Universal complementarity between coherence and intrinsic concurrence for two-qubit states

Abstract Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there is a direct link between them. In this work, we propose a definition of intrinsic concurrence for two-qubit states. Although the intrinsic concurrence is not a measure of entanglement, it embodies the concurrence of four pure states which are members of a special pure state ensemble for an arbitrary two-qubit state. And we show that intrinsic concurrence is always complementary to first-order coherence. In fact, this relation is an extension of the complementary relation satisfied by two-qubit pure states. Interestingly, we apply the complementary relation in some composite systems composed by a single-qubit state coupling with four typical noise channels respectively, and discover their mutual transformation relation between concurrence and first-order coherence. This universal complementarity provides reliable theoretical basis for the interconversion of the two important quantum resources.