  Quantum detector tomography is a fundamental technique for calibrating
quantum devices and performing quantum engineering tasks. In this paper, a
novel quantum detector tomography method is proposed. First, a series of
different probe states are used to generate measurement data. Then, using
constrained linear regression estimation, a stage-1 estimation of the detector
is obtained. Finally, the positive semidefinite requirement is added to
guarantee a physical stage-2 estimation. This Two-stage Estimation (TSE) method
has computational complexity $O(nd^2M)$, where $n$ is the number of
$d$-dimensional detector matrices and $M$ is the number of different probe
states. An error upper bound is established, and optimization on the coherent
probe states is investigated. We perform simulation and a quantum optical
experiment to testify the effectiveness of the TSE method.
