Disturbance-Based Measure of Macroscopic Coherence

TL;DR

This paper introduces a new operational measure of macroscopic quantum coherence based on measurement disturbance, addressing inconsistencies in previous criteria and linking coherence to state fragility and decoherence effects.

Contribution

It proposes a disturbance-based measure of macroscopic coherence, establishes an inequality relating skew information and disturbance, and offers a framework for quantifying coherence from an operational perspective.

Findings

The measure resolves inconsistencies in previous criteria.

An inequality relates skew information to measurement disturbance.

The measure quantifies state fragility to decoherence.

Abstract

We propose a measure of macroscopic coherence based on the degree of disturbance caused by a coarse-grained measurement. Based on our measure, we point out that recently proposed criteria of macroscopic coherence may lead to inconsistent results when considering certain states such as a product of microscopic superpositions. An inequality relation is proved that relates the Wigner-Yanase-Dyson skew information and the measurement disturbance, providing arguments as to why our approach is able to rule out such inconsistencies. We show that our measure can also quantify the fragility of a quantum state to a certain type of decoherence. Our work provides a general framework of quantifying macroscopic coherence from an operational point of view, based on the relationship between the precision of the measurement and disturbance of the quantum state.