Relationship Between Entanglement and Coherence in Some Two-Qubit States

Quantum coherence and quantum entanglement are two of the most important quantum properties, while the relationship between them hasn't been revealed completely, even though revealing their relationship is conducive to the development of quantum theory. In this work, we investigate their relationship in two-qubit pure states and Bell diagonal states, and we propose a relationship between coherence and entanglement. That is the sum of concurrence, l(1) norm coherence of each subsystems and compensate factor equals to the intuitive l(1) norm of coherence of the quantum system. Furthermore, we also investigate the relationship between Bell nonlocality and coherence. Then we check the correctness of our theories in some typical open systems by assuming one of the qubits passes through the noisy environment. The relationship we proposed here may deepen our understanding about quantum world.