Extreme nonlocality with one photon

TL;DR

This paper demonstrates that a single particle superposed over multiple spatial modes can exhibit nonlocality, with proofs and inequalities that become more pronounced as the number of modes increases, approaching GHZ-like contradictions.

Contribution

It introduces a Hardy-like proof and Bell inequality for single-particle superpositions over N modes, extending nonlocality tests to single-particle systems.

Findings

Hardy-like proof becomes GHZ-like as N increases

Bell inequality gap approaches that of three-particle GHZ experiments

Methodology for testing nonlocality in realistic systems

Abstract

Quantum nonlocality is typically assigned to systems of two or more well separated particles, but nonlocality can also exist in systems consisting of just a single particle, when one considers the subsystems to be distant spatial field modes. Single particle nonlocality has been confirmed experimentally via a bipartite Bell inequality. In this paper, we introduce an N-party Hardy-like proof of impossibility of local elements of reality and a Bell inequality for local realistic theories for a single particle superposed symmetrical over N spatial field modes (i.e. a N qubit W state). We show that, in the limit of large N, the Hardy-like proof effectively becomes an all-versus nothing (or GHZ-like) proof, and the quantum-classical gap of the Bell inequality tends to be same of the one in a three-particle GHZ experiment. We detail how to test the nonlocality in realistic systems.