Estimating Pre- and Post-Selected Ensembles

TL;DR

This paper develops a theoretical framework for estimating quantum states in pre- and post-selected ensembles, revealing unique features like bidirectional information flow and the ability to exclude certain measurement outcomes, thus extending traditional state estimation.

Contribution

It introduces a comprehensive theory for quantum state estimation in pre- and post-selected ensembles, highlighting new physical features and establishing foundational principles.

Findings

Information flows from both past and future in these ensembles.

Certain measurement outcomes can be prevented due to post-selection.

A theorem relates future information flow to complex conjugate past information.

Abstract

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 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.