Estimating Pre- and Post-Selected Ensembles

Serge Massar, Sandu Popescu

In analogy with the usual state estimation problem, we introduce the problem of state estimation for a pre- and post-selected ensemble. The problem has fundamental physical significance since, as argued by Y. Aharonov and collaborators, pre- and post-selected ensembles are the most basic quantum ensembles. Two new features are shown to appear: 1) information is flowing to the measuring device both from the past and from the future; 2)because of the post-selection, certain measurement outcomes can be forced never to occur. Due to these features, state estimation in such ensembles is dramatically different from the case of ordinary, pre-selected only ensembles. Here we develop a general theoretical framework for studying this problem, and illustrate it through several examples. We also prove a general theorem showing that information flowing from the future is related to the complex conjugate information flowing from the past. We emphasize that {\it all} state estimation problems can be extended to the pre- and post-selected situation. The present work thus lays the foundations of a much more general theory of quantum state estimation.

Référence journal
Phys. Rev. Lett. 98, 010401 (2007)

Lien journal

Lien arxiv

Fichier pdf