Weak value measurements have been a real breakthrough in the quantum measurement framework. In particular, quantum measurements may take advantage by anomalous weak values, i.e. values out of the eigenvalues spectrum of the measured observable, both for implementing new measurement techniques and studying Quantum Mechanics foundations. In this report we show three experiments with single photons presenting anomalous weak values: the first one tests the incompatibility between quantum mechanics and noncontextual hidden variables theories, the second one is the first realization of a sequential weak value evaluation of two incompatible observables on the same photon, and the last one shows how sequential weak values can be used to test Leggett-Garg inequalities extended to multiple-measurements scenarios.

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Enrico Rebufello, Salvatore Virzì, Fabrizio Piacentini, Alessio Avella, Franco Zappa, Rudi Lussana, Federica Villa, Alberto Tosi, Marco Gramegna, Giorgio Brida, Eliahu Cohen, Marco Barbieri, Ivo Pietro Degiovanni, and Marco Genovese, "Quantum weak-interaction-based measurement: from sequential weak measurement to protective measurement," Proc. SPIE 10771, Quantum Communications and Quantum Imaging XVI, 107710X (Presented at SPIE Optical Engineering + Applications: August 20, 2018; Published: 19 September 2018); https://doi.org/10.1117/12.2319186.