On the regularization and optimization in quantum detector tomography

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