Weak value beyond conditional expectation value of the pointer readings

TL;DR

This paper argues that weak values are intrinsic properties of pre- and post-selected quantum systems, affecting other systems as if in an eigenstate with the weak value, and explores their physical meaning beyond simple averages.

Contribution

It demonstrates that weak values are robust, physical properties of quantum systems, distinct from expectation values, and extends the concept to mixed states and practical examples.

Findings

Weak values influence other systems as if in an eigenstate with the weak value.

Weak values differ fundamentally from expectation values in their physical effects.

The concept is extended to systems in mixed states.

Abstract

It is argued that a weak value of an observable is a robust property of a single pre- and post-selected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affects other systems as if it were in an eigenstate with eigenvalue equal to the weak value. This differs significantly from the action of a system pre-selected only and possessing a numerically equal expectation value. The weak value has a physical meaning beyond a conditional average of a pointer in the weak measurement procedure. The difference between the weak value and the expectation value has been demonstrated on the example of photon polarization. In addition, the weak values for systems pre- and post-selected in mixed states are considered.