The size of quantum superpositions as measured with "classical" detectors

TL;DR

This paper introduces a criterion based on classical detectors to define and measure the macroscopicity of quantum superpositions, highlighting their sensitivity to noise and phase fluctuations.

Contribution

It proposes a novel measure of superposition size using classical detector distinguishability and extends this to quantify macroscopicity.

Findings

Superpositions meeting the criterion are highly sensitive to phase fluctuations.

The measure correlates superposition size with noise tolerance in classical detection.

The approach explains the difficulty of observing macroscopic superpositions.

Abstract

We propose a criterion which defines whether a superposition of two photonic components is macroscopic. It is based on the ability to discriminate these components with a particular class of "classical" detectors, namely a photon number measurement with a resolution coarse-grained by noise. We show how our criterion can be extended to a measure of the size of macroscopic superpositions by quantifying the amount of noise that can be tolerated and taking the distinctness of two Fock states differing by N photons as a reference. After applying our measure to several well-known examples, we demonstrate that the superpositions which meet our criterion are very sensitive to phase fluctuations. This suggests that quantifying the macroscopicity of a superposition state through the distinguishability of its components with "classical" detectors is not only a natural measure but also explains why it is difficult to observe superpositions at the macroscopic scale.