Distribution Relationship of Quantum Battery Capacity

Abstract

The distribution relationship of quantum battery capacity is investigated. First, it is proved that for two-qubit $X$-states, the sum of the subsystem battery capacities does not exceed the total system's battery capacity, and the conditions are provided under which they are equal. Then define the difference between the total system's and subsystems' battery capacities as the residual battery capacity ($RBC$) and show that this can be divided into coherent and incoherent components. Furthermore, it is observed that this capacity monogamy relation for quantum batteries extends to general $n$-qubit $X$ states and any $n$-qubit $X$ state's battery capacity distribution can be optimized to achieve capacity gain through an appropriate global unitary evolution. Specifically, for general three-qubit $X$ states, stronger distributive relations are derived for battery capacity. Quantum batteries are believed to hold significant potential for outperforming classical counterparts in the future. These findings contribute to the development and enhancement of quantum battery theory.