Visualizing coherence, Bell-nonlocality and their interrelation for two-qubit X states in quantum steering ellipsoid formalism

Quantum steering ellipsoid has been regarded as a faithful representation of arbitrary two-qubit state and provides a visualized geometry for quantum resources. Herein, considering two-qubit X states, the generally form of quantum steering ellipsoid is derived. It shows the l(1) norm of coherence can be visually denoted by the x or y semiaxis length of the ellipsoid. By using ellipsoid with largest volume, we obtain the upper bounds of the l(1) norm and relative entropy of coherence for two-qubit X states. We also reveal that the dynamics of l(1) norm of coherence can be exhibited by the evolution of quantum steering ellipsoid under noisy channels. In addition, the expression of Bell-nonlocality for two-qubit X states is provided in the frame of quantum steering ellipsoids, and this expression is relevant to semiaxis lengths of ellipsoid. Based on this, we investigate relationship between the l(1) norm of coherence and Bell-nonlocality. Notably, Bell-nonlocality of two-qubit X states can be detected according to the l(1) norm of coherence. Finally, Bell-nonlocality and l(1) norm of coherence for two-qubit Heisenberg spin-1/2 XX model with inhomogeneous field are researched as a verification of our results.