Enabling CV-MDI-QKD for weakly squeezed states using non-Gaussian operations

We propose a new non-Gaussian version of the continuous variables measurement device independent quantum key distribution (CV-MDI-QKD) protocol by utilizing a photon added-then-subtracted (PAS) state. We report that our single- and two-mode PAS-CV-MDI-QKD protocols outperform pure state CV-MDI-QKD protocol when considering weak squeezing and high noise, which is the practical regime. With such resources, CV-MDI-QKD is inaccessible when using a pure TMSV state, while PAS-CV-MDI-QKD can generate a useful key rate in this regime. We also compare PAS-CV-MDI-QKD with a two-mode photon replaced (2PR) state, which was not studied in low squeezing for MDI-QKD before.