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.
Highlights
A quantum particle is fundamentally different than its classical counterpart
The quantity I2 is well-known in the study of double-slit experiments [31–33], and here we prove that its vanishing is essentially the only constraint that assures the multiple-access channel (MAC) has an implementation using a single classical particle
We focus on MACs that can be generated by a single particle and so we will take
Summary
A quantum particle is fundamentally different than its classical counterpart. From the second quantization picture, a quantum “particle” can be regarded as a single mode excitation of some field, and it is. Methods are known for mapping multi-qubit quantum information into the spatial or temporal degrees of freedom of a single photon [22, 23] These results reveal the resource character of single-particle superposition states for building enhanced multipartite classical communication channels. This has the advantage that, when expressed in terms of these probabilities, the collection of MACs generated by a single classical particle forms a convex polytope, provided the output variable is binary This allows us to employ standard techniques from convex analysis to construct experimentally-implementable methods for certifying non-classical MACs. The main results of this paper and its organization are as follows. The setup in their paper involves local encoding in an N -path interformeter, the restriction to a single particle is not made and the analysis focuses on the emergence of higher-order interference effects The latter refers to realizing nonzero values for the quantities. We see Ref. [35] and this work as being complementary and reflecting once again the richness of N -path interforemeter experiments for demonstrating quantum information primitives
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