Determination of weak values of quantum operators using only strong measurements

Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that, in principle, the real and imaginary parts of the weak value of any operator may be elucidated from expectation values of suitably defined density, flux, and Hermitian commutator operators. Expectation values are the outcomes of strong (projective) measurements, implying that weak values are general properties of operators in association with pre- and postselection and they need not be preferentially associated with weak measurements. They should be considered as an important measurable property which provides added information compared with the "standard" diagonal expectation value of an operator. As the first specific example we consider the determination of the real and imaginary parts of the weak value of the momentum operator employing projective time-of-flight experiments. Then the results are analyzed from the point of view of Bohmian mechanics. Finally, we consider recent neutron interferometry experiments used to determine the weak values of the neutron spin.