Continuous-variable measurement-device-independent quantum key distribution over fluctuated free space quantum channels

The fluctuations in transmittance caused by atmospheric turbulence will impact the free space continuous-variable measurement-device-independent quantum key distribution (CV MDI QKD). Recently, a study in Ghalaii and Pirandola (2023) has demonstrated that the CV MDI QKD protocol is capable of achieving composable security over hundreds of meters free-space channels without concerning fluctuations even in strong collective eavesdropping scenario. In this paper, we investigate the free-space CV MDI QKD by taking the transmittance fluctuations into account. We analyze the security of free-space CV MDI QKD with the methodology of ensemble average. Also, the secret key rates are evaluated by use of the post-selection strategy with respect to the fluctuated transmittance. It is concluded that the post-selection strategy can significantly improves the secret key rate, especially when dealing with the finite size effect. Additionally, the post-selection enables a higher secret key rate compared to solely using ensemble average without post-selection as well as fluctuation-free strategy in Ghalaii and Pirandola (2023).