Experimental verification of the relationship between first-order coherence and linear steerability.

Coherence and steerability are two essential characteristics of quantum systems. For a two-qubit state, the first-order coherence and the maximal violation of linear steering inequality are used to operationally measure the degree of coherence and steerability, respectively. Recently, a complementary relation between first-order coherence and linear steerability has been proposed. In this paper, we report an experimental verification of the complementary relation by preparing biphoton polarization entangled states in an all-optical setup. We propose an operable method for experimental measurement of the first-order coherence and linear steerability and calculate the purity of the initial states by reconstructing the density matrices of them. The experimental results coincide with the theoretical predictions very well, which provides a valuable reference for the application of optical quantum technology.