Gravitationally induced unified relation among duality, coherence, steering, and maximal average fidelity

Recently, numerous measures have been proposed for quantifying the quantumness of a given system, and the existence of intrinsic connections among quantum resource measures has been proven. Here, we study the unified relationship between duality, first-order coherence, three-setting linear steering inequality, and maximum average fidelity between two masses due to gravity. Under gravitational inducement, an equivalent relationship was identified between the first-order coherence and duality. The coherence of a system can be controlled by adjusting arm lengths and the distance between the arms of an interferometer. In most cases, the first-order coherence of a system cannot be maximised. Furthermore, a trade-off relationship between gravitationally induced duality and steering violations was derived. We can adjust the arm length and distance between the arms of the interferometer such that the steering violation reaches its maximum at phase π . The results show that the value of the steering violation is always greater than 1; that is, the state of the system is steerable. In addition, we explored the intrinsic relationship between duality and the maximal average fidelity due to gravity. In most cases, the maximum average fidelity of the system is greater than 2/3, indicating that the state is useful for quantum teleportation. These results are important for investigating the intrinsic relationships among various quantum resources within the framework of gravity.