  Quantum detector tomography (QDT) is a fundamental technique for calibrating
quantum devices and performing quantum engineering tasks. In this paper, we
utilize regularization to improve the QDT accuracy whenever the probe states
are informationally complete or informationally incomplete. In the
informationally complete scenario, without regularization, we optimize the
resource (probe state) distribution by converting it to a semidefinite
programming problem. Then in both the informationally complete and
informationally incomplete scenarios, we discuss different regularization forms
and prove the mean squared error scales as $ O(\frac{1}{N}) $ or tends to a
constant with $ N $ state copies under the static assumption. We also
characterize the ideal best regularization for the identifiable parameters,
accounting for both the informationally complete and informationally incomplete
scenarios. Numerical examples demonstrate the effectiveness of different
regularization forms and a quantum optical experiment test shows that a
suitable regularization form can reach a reduced mean squared error.
