Demystifying weak measurements

TL;DR

This paper clarifies that weak measurements are fundamentally strong projective measurements on entangled systems, and their purported subtlety and ontological implications are misrepresented in the literature.

Contribution

It provides a clear explanation that weak measurements involve standard quantum mechanics and are not inherently 'weak' or non-disturbing, challenging common misconceptions.

Findings

Weak measurements involve strong projective measurements on entangled systems.

Observed statistics are fully predicted by standard quantum mechanics.

Post-selection is a standard quantum procedure, not unique to weak measurements.

Abstract

A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper attempts to clarify the fact that 'weak measurements' involve strong (projective) measurements on one (pointer) member of an entangled system. The only thing 'weak' about such measurements is that the correlation established via the entanglement does not correspond to eigenstates of the 'weakly measured observable' for the remaining component system(s) subject to the weak measurement. All observed statistics are straightforwardly and easily predicted by standard quantum mechanics. Specifically, it is noted that measurement of the pointer steers the remaining degree(s) of freedom into new states with new statistical properties-constituting a non-trivial (even if generally small) disturbance. In addition, standard quantum mechanics readily allows us to conditionalize on a final state if we choose, so the 'post-selection' that features prominently in time-symmetric formulations is also equipment from standard quantum theory. Assertions in the literature that weak measurements leave a system negligibly disturbed, and/or that standard quantum theory is cumbersome for computing the predicted measurement results, are therefore unsupportable, and ontological claims based on such assertions need to be critically reassessed.