CV-MDI-QKD with coherent state: beyond one-mode Gaussian attacks

A general security proof of continuous variable (CV) measurement device independent (MDI) quantum key distribution (QKD) should not be automatically reduced to the analysis of one-mode Gaussian attacks (in particular, independent entangling-cloner attacks). To stress this point, the present work provides a very simple (almost trivial) argument, showing that there are an infinite number of two-mode Gaussian attacks that cannot be reduced to or simulated by one-mode Gaussian attacks. This result further confirms that the security analysis of CV-MDI-QKD must generally involve a careful minimization over two-mode attacks as originally performed in (Pirandola et al, 2015 Nature Photon. 9, 397–402; arXiv:1312.4104 (2013)).