Weak Value review

The paper is an accessible review of some of the interesting (and important) experiments that use the weak value in various ways. First, as a large interaction parameter it can amplify small signals above technical background noise: my group has been involved with this research, working with John Howell's group in the original interferometric amplification work, as well as our recent paper with Paul Kwiat's group.

Second, as a measurable complex value it enables novel techniques for quantum state tomography and geometric phase determination. Jeff S. Lundeen, Charles Bamber, et al., demonstrated a technique where one can "directly measure" the wavefunction. It is essentially a new kind of tomography technique using post-selection. We show how this can be used to find the polarization state of a photon in this new approach. Bob's group has also been involved in this work.

Third, as a conditioned average of generalized observable eigenvalues it provides a measurable window into nonclassical features of quantum mechanics. In my paper with Justin, we show in what sense the weak value is a conditioned average, effectively giving a definition. We apply this here to the polarization example, and review some of the applications of the conditioned averages of an operator.

In the past, the weak value has been discussed in a rather idiosyncratic way, and one of our goals in this review paper was to present the manifestations of the weak value in an accessible way. This was done by using a single physical system to present the physics in a new and unified way. We used a simple operational definition which captures all these features that I think will be helpful to the community:

Weak values characterise the relative correction to a detection probability due to a small intermediate perturbation that results in a modified detection probability.