Coarse Graining Makes It Hard to See Micro-Macro Entanglement

TL;DR

This paper demonstrates that coarse-grained measurements significantly hinder the detection of micro-macro entanglement in quantum systems, making it increasingly difficult to observe quantum effects in larger systems.

Contribution

It analyzes how measurement coarse-graining affects the observability of micro-macro entanglement, comparing quantum and measure-and-prepare cloners, highlighting the challenges in detecting entanglement.

Findings

Coarse-graining reduces distinguishability of measurement results.

Detection of micro-macro entanglement becomes harder with system size.

Probability distributions for different cloners become indistinguishable under coarse-graining.

Abstract

Observing quantum effects such as superpositions and entanglement in macroscopic systems requires not only a system that is well protected against environmental decoherence, but also sufficient measurement precision. Motivated by recent experiments, we study the effects of coarse-graining in photon number measurements on the observability of micro-macro entanglement that is created by greatly amplifying one photon from an entangled pair. We compare the results obtained for a unitary quantum cloner, which generates micro-macro entanglement, and for a measure-and-prepare cloner, which produces a separable micro-macro state. We show that the distance between the probability distributions of results for the two cloners approaches zero for a fixed moderate amount of coarse-graining. Proving the presence of micro-macro entanglement therefore becomes progressively harder as the system size increases.