Quantum state estimation with informationally overcomplete measurements

Understand

We study informationally overcomplete measurements for quantum state estimation so as to clarify their tomographic significance as compared with minimal informationally complete measurements.

• We show that informationally overcomplete measurements can improve the tomographic efficiency significantly over minimal measurements when the states of interest have high purities.
• Nevertheless, the efficiency is still too limited to be satisfactory with respect to figures of merit based on monotone Riemannian metrics, such as the Bures metric and quantum Chernoff metric.
• In this way, we also pinpoint the limitation of nonadaptive measurements and motivate the study of more sophisticated measurement schemes.