Optimization of state parameters in displacement assisted photon subtracted measurement-device-independent quantum key distribution

TL;DR

This paper investigates non-Gaussian photon subtracted states in CV-MDI-QKD, optimizing their parameters, but finds that these states underperform compared to traditional TMSV states, questioning the benefit of PS operations.

Contribution

It derives the Wigner characteristic function for photon subtracted resource states and evaluates their performance, revealing limitations of PS operations in this context.

Findings

Photon subtracted states underperform TMSV states in CV-MDI-QKD.

Optimization of state parameters identifies the most suitable non-Gaussian resources.

Displacement and PS operations are found to be undesirable for these states.

Abstract

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.