Order Symmetry of Weak Measurements

TL;DR

This paper reveals a symmetry in weak measurements related to the order of measurement, connecting quantum weak values with classical mechanics, and proposes new experimental approaches.

Contribution

It generalizes the concept of weak measurements to include order symmetry and links quantum weak values to classical correlations.

Findings

Weak values are proportional to pointer correlations in successive measurements.

Order symmetry conditions are identical to those in classical mechanics.

The imaginary part of weak values has a classical mechanics counterpart.

Abstract

Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement. We show that this generalized concept of weak measurements displays a symmetry under reversal of measurement order. We show that the conditions for order symmetry are the same as in classical mechanics. We also find that the imaginary part of the weak value has a counterpart in classical mechanics. This scheme suggests new experimental possibilities.