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

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)].