Quantum theory is inherently statistical. This entails repetition of experiments over a number of identically prepared quantum objects, if one wants to know the "true state" or the "true value" of the parameter that specifies the quantum state. In applications, one needs to design the estimation procedure in such a way that the estimated value of the parameter should be close to the true value (consistency), and that the uncertainty of the estimated value should be as small as possible (efficiency). To realize these requirements, an adaptive quantum estimation (AQE) was proposed, and recently was proved to have the strong consistency and asymptotic efficiency.
In the presentation, we will report the first experimental demonstration of AQE. The angle of a half wave plate that initializes the linear polarization of input photons is estimated using AQE. The statistical analysis of these results verifies the strong consistency and asymptotic efficiency of AQE. It is expected that AQE will provide a useful methodology in the broad area of quantum information processing, communication, and metrology.