The measurement errors defined in Ozawa’s inequality appear to be equivalent to classical errors in the special case of two-level systems, so they can be evaluated easily using only classical statistics. However, it is shown that the contribution of non-classical correlation between the measurement outcome and additional data obtained from the output can reduce the measurement errors based on the additional information regarding a complementary observable. For pure states, the error can then be ideally reduced to zero. We estimated the errors for an experimental quantum measurement of photon polarization and confirmed that the errors of estimates that include the output value of a complimentary polarization component are much smaller than errors of the measurement itself.