  Von Neumann measurement framework describes a dynamic interaction between a
target system and a probe. In contrast, a quantum controlled measurement
framework uses a qubit probe to control the actions of different operators on
the target system, and convenient for establishing universal quantum
computation. In this work, we use a quantum controlled measurement framework
for measuring quantum states directly. We introduce two types of the quantum
controlled measurement framework and investigate the systematic error (the bias
between the true value and the estimated values) that caused by these types. We
numerically investigate the systematic errors, evaluate the confidence region,
and investigate the effect of experimental noise that arises from the imperfect
detection. Our analysis has important applications in direct quantum state
tomography.
