Trade-off relations and enhancement protocol of quantum battery capacities in multipartite systems

First, we investigate the trade-off relations of quantum battery capacities in two-qubit system. We find that the sum of subsystem battery capacity is governed by the total system capacity, with this trade-off relation persisting for a class of Hamiltonians, including Ising, XX, XXZ and XXX models. Then building on this relation, we define residual battery capacity for general quantum states and establish coherent/incoherent components of subsystem battery capacity. Furthermore, we introduce the protocol to guide the selection of appropriate incoherent unitary operations for enhancing subsystem battery capacity in specific scenarios, along with a sufficient condition for achieving subsystem capacity gain through unitary operation. Numerical examples validate the feasibility of the incoherent operation protocol. Additionally, for the three-qubit system, we also established a set of theories and results parallel to those for two-qubit case. Finally, we determine the minimum time required to enhance subsystem battery capacity via a single incoherent operation in our protocol. Our findings contribute to the development of quantum battery theory and quantum energy storage systems.

💡 Research Summary

**
The paper investigates fundamental limits and optimization strategies for quantum battery capacities in multipartite systems, focusing on two‑qubit and three‑qubit models. The authors adopt the recent definition of quantum battery capacity (C(\rho;H)=\sum_i \epsilon_i(\lambda_i-\lambda_{d-1-i})), where ({\lambda_i}) are the eigenvalues of the state (\rho) and ({\epsilon_i}) the energy levels of the Hamiltonian (H).

Trade‑off relation (Theorem 1).
Using the quantum marginal problem (QMP), they prove that for any two‑qubit state (\rho_{AB}) the sum of the capacities of the reduced states cannot exceed the capacity of the global state: \