Weak and semiweak values in non-ideal spin measurements: an exact treatment beyond the asymptotic regime

TL;DR

This paper provides an exact analysis of weak and semiweak spin measurements in quantum mechanics, extending beyond the asymptotic regime to reveal new eccentric values and meter behaviors that differ from traditional predictions.

Contribution

It introduces an exact, non-asymptotic treatment of weak measurements, uncovering semiweak values and distinct meter behaviors in non-ideal regimes.

Findings

Identification of semiweak eccentric values differing from weak values

Exact meter behavior can significantly differ from traditional weak measurement predictions

Application to distinguishing different realizations of the same density matrix

Abstract

We consider weak measurements (WM) of a spin observable in quantum mechanics beyond the usual asymptotic regime. This is done by obtaining the exact time-dependent wave functions of the measuring apparatus for general non-ideal measurements. Ideal strong measurements and the usual WM regime are obtained as the two extreme limiting cases of our exact treatment. We show that in the intermediate regime non-ideal measurements lead to "semiweak" eccentric values that differ from the usual weak values. We further show that even in the WM regime the exact treatment leads to a meter behavior that can be markedly distinct from the one predicted by the usual WM formalism. We give several illustrations and discuss an application to the distinction of different realizations of the same density matrix.