Measurement of weak values for all powers of an observable

Weak values of an observable can be found using weak measurements with pre- and post selections for target states. For example, when weak values are small, the expectation value of the pointer position (momentum) shows a shift proportional to the real (imaginary) part of the weak value. In this paper, we introduce the foundations of a new method for obtaining weak values that need not the weakness of the measurement. Using this method, not only the weak values of an observable but also weak values of all powers of the observable can be determined. The key point in this method is that instead of conditional expectation values of the device position and momentum in the standard method we use a complete set of marginal distributions to reconstruct device quantum state.