Impact of imperfect homodyne detection on measurements of vacuum states shot noise

The secret key rate of a continuous variables quantum key distribution system (CV-QKD) depends highly on the loss and excess noise of the quantum channel. A proper modelling of the quantum channel is essential to detect and prevent an eavesdropping attack. In CV-QKD, homodyne detection is widely used to measure the quadratures of the modulated optical signal. Nevertheless, the homodyne detector (HD) can be a source of noise for the CV-QKD system. In this paper, a HD is modelled considering intrinsic imperfections. Moreover, an improved method is proposed to obtain mean, variance and auto-covariance functions for estimation of the HD performance, considering ideal and unbalanced HD operation modes with ideal and non-ideal local oscillator pulse intensity functions being compared. The imbalance of the HD leads to non-zero mean output and a quadratic relation of voltage variance. Despite that, the rebalance of the system was attained with the cost of lowering the system voltage output intensity.