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.
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This work has received funding from the European Union’s Horizon 2020 and the EMPIR Participating States in the context of the project EMPIR-14IND05 ‘MIQC2’, and from the INRIM ‘Seed’ project ‘GeQuM’. E.C. was supported by ERC AdG NLST. L.V. acknowledges support of the Israel Science Foundation Grant No. 1311/14 and the German-Israeli Foundation for Scientific Research and Development Grant No. I-1275-303.14. We wish to thank Y. Aharonov, S. Popescu and M. G. A. Paris for helpful discussion.
The authors declare no competing financial interests.
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Piacentini, F., Avella, A., Rebufello, E. et al. Determining the quantum expectation value by measuring a single photon. Nature Phys 13, 1191–1194 (2017). https://doi.org/10.1038/nphys4223
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