  Continuous Variable (CV) quantum key distribution (QKD) is a promising
candidate for practical implementations due to its compatibility with the
existing communication technology. A trusted device scenario assuming that an
adversary has no access to imperfections such as electronic noises in the
detector is expected to provide significant improvement in the key rate, but
such an endeavor so far was made separately for specific protocols and for
specific proof techniques. Here, we develop a simple and general treatment that
can incorporate the effects of Gaussian trusted noises for any protocol that
uses homodyne/heterodyne measurements. In our method, a rescaling of the
outcome of a noisy homodyne/heterodyne detector renders it equivalent to the
outcome of a noiseless detector with a tiny additional loss, thanks to a
noise-loss equivalence well-known in quantum optics. Since this method is
independent of protocols and security proofs, it is applicable to
Gaussian-modulation and discrete-modulation protocols, to the finite-size
regime, and to any proof techniques developed so far and yet to be discovered
as well.
