Anomalous values, Fisher information, and contextuality, in generalized quantum measurements

Post selection following weak measurements has long been investigated for its peculiar manifestation of quantum signatures. In particular, the post selected events can give rise to anomalous values lying outside the spectrum of the measured quantity, and may provide enhanced Fisher information. Furthermore, the Pusey inequality highlights that, for extremely weak measurements, non-contextual models cannot account for the outcome probabilities. It is then interesting to investigate whether these are linked in a unified framework. Here we discuss on the existence of a possible connection in the case of qubits. We show that when performing generic post selected measurements there exist no one-to-one mapping between them, an instance that leads to drawing more involved considerations.