One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators due to quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak measurements [1-3] have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both theoretical and applicative points of view. I will describe how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment [4]. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them. I will then briefly outline our more recent experiment [5], partially based on the above scheme, for measuring the polarization expectation value of a single photon without any statistics.

References:

[1] Y. Aharonov, D.Z. Albert, L. Vaidman, How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100, Phys. Rev. Lett. 60, 1351 (1988).

[2] Y. Aharonov, E. Cohen, A.C. Elitzur, Foundations and applications of weak quantum measurements, Phys. Rev. A 89, 052105 (2014).

[3] A. Brodutch, E. Cohen, Weak measurements via quantum erasure, Phys. Rev. Lett. 116, 070404 (2016).

[4] F. Piacentini, M.P. Levi, A. Avella, E. Cohen, R. Lussana, F. Villa, A. Tosi, F. Zappa, M. Gramegna, G. Brida, I.P. Degiovanni, M. Genovese, Measuring incompatible observables of a single photon, Phys. Rev. Lett. 117, 170402 (2016).  

[5] F. Piacentini, A. Avella, R. Lussana, F. Villa, A. Tosi, F. Zappa, M. Gramegna, G. Brida, E. Cohen, L. Vaidman, I.P. Degiovanni, M. Genovese, Determining the quantum expectation value by measuring a single photon, forthcoming.