Tradeoff Relations in Quantum Resource Theory

Abstract Entanglement and coherence are deemed as two unreplaceable and important quantum resources in the regime of quantum physics, which are widely applied to quantum information processing and quantum computation. It is therefore natural to ask if there exists any intrinsic relationship between entanglement and coherence. In this work, the authors originally put forward tradeoff relations between intrinsic concurrence and first‐order coherence in the context of an arbitrary three‐qubit state. To do so, an equality relation related to the quantum entanglement and first‐order coherence for arbitrary three‐qubit pure states is derived first, and then extended to present another tradeoff relation regarding arbitrary three‐qubit states. Notably, physical explanation is offered for how coherence migrates in three‐qubit systems from first‐order coherence of a given subsystem to quantum correlations between subsystems. The result shows that the derived tradeoff relations can reveal the complementarity between intrinsic concurrence and first‐order coherence, which provides reliable theoretical basis of transformation and flow for quantum resources.