Detecting and estimating coherence based on coherence witnesses

TL;DR

This paper introduces practical methods to detect and quantify quantum coherence using coherence witnesses, which are applicable to finite-dimensional states and can estimate various coherence measures, with demonstrated advantages in quantum metrology.

Contribution

The paper presents a novel, feasible approach to construct coherence witnesses for finite-dimensional states, enabling detection and estimation of coherence measures, and shows their superiority over previous witnesses.

Findings

Proposed two typical coherence witnesses for finite-dimensional states.

Our witness can estimate robustness, $l_1$-norm, and $l_2$-norm of coherence.

Our witness is strictly stronger than a previously known witness.

Abstract

Quantum coherence has wide-ranging applications from quantum thermodynamics to quantum metrology, quantum channel discrimination and even quantum biology. Thus, detecting and quantifying coherence are two fundamental problems in quantum resource theory. Here, we introduce feasible methods to detect and estimate the coherence by constructing coherence witnesses for any finite-dimensional states. Our coherence witnesses detect coherent states by testing whether the expectation value of the witness is negative or not. Two typical coherence witnesses are proposed and discussed based on our witness-constructing method, which are also used to estimate the robustness of coherence, $l_1$-norm and $l_2$-norm of coherence measures. Furthermore, we compare one of our coherence witness with a previously introduced witness, by proving that our witness is strictly stronger than that previous witness. We also present an application of coherence in a quantum metrology task, in which we estimate an unknown parameter by measuring our coherence witness.