Weak measurement of the Dirac distribution

Abstract: Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. strong') measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of the product of the two observables, which, as a non-Hermitian operator, is normally unobservable. This generalized method provides mixed states an operational definition related to the operator representation proposed by Dirac. Uniquely, it can be performedin situ', determing the quantum state without destroying it.