Weak Values Beyond Post-selection

Weak values are usually encountered in weak measurements on pre- and post-selected systems. Here we consider experiments where a final post-selection is replaced with an initial projector measurement. We show how weak values may be observed both for strong and weak measurements of the projector. We also show that the real part of the weak value emerges uniquely as a generalized conditional expectation from a symmetry principle applied to strong measurements. [Editors note: for a video of the talk given by Prof. Johansen at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-26.]