Conditional average in a quantum system with postselection

Abstract

A conditional average of an observable is considered for a quantum system, where measurement on a system is performed between an initial preparation and a postselection. It is shown that when the effect of measurement performed on a system can be described only in terms of eigenprojectors of a measured observable, the conditional average is represented by a mixture of the strong and weak values of the observable. Furthermore, a measurement process is constructed which provides the conditional average from measurement outcomes of pointer observables of an apparatus. In particular, when a qubit system is considered, the measurement apparatus consists of a lossless beam splitter, a single-qubit unitary gate and two controlled NOT gates.