Criteria for generalized macroscopic and mesoscopic quantum coherence

TL;DR

This paper develops criteria to identify and analyze macroscopic and mesoscopic quantum superpositions based on observable outcomes, providing experimental signatures and implications for EPR-type experiments.

Contribution

It introduces a formal definition of superposition size relative to an observable and derives criteria to detect generalized S-scopic superpositions in experiments.

Findings

Criteria for detecting S-scopic superpositions using observable statistics

Signatures applicable in systems demonstrating squeezing

Framework enabling new EPR gedanken experiments

Abstract

We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size $S$ of a superposition, with respect to an observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that superposition. Such superpositions are referred to as generalized $S$-scopic superpositions to distinguish them from the extreme superpositions that superpose only the two states that have a difference $S$ in their prediction for the observable. We also consider generalized $S$-scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalized $S$-scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing. We also discuss how the signatures enable a new type of Einstein-Podolsky-Rosen gedanken experiment.