  Non-Gaussian operations, in particular, photon subtraction (PS), have been
shown to enhance the performance of various quantum information processing
tasks including continuous variable measurement device independent quantum key
distribution (CV-MDI-QKD). This work investigates the role of non-Gaussian
resource states, namely, the photon subtracted two-mode squeezed coherent
(PSTMSC) (which include photon subtracted two-mode squeezed vacuum (PSTMSV) as
a special case) states in CV-MDI-QKD. To this end, we derive the Wigner
characteristic function for the resource states, from which the covariance
matrix and, finally, the secret key rate expressions are extracted. The
optimization of the state parameters is undertaken to find the most suitable
resource states in this family of states. There have been previous studies on
the PSTMSV and PSTMSC states in CV-MDI-QKD that make use of PS operation. We
evaluate such proposals and find to our surprise that both PSTMSC and PSTMSV
resource states underperform as compared to the TMSV state rendering PS
operation and displacement undesirable.
