantum particles being in superposition states are employed, non-classical interference can be observed. Here we consider different multiple access communication channels, in which, multiple specially separated senders are trying to forward messages to a single receiver

Our discussion begins with building the framework of multiple access channels with a single particle. We then fully characterize the structures of different multiple access channels built with a single classical particle. Different non-trivial equalities and inequalities that constrain the classical multiple access channel are found and analyzed, where the equalities are intimately related to the multi-slit experiment. We demonstrate the much more fruitful structure of quantum multiple access channels by showing violation of those equalities and inequalities found in classical multiple access communication sceneries. We also draw a connection between the multilevel coherent of a quantum particle and its power in different communication scenarios we framed.

The fundamental differences of single classical particle and quantum particle in the multiple access communication scenarios are beneficial for quantum-enhanced multi-party communication, and the connection of our results and multi-level coherence theory can also be applied to other quantum technologies including quantum sensing and quantum biology.

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