**Quantum Optics INRIM**

**Measurement Paradigms in Quantum Mechanics**

**Measurement Paradigms in Quantum Mechanics**

Measurements represent a fundamental aspect in any field of physics. Their role is even more relevant in quantum mechanics, because they engrave directly on the theory foundational aspect. The meaning, capability and limits of quantum measurements are currently a hot-debated topic, representing a lively theoretical and experimental research field.

In our laboratories, we develop, implement and study novel quantum measurement paradigms, with the goal to overcome the usual limits of classical as well as quantum measurements, demonstrating unprecedented measurement capability allowing for several multidisciplinary applications.

Furthermore, we exploit these innovative measurement paradigms for fundamental research, investigating the very foundations of quantum mechanics. As an example, we realised many experimental works on weak-interaction-based measurements (a completely new approach with respect to traditional “strong” quantum measurements), e.g.: the measurement of non-commuting observables on the same quantum state, by exploiting sequential weak measurements; the first realisation of protective measurements, able to extract the average value of a quantity from a single particle; experimental tests on the link between weak values and foundational aspects, like contextuality and macroscopic realism. We also performed several experiments in the framework of quantum state estimation, a key factor for quantum technologies.

## Recent highlights

### Determining the quantum expectation value by measuring a single photon

F. Piacentini et al., Nature Physics volume 13, pages1191–1194 (2017)

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.

### Anomalous weak values via a single photon detection

E. Rebufello et al., Light: Science & Applications volume 10, Article number: 106 (2021)

Is it possible that a measurement of a spin component of a spin-1/2 particle yields the value 100? In 1988 Aharonov, Albert and Vaidman argued that upon pre- and postselection of particular spin states, weakening the coupling of a standard measurement procedure ensures this paradoxical result^{1}. This theoretical prediction, called *weak value*, was realised in numerous experiments, but its meaning remains very controversial, since its “anomalous” nature, i.e., the possibility to exceed the eigenvalue spectrum, as well as its “quantumness” are debated. We address these questions by presenting the first experiment measuring anomalous weak values with just a single click, without the need for statistical averaging. The measurement uncertainty is significantly smaller than the gap between the measured weak value and the nearest eigenvalue. Beyond clarifying the meaning of weak values, demonstrating their non-statistical, single-particle nature, this result represents a breakthrough in understanding the foundations of quantum measurement, showing unprecedented measurement capability for further applications of weak values to quantum photonics.

### Quantum Zeno and Anti-Zeno Probes of Noise Correlations in Photon Polarization

We experimentally demonstrate, for the first time, noise diagnostics by repeated quantum measurements, establishing the ability of a single photon subjected to random polarization noise to diagnose non-Markovian temporal correlations of such a noise process. Both the noise spectrum and temporal correlations are diagnosed by probing the photon with frequent (partially) selective polarization measurements. We show that noise with positive temporal correlations corresponds to our single photon undergoing a dynamical regime enabled by the quantum Zeno effect (QZE), whereas noise characterized by negative (anti) correlations corresponds to regimes associated with the anti-Zeno effect (AZE). This is the first step toward a novel noise spectroscopy based on QZE and AZE in single-photon state probing able to extract information on the noise while protecting the probe state, a conceptual paradigm shift with respect to traditional interferometric measurements.

## Most relevant pubblications

Salvatore Virzì et al., "Quantum Zeno and Anti-Zeno Probes of Noise Correlations in Photon Polarization", Phys. Rev. Lett. 129, 030401 (2022)

E. Rebufello et al. "Anomalous weak values via a single photon detection" Light: Science & Applications 10, 106 (2021)

E. Rebufello et al. "Protective Measurement - a new quantum measurement paradigm: detailed description of the first realisation", Applied Sciences 11(9), 4260 (2021)

S. Virzì et al. "Optimal estimation of entanglement and discord in two-qubit states" Scientific Reports 9 (1), 1-9 (2019)

F. Piacentini et al. "Investigating the effects of the interaction intensity in a weak measurement" Scientific reports 8 (1), 1-7 (2018)

F. Piacentini et al. "Determining the quantum expectation value by measuring a single photon" Nature Physics 13 (12), 1191-1194 (2017)

A. Avella et al. "Anomalous weak values and the violation of a multiple-measurement leggett-garg inequality" Physical Review A 96 (5), 052123 (2017).

F. Piacentini et al. "Measuring incompatible observables by exploiting sequential weak values" Physical review letters 117 (17), 170402 (2016).

F. Piacentini et al. "Experiment investigating the connection between weak values and contextuality" Physical Review Letters 116 (18), 180401 (2016).