Analyzing quantum foundations and applications with single photon experiments
Quantum optics experiments employing a single photon source, as well as a single photon detector, allow us to probe the foundations of quantum theory. In the last few years I have designed a line of experiments based on weak measurements  for this purpose. Two of them have already been performed:
- Measuring incompatible observables by exploiting sequential weak values  – We measured for the first time the polarization of single photons in two incompatible bases. By performing a sequence of two weak measurements over a large ensemble of single photons, we were thus able to infer the information regarding two noncommutative operators, practically measured on the same state.
- Determining the quantum expectation value by measuring a single photon  – Here we did not use an ensemble of photons, but rather employed the quantum Zeno effect for inferring the polarization expectation value using a genuine single photon. This was the first demonstration of protective measurement , similar in spirit to our proposal in . The protection mechanism allows to defy the statistical character of the expectation value, which up to now was always evaluated using a large ensemble of similarly prepared particles.
I will discuss some consequences of these experiments, both theoretical (e.g. the meaning of the wavefunction) and practical (e.g. state and process tomography).
If time allows me, I will outline some of our upcoming experiments, such as those concerned with the study of entanglement and nonlocality [6,7].
 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).
 F. Piacentini, A. Avella, M.P. Levi, M. Gramegna, G. Brida, I.P. Degiovanni, E. Cohen, R. Lussana, F. Villa, A. Tosi, F. Zappa, M. Genovese, Measuring incompatible observables by exploiting sequential weak values, Phys. Rev. Lett. 117, 170402 (2016).
 F. Piacentini, A. Avella, E. Rebufello, R. Lussana, F. Villa, A. Tosi, M. Gramegna, G. Brida, E. Cohen, L. Vaidman, I.P. Degiovanni, M. Genovese, Determining the quantum expectation value by measuring a single Photon, forthcoming in Nat. Phys., doi:10.1038/nphys4223 (2017).
 Y. Aharonov, L. Vaidman, Measurement of the Schrödinger wave of a single particle, Phys. Lett. A 178, 38–42 (1993).
 Y. Aharonov, E. Cohen, A.C. Elitzur, Foundations and applications of weak quantum measurements, Phys. Rev. A 89, 052105 (2014).
 Y. Aharonov, E. Cohen, A.C. Elitzur, Can a future choice affect a past measurement’s outcome?, Ann. Phys. 355, 258-268 (2015).  A. Brodutch, E. Cohen, Nonlocal Measurements via Quantum Erasure, Phys. Rev. Lett. 116, 070404 (2016).