Back and forth nudging for quantum state reconstruction

A. Donovan (1) , Mazyar Mirrahimi (2) , Pierre Rouchon (3)

1 Department of Chemistry
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
3 CAS - Centre Automatique et Systèmes

We propose an estimation method allowing to identify the initial state of a quantum system based on the continuous weak measurement of a certain physical observable over a fixed interval of time. The algorithm is based on the back- and-forth nudging method consisting in iterative application of Luenberger observers for the time-forward and time-backward dynamics. A clever change of variables unveils the needed symmetry in the observer design leading to the decrease of a certain distance (in an appropriate metric) between the estimator and the main system, both in forward and backward directions.

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

A. Donovan, Mazyar Mirrahimi, Pierre Rouchon. Back and forth nudging for quantum state reconstruction. 4th International Symposium on Communications, Control and Signal Processing, Mar 2010, Limassol, Cyprus. pp.1-5, ⟨10.1109/ISCCSP.2010.5463439⟩. ⟨hal-00523603⟩