Characterizing Quantum Correlation With The Correlated Part Of Partial Coherence

One of the fundamental features of the quantum world that distinguishes it from the classical counterpart is the existence of quantum correlations. In this paper, we study the quantum correlation from the viewpoint of partial coherence. Partial coherence in a bipartite system often contains local coherence of a subsystem. By removing the local coherence, we show that the remaining part of partial coherence can be regarded as quantum correlations. In this way, we introduce two quantum correlations: partial correlated coherence (PCC) and minimal partial correlated coherence (MPCC). Furthermore, we prove that PCC and MPCC induced by contractive pseudodistances are good candidates of quantum correlations. For contractive pseudodistances, we also show that the induced geometric partial correlated coherence (GPCC) and geometric minimal partial correlated coherence are actually the upper and lower bound of corresponding geometric quantum discord. Particularly, GPCCs based on a family of distances are proved to be bona fide measures of quantum correlations. By connecting to local quantum uncertainty, we provide an operational meaning for geometric quantum discord and GPCC induced by affinity of distance.