  Non-Gaussian operations have been studied intensively in recent years due to
their ability to increase the secret key rate for certain CV-QKD protocols.
However, most previous studies on such protocols are carried out in a
single-mode setting, even though in reality any quantum state contains
multi-mode components in frequency space. In this work we investigate the use
of non-Gaussian operations in a multi-mode CV-QKD system. Our main finding is
that, contrary to single-mode CV-QKD systems, in generic multi-mode CV-QKD
systems it is possible to use non-Gaussian operations to increase the optimized
secret key rate. More specifically, we find that at losses of order 30dB, which
represents a distance of order 160km and the effective maximum distance for
CV-QKD, the key rate for multi-mode non-Gaussian operations can be orders of
magnitude higher than single-mode operations. Our results are important for
real-world CV-QKD systems especially those dependent on quantum error
correction - a process that requires non-Gaussian effects.
