  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.
