  Systematic errors are inevitable in most measurements performed in real life
because of imperfect measurement devices. Reducing systematic errors is crucial
to ensuring the accuracy and reliability of measurement results. To this end,
delicate error-compensation design is often necessary in addition to device
calibration to reduce the dependence of the systematic error on the
imperfection of the devices. The art of error-compensation design is well
appreciated in nuclear magnetic resonance system by using composite pulses. In
contrast, there are few works on reducing systematic errors in quantum optical
systems. Here we propose an error-compensation design to reduce the systematic
error in projective measurements on a polarization qubit. It can reduce the
systematic error to the second order of the phase errors of both the half-wave
plate (HWP) and the quarter-wave plate (QWP) as well as the angle error of the
HWP. This technique is then applied to experiments on quantum state tomography
on polarization qubits, leading to a 20-fold reduction in the systematic error.
Our study may find applications in high-precision tasks in polarization optics
and quantum optics.
