Manifestation of pointer state correlations in complex weak values of quantum observables

TL;DR

This paper investigates how correlations among pointer degrees of freedom influence the measurement of complex weak values in quantum systems, extending previous models to include multidimensional pointer states and sequential weak interactions.

Contribution

It introduces a comprehensive framework accounting for pointer state correlations in weak measurements, revealing their impact on the relation between weak values and measurement shifts.

Findings

Pointer correlations affect the imaginary parts of weak values.

Sequential weak interactions are influenced by pointer state correlations.

Extended model applies to multidimensional pointer states.

Abstract

In the weak measurement (WM) scenario involving weak interaction and postselection by projective measurement, the empirical significance of weak values is manifested in terms of shifts in the measurement pointer's mean position and mean momentum. In this context, a general quantitative treatment is presented in this paper by taking into account the hitherto unexplored effect of correlations among the pointer degrees of freedom which pertain to an arbitrary multidimensional preselected pointer state. This leads to an extension of the earlier results, showing that, for complex weak values, the correlations among different pointer degrees of freedom can crucially affect the way the imaginary parts of the weak values are related to the observed shifts of the mean pointer position and momentum. The particular relevance of this analysis is discussed in the case of sequential weak interactions, followed by a postselection (called sequential WM) which, in the special case, reduces to the usual WM scheme involving a single weak interaction and postseletion, modified by the effect of pointer state correlations.