No real advantage of photon subtraction and displacement in continuous variable measurement device independent quantum key distribution

Abstract: We critically analyse the role of single photon subtraction (SPS) and displacement in improving the performance of continuous variable measurement device independent quantum key distribution (CV-MDI-QKD). We consider CV-MDI-QKD with resource states generated by SPS on a displaced two-mode squeezed vacuum state. Optimizing the secret key rate with state parameters reveals that implementing SPS yields no benefits in improving the loss tolerance of CV-MDI-QKD. Additionally, we find that displacement too is not useful in improving the performance of CV-MDI-QKD. While our result is in contradistinction with the widely held belief in the field regarding the utility of SPS and displacement in CV-MDI-QKD, it also calls for a re-examination of the role of non-Gaussian operations in increasing the efficiency of various quantum information processing protocols.