Practical security of continuous-variable quantum key distribution under finite-dimensional effect of multi-dimensional reconciliation

The well-known multi-dimensional reconciliation is an effective method used in the continuous-variable quantum key distribution in the long-distance and the low signal-to-noise-ratio scenarios. The virtual channel employed to exchange data is generally established by using a finite-dimensional rotation in the reconciliation procedure. In this paper, we found that the finite dimension of the multi-dimensional reconciliation inevitably leads to the mismatch of the signal-to-noise-ratio between the quantum channel and the virtual channel, which may be called the finite-dimension effect. Such an effect results in an overestimation on the secret key rate, and subsequently induces vital practical security loopholes.