Weak Measurements Beyond the Aharonov-Albert-Vaidman Formalism

TL;DR

This paper generalizes weak measurements beyond the traditional formalism, analyzing regimes with nearly orthogonal and exactly orthogonal pre- and post-selected states, revealing optimal amplification conditions and new quantities analogous to weak values.

Contribution

It provides a comprehensive extension of weak measurement theory, including cases with orthogonal pre- and post-selected states, and identifies optimal conditions for signal amplification.

Findings

Existence of a maximum signal amplification for fixed interaction strength.

Identification of quantities analogous to weak values in the orthogonal regime.

Analysis of weak measurements beyond the Aharonov-Albert-Vaidman formalism.

Abstract

We extend the idea of weak measurements to the general case, provide a complete treatment and obtain results for both the regime when the pre-selected and post-selected states (PPS) are almost orthogonal and the regime when they are exactly orthogonal. We surprisingly find that for a fixed interaction strength, there may exist a maximum signal amplification and a corresponding optimum overlap of PPS to achieve it. For weak measurements in the orthogonal regime, we find interesting quantities that play the same role that weak values play in the non-orthogonal regime.