Estimating parameters of quantum systems (e.g., parameters in their Hamiltonians) is important from both practical and fundamental aspects. In standard strategies, parameters are estimated from the data accumulated by many independent and identical experiments: every time one performs a measurement, the system needs to be reset in a specific initial state.
In this talk, I present a scheme in which we are not required to re-initialize the system after every measurement: we simply repeat measurements, and a parameter is estimated from a *single* sequence of measurement data. Our idea is to make use of a quantum mixing channel: a quantum channel (a CPTP map) is called mixing if its repeated actions on a quantum system drive it from an arbitrary initial state to a unique final state. This feature enables us to estimate a parameter irrespective of the initial state of the system, and provides us with *self-averaging* quantities on the basis of a central limit theorem, which allow us to estimate a parameter just by a *single run*. Moreover, in contrast to standard strategies, the correlations among measurement data are available for the estimation in the present scheme, with which we can enhance the precision of the estimation beyond standard strategies, when only weak (unsharp) measurement is available.
This work is in collaboration with Daniel Burgarth (Aberystwyth Univ., UK), Vittorio Giovannetti (Scuola Normale Superiore, Pisa), and Airi Kato (Univ. Tokyo).