Structural Features of Sequential Weak Measurements

TL;DR

This paper explores the structure and correlations of sequential weak measurements, revealing their connection to quantum tomography and uncovering new anomalies in post-selected scenarios, especially for spin-half systems.

Contribution

It provides a theoretical framework for understanding sequential weak measurements and identifies a novel divergence anomaly in post-selected cases.

Findings

Sequential WMs relate to Wigner function correlations.

Double WMs of polarization can diverge for certain states.

Sequential WMs without post-selection enable quantum tomography.

Abstract

We discuss the abstract structure of sequential weak measurement (WM) of general observables. In all orders, the sequential WM correlations without post-selection yield the corresponding correlations of the Wigner function, offering direct quantum tomography through the moments of the canonical variables. Spin-half sequential measurements are, on the contrary, constrained kinematically, they are equivalent with single WMs. In sequential WMs with post-selection, a new anomaly occurs, different from the weak value anomaly of single WMs. In particular, the spread of polarization $\hat\sigma$, as measured in double WMs of $\hat\sigma$, will diverge for certain orthogonal pre- and post-selected states.