Detecting and estimating coherence based on coherence witnesses

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