Local-projective-measurement-enhanced quantum battery capacity

Quantum batteries have significant potential applications for future industry and daily life. The capacity is an important indicator for a battery. Methods to improve the capacity of quantum batteries are important. We consider quantum batteries given by bipartite quantum systems and study the enhancement of the battery capacity under local projective measurements on a subsystem of the quantum state. By using two-qubit Bell-diagonal states and $X$-type states as examples, we show that quantum battery capacity with respect to the whole system or a subsystem can be improved by local projective measurements. Our theoretical analysis will provide ideas for the experimental development of quantum batteries.

Figure 1

An initially shared bipartite quantum state ${\rho }_{AB}$ undergoes local projective measurements ${\left\{B_k\right\}}_{k=0}^{n-1}$ on subsystem $B$. States ${\rho }_{AB}^k$ are obtained with probability $P_k$. From the final state ${\rho }_{AB}^{\prime }$ and its reduced density matrix ${\rho }_A^{\prime }$, we study the changes in the battery capacities before and after the measurement.

Figure 2

The amount of change in the battery capacity of subsystem $A$ for ${\rho }_{AB}$ in Example 2, where $f=C({\rho }_A^{\prime },H_A)-C({\rho }_A,H_A)$ as a function of $x$ for ${\epsilon }^A=0.5$; it reflects the variable of battery capacity of subsystem $A$.

Figure 3

The amount of change in the battery capacity of the whole system for ${\rho }_{AB}$ in Example 2. Here, $F=C({\rho }_{AB}^{\prime },H_{AB})-C({\rho }_{AB},H_{AB})$ as a function of $x$ for ${\epsilon }^A=0.5, {\epsilon }^B=0.3, {\mu }_1=0.9$, and ${\mu }_0=0.1$, where ${\mu }_1$ and ${\mu }_2$ correspond to the probabilities of choosing different measurement operators.