  The assumption that detection and/or state-preparation devices used for
continuous-variable quantum key distribution (CV-QKD) are beyond influence of
potential eavesdroppers leads to a significant performance enhancement in terms
of achievable key rate and transmission distance. We provide a detailed and
comprehensible derivation of the Holevo bound in this so-called trusted-device
scenario. Modelling an entangling-cloner attack and using some basic algebraic
matrix transformations, we show that the computation of the Holevo bound can be
reduced to the solution of a quadratic equation. As an advantage of our
derivation, the mathematical complexity of our solution does not increase with
the number of trusted-noise sources. Finally, we provide a numerical evaluation
of our results, illustrating the counter-intuitive fact that an appropriate
amount of trusted receiver loss and noise can even be beneficial for the key
rate.
