Protective measurement is a subtle kind of quantum measurement which enables to fully measure the wavefunction of a single particle, without changing its state [1-3].

In cases where the measured state is an energy eigenstate, this procedure can be performed by a slow enough (i.e. adiabatic) von Neumann measurement, where the conservation of energy acts like an effective protection. In the general case, an external protection in the form of Quantum Zeno Effect [4] is needed [1-3].

After a short review of this concept, we will follow the lines of [1] to analyze the case of post-selection. As we already shown in [5], when performing post-selection, deeper understanding of the quantum system becomes available. Indeed, post-selection does not change the protective measurement's results, but suggests redistributing them differently, thus enabling to effectively sketch two wavefunctions rather than one in the Schrӧdinger representation. In the Heisenberg representation, a full description of non-commuting operators emerges. As claimed in [5], choosing a specific final state amounts to outlining another (sometimes completely different) history for the same initial state. Further conclusions concerning quantum ergodicity and statistical physics are presented as well [1].

In addition, we will describe our collaboration with the Italian National Institute for the Research of Metrology (INRIM) where the above scheme will be experimentally demonstrated using an optical setup. We show that the photons' state can be effectively protected while undergoing arbitrary polarization measurements.

References:

1. 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.

2. Y. Aharonov and L. Vaidman, The Schrödinger Wave is Observable After All!, Quantum Control and Measurement, H. Ezawa and Y. Murayama (Eds.) (Elsevier Publ., Tokyo, 1993), hep-th/9305001.

3. Y. Aharonov, J. Anandan, L. Vaidman, The Meaning of Protective Measurements, Found. Phys. 26, (1996) 117-126 . hep-th/9408153.

4. E.C.G. Sudarshan, B. Misra, The Zeno's paradox in quantum theory, J. Math. Phys. 18 (1977) 756–763.

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

Note: This abstract might fit the quantum foundations session as well