Nonlinear improvement of measurement-device-independent quantum key distribution using multimode quantum memory

This paper proposes a quantum key distribution (QKD) scheme for measurement-device-independent QKD (MDI-QKD) utilizing quantum memory (QM), which is based on two distinct functions of QM: on-demand storage and multimode storage. We demonstrate a nonlinear increase in the secure key rate due to the utilization of QM. In the protocol incorporating on-demand storage, it is acknowledged that the secure key rate is scaled by $R=O(\sqrt{\eta_{ch}})$ as $\eta_{ch}$, while as an alternative approach, we reveal that the improvement is $O(m_s^2)$, with $m_s$ being the number of modes in frequency (spatial) multiplexing in the scheme incorporating multimode storage. We adopt an atomic frequency comb as a QM that incorporates the two functions and propose an architecture based on MDI-QKD to attain experimental feasibility. This scheme can be extended to quantum repeaters, and even for a single quantum-repeater node, there is a nonlinear enhancement and an experimental incentive to increase the number of modes.