Abstrac--Kramers-Kronig (KK) receiver, which is equivalent to heterodyne
detection with one single photodetector, provides an efficient method to
reconstruct the complex-valued optical field by means of intensity detection
given a minimum-phase signal. In this paper, quantum noise of the KK receiver
is derived analytically and compared with that of the balanced heterodyne
detection. We show that the quantum noise of the KK receiver keeps the radical
fluctuation of the measured signal the same as that of the balanced heterodyne
detection, while compressing the tangential noise to 1/3 times the radical one
using the information provided by the Hilbert transform. In consequence, the KK
receiver has 3/2 times the signal-to-noise ratio of balanced heterodyne
detection while presenting an asymmetric distribution of fluctuations, which is
also different from that of the latter. More interestingly, the projected
in-phase and quadrature field operators of the retrieved signal after down
conversion have a time dependent quantum noise distribution depending on the
time-varying phase. This property provides a feasible scheme for controlling
the fluctuation distribution according to the requirements of measurement
accuracy in the specific direction. Under the condition of strong carrier wave,
the fluctuations of the component requiring to be measured more accurately can
be compressed to 1 / 6, which is even lower than 1/4 by measuring a coherent
state. Finally, we prove the analytic conclusions by simulation results