Re-examination of the role of displacement and photon catalysis operation in continuous variable measurement device-independent quantum key distribution

TL;DR

This paper re-examines the impact of displacement and photon catalysis operations on continuous variable measurement device-independent quantum key distribution, finding limited benefits from these techniques for enhancing transmission distance.

Contribution

It derives the Wigner characteristic function for $m$-photon catalyzed states and evaluates their effectiveness in CV-MDI-QKD, revealing minimal improvements from photon catalysis and displacement.

Findings

Zero-photon catalyzed state is Gaussian and less effective than vacuum state.

Photon catalysis offers only marginal benefits for transmission distance.

Displacement does not improve CV-MDI-QKD performance.

Abstract

We investigate the benefits of using $m$-photon catalysed two-mode squeezed coherent ($m$-PCTMSC) state in continuous variable measurement device-independent quantum key distribution (CV-MDI-QKD). To that end, we derive the Wigner characteristic function of the $m$-PCTMSC state and show that the 0-PCTMSC state is a Gaussian state and is an inferior choice as compared to the zero photon catalyzed two-mode squeezed vacuum state for CV-MDI-QKD. We carry out the optimization of the secret key rate with respect to all state parameters, namely variance, transmissivity, and displacement. Contrary to many recent proposals, the results show that zero- and single-photon catalysis operation provides only a marginal benefit in improving the maximum transmission distance. Secondly, we find that displacement offers no benefit in improving CV-MDI-QKD.