Common Coherence Witnesses and Common Coherent States

TL;DR

This paper explores the properties and construction of coherence witnesses, investigates conditions for common witnesses among states, and introduces methods to identify when different states share detection capabilities in quantum coherence.

Contribution

It provides a characterization of coherence witnesses, criteria for common witnesses among states, and a novel approach to constructing optimal witnesses for various quantum states.

Findings

Finitely many witnesses can detect common states if their weighted sum remains a witness.

Coherent states act as high-level witnesses for coherence detection.

Certain states, like a coherent state and its robust state, do not share common witnesses.

Abstract

We show the properties and characterization of coherence witnesses. We show methods for constructing coherence witnesses for an arbitrary coherent state. We investigate the problem of finding common coherence witnesses for certain class of states. We show that finitely many different witnesses $W_1, W_2, \cdots, W_n$ can detect some common coherent states if and only if $\sum_{i=1}^nt_iW_i$ is still a witnesses for any nonnegative numbers $t_i(i=1,2,\cdots,n)$. We show coherent states play the role of high-level witnesses. Thus, the common state problem is changed into the question of when different high-level witnesses (coherent states) can detect the same coherence witnesses. Moreover, we show a coherent state and its robust state have no common coherence witness and give a general way to construct optimal coherence witnesses for any comparable states.