Structural Features of Sequential Weak Measurements

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.

4pp, small corrections

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