Characterizing coherence with quantum observables

TL;DR

This paper presents a practical method to quantify quantum coherence directly from measurement data, avoiding full state tomography, and reveals its behavior in quantum phase transitions.

Contribution

It introduces a coherence measure based on measurement expectation values that can be computed without state tomography and applies it to various bipartite systems.

Findings

The measure captures non-classical correlations and local contributions.

It detects singular behavior at quantum phase transitions.

The method works with incomplete measurement data.

Abstract

We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be directly calculated from measurement expectation values. This definition of coherence allows the decomposition into contributions corresponding to the non-classical correlations between the subsystems and localized on each subsystem. The method can also be applied to cases where the full set of measurement operators is unavailable. An estimator using the truncated measurement operators can be used to obtain lower bound to the genuine value of coherence. We illustrate the method for several bipartite systems, and show the singular behavior of the coherence measure in a spin-1 chain, characteristic of a quantum phase transition.