## Enrico Rebufello

*INRIM, Politecnico di Torino*

Enrico Rebufello is a PhD student in Metrology at the Italian National Metrology Institute (INRiM) and the Politecnico of Turin. He received his Master’s Degree in Physics of Complex Systems from the University of Turin in 2016, with a thesis on protective measurements. His research focuses in quantum optics, experiments on foundations of quantum mechanics and measurements in quantum mechanics.

**Introduction**

In quantum mechanics, the expectation value of a physical observable is specified by the eigenvalues and the corresponding probabilities, and it is a statistical property of an ensemble of quantum systems. In contrast to this paradigm, we demonstrate a method for measuring the expectation value of a single particle with a single experiment. This is the first realization of quantum protective measurements (PMs).

**Methods**

We achieved this result with heralded single photons generated by parametric down-conversion.

Following the traditional prepare-and-measure scheme, the single photons are prepared in a linearly-polarized state and then made them interact with N=7 thin birefringent crystals, each slightly separating the horizontal and vertical polarizations, inducing a small decoherence in the quantum state.

At the end, the two polarizations are completely separated, and the initial pure state is turned into a decoherent mixture of horizontal and vertical polarization.

In our PM scheme, after each birefringent crystal a Zeno-effect-based “protection” of the initial state is implemented, with a polarizer oriented along the same polarization as the initial state restoring its coherence. The combined effect of weak interaction and protection causes a spatial shift of the photons proportional to the expectation value of their polarization, meaning that even one single photon can provide information about its polarization expectation value.

**Results**

Without protection, at the end of the process we have an almost completely decoherent mixture. On the contrary, PM protection mechanism preserves the initial state coherence (fidelities always above 99%).

Furthermore, with PMs each photon is detected in a position corresponding to the expectation value of its polarization, i.e., expectation values can be obtained with a single shot instead of accumulating statistics.

**Discussion**

Comparing PM with traditional projective measurement, we demonstrate that PMs can bring significant advantage in terms of uncertainty.

This means that PMs could find applications not only in foundational studies, but also in the quantum-enhanced measurements framework.

Fundamental science for quantum technologies , Quantum optics and non-classical light sources