Can coarse measurements reveal macroscopic quantum effects?

TL;DR

This paper investigates whether macroscopic quantum effects can be detected with coarse measurements, concluding that either measurement outcome precision or control precision must increase with system size.

Contribution

It refines the conjecture on measurement precision by showing control precision must also scale with system size for detecting quantum effects.

Findings

Coarse measurements can detect quantum effects if control precision increases.

Detection of macroscopic quantum effects requires either outcome or control precision to scale with system size.

Counter-example involving macroscopic coherent states supports the refined conjecture.

Abstract

It has recently been conjectured that detecting quantum effects such as superposition or entanglement for macroscopic systems always requires high measurement precision. Analyzing an apparent counter-example involving macroscopic coherent states and Kerr non-linearities, we find that while measurements with coarse outcomes can be sufficient, the phase control precision of the necessary non-linear operations has to increase with the size of the system. This suggests a refined conjecture that either the {\it outcome precision} or the {\it control precision} of the measurements has to increase with system size.