Coherence Equality and Communication in a Quantum Superposition

TL;DR

This paper introduces a coherence equality distinguishing classical from quantum communication, demonstrating that quantum superpositions violate this equality and can be used to witness spatial quantum superpositions without interferometers.

Contribution

The paper presents a new coherence equality for classical communication and shows its violation by quantum superpositions, providing a practical method to detect spatial quantum superpositions.

Findings

Classical communication satisfies the coherence equality with success probability 1/2.

Quantum schemes violate the coherence equality, exceeding the classical success probability.

Violation of the coherence equality can serve as an operational witness of spatial quantum superpositions.

Abstract

In this paper, we introduce a "coherence equality" that is satisfied by any classical communication -- i.e., conveyed by a localized carrier traveling along well defined directions. In contrast, this equality is violated when the carrier is prepared in a quantum superposition of communication directions. This is phrased in terms of the success probability of a certain communication task, which results to be always constant and equal to 1/2 in the classical case. On the other hand, we develop two simple quantum schemes that deviate systematically from the classical value, thus violating the coherence equality. Such a violation can also be exploited as an operational way to witness spatial quantum superpositions without requiring the use of an interferometer, but only by means of spatially separated local measurements.