# Determining the Quantum Expectation Value by Measuring a Single Photon (and other recent applications of weak measurements)

`2016-11-30 14:00:00``2016-11-30 15:00:00``Determining the Quantum Expectation Value by Measuring a Single Photon (and other recent applications of weak measurements)``Quantum mechanics exhibits several peculiar properties, differentiating it from classical mechanics. One of the most intriguing is that variables might not have definite values. A complete quantum description provides only probabilities for obtaining various eigenvalues of a quantum variable. The eigenvalues and corresponding probabilities specify the expectation value of a physical observable, but they are known to be statistical properties of large ensembles. In contrast to this paradigm, we demonstrate a unique method allowing to measure the expectation value of a physical variable on a single particle, namely, the polarization of a single protected photon. This is the first realization of quantum protective measurements [1,2], which are based on a combination of weak measurements and the quantum Zeno effect. Before discussing these issues, I will review the notion of weak measurements [3-5] and discuss their realization by presenting our previous experiment [6], where we measured two non-commuting observables, on one and the same photon, using sequential weak measurements. I will conclude by discussing a few applications of these methods, both in metrology and in the study of foundational questions. References [1] Y. Aharonov, L. Vaidman, Measurement of the Schrӧdinger wave of a single particle, Phys. Lett. A 178, 38 (1993). [2] Y. Aharonov, E. Cohen, Protective measurement, Post-selection and the Heisenberg representation, in Protective measurement and quantum reality: Towards a new understanding of quantum mechanics, Shan Gao (Ed.), Cambridge University Press (2014), arXiv: 1403.1084. [3] 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). [4] Y. Aharonov, E. Cohen, A.C. Elitzur, Foundations and applications of weak quantum measurements, Phys. Rev. A 89, 052105 (2014). [5] Y. Aharonov, E. Cohen, A.C. Elitzur, Can a future choice affect a past measurement's outcome?, Ann. Phys. 355, 258-268 (2015). [6] 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).``Nanotechnology, 9th floor seminar room``Department of Physics``physics.dept@mail.biu.ac.il``Asia/Jerusalem``public`Quantum mechanics exhibits several peculiar properties, differentiating it from classical mechanics. One of the most intriguing is that variables might not have definite values. A complete quantum description provides only probabilities for obtaining various eigenvalues of a quantum variable. The eigenvalues and corresponding probabilities specify the expectation value of a physical observable, but they are known to be statistical properties of large ensembles. In contrast to this paradigm, we demonstrate a unique method allowing to measure the expectation value of a physical variable on a single particle, namely, the polarization of a single protected photon. This is the first realization of quantum protective measurements [1,2], which are based on a combination of weak measurements and the quantum Zeno effect. Before discussing these issues, I will review the notion of weak measurements [3-5] and discuss their realization by presenting our previous experiment [6], where we measured two non-commuting observables, on one and the same photon, using sequential weak measurements. I will conclude by discussing a few applications of these methods, both in metrology and in the study of foundational questions.

**References**

[1] Y. Aharonov, L. Vaidman, Measurement of the Schrӧdinger wave of a single particle, Phys. Lett. A 178, 38 (1993).

[2] Y. Aharonov, E. Cohen, Protective measurement, Post-selection and the Heisenberg representation, in Protective measurement and quantum reality: Towards a new understanding of quantum mechanics, Shan Gao (Ed.), Cambridge University Press (2014), arXiv: 1403.1084.

[3] 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).

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

[5] Y. Aharonov, E. Cohen, A.C. Elitzur, Can a future choice affect a past measurement's outcome?, Ann. Phys. 355, 258-268 (2015).

[6] 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).

Last Updated Date : 23/11/2016