CV-MDI-QKD: One-mode Gaussian attacks are not enough

TL;DR

The paper demonstrates that security analysis of CV-MDI-QKD cannot rely solely on one-mode Gaussian attacks, as two-mode attacks can be more powerful and cannot be simulated by simpler models.

Contribution

It provides a simple argument showing the insufficiency of one-mode Gaussian attacks for CV-MDI-QKD security analysis, emphasizing the need to consider two-mode attacks.

Findings

Two-mode Gaussian attacks cannot be reduced to one-mode attacks.

Security analysis must include two-mode attack minimization.

One-mode Gaussian attacks are insufficient for comprehensive security proof.

Abstract

The security proof of continuous variable (CV) measurement device independent (MDI) quantum key distribution (QKD) cannot be reduced to the analysis of one-mode Gaussian attacks (in particular, independent entangling-cloner attacks). To stress this point, the present note provides a very simple (almost trivial) argument, showing that there are an infinite number of two-mode Gaussian attacks which cannot be reduced to or simulated by one-mode Gaussian attacks. This result further confirms that the security analysis of CV-MDI-QKD must involve a careful minimization over two-mode attacks as originally performed in [S. Pirandola et al., Nature Photon. 9, 397-402 (2015)].