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One description provides only probabilities for obtaining various eigenvalues of a quantum variable. The eigenvalues and the corresponding probabilities specify the expectation value of a physical observable, which is known to be a statistical property of an ensemble of quantum systems. In contrast to this paradigm, here we demonstrate a method for measuring the expectation value of a physical variable on a single particle, namely, the polarization of a single protected photon. This realization of quantum protective measurements could find applications in the foundations of quantum mechanics and quantum-enhanced measurements.

We present the first experimental test that distinguishes between an event-based corpuscular model (EBCM) [H. De Raedt et al.: J. Comput. Theor. Nanosci. 8(2011) 1052] of the interaction of photons with matter and quantum mechanics. The test looks at the interference that results as a single photon passes through a Mach--Zehnder interferometer [H. De Raedt et al.: J. Phys. Soc. Jpn. 74(2005) 16]. The experimental results, obtained with a low-noise single-photon source [G. Brida et al.: Opt. Express 19(2011) 1484], agree with the predictions of standard quantum mechanics with a reduced $\chi^{2}$ of 0.98 and falsify the EBCM with a reduced $\chi^{2}$ of greater than 20.