Weak values and the quantum phase space

Abstract

We address the issue of how to properly treat, and in a more general setting, the concept of a weak value of a weak measurement in quantum mechanics. We show that for this purpose, one must take in account the effects of the measuring process on the entire phase space of the measuring system. By using coherent states, we go a step further than Jozsa in a recent paper, and we present an example where the result of the measurement is symmetrical in the position and momentum observables and seems to be much better suited for quantum optical implementation.