Geometric coherence and quantum state discrimination.
Impossibility of distinguishing non-orthogonal quantum states without any error is one of the fundamental properties in quantum mechanics. As a result, constructing the optimal measurement to discriminate a collection of quantum states plays an important role in quantum theory. In this paper, we prove that the geometric coherence of a quantum state is the minimal error probability to discrimination a set of linear independent pure states, which provides an operational interpretation for geometric coherence. Moreover, the closest incoherent states are given in terms of the corresponding optimal von Neumann measurements. Based on this idea, the explicitly expression of geometric coherence are given for a class of states, generalized X-states. On the converse, we show that, any discrimination task for a collection of linear independent pure states can be also regarded as the problem of calculating the geometric coherence for a quantum state, and the optimal measurement can be obtained through the corresponding closest incoherent state.
Publisher URL: http://arxiv.org/abs/1801.06031