# Determining the Quantum Expectation Value by Measuring a Single Photon

## TL;DR

This paper introduces a novel method to measure the expectation value of a quantum observable, specifically photon polarization, on a single particle using quantum protective measurements, challenging traditional ensemble-based approaches.

## Contribution

It presents the first experimental realization of quantum protective measurements, enabling expectation values to be obtained from a single quantum system rather than an ensemble.

## Key findings

- Successful measurement of photon polarization expectation value on a single photon.
- First experimental demonstration of quantum protective measurement.
- Shows potential for single-particle quantum state characterization.

## Abstract

Quantum mechanics, one of the keystones of modern physics, 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. These and 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, we demonstrate a unique method allowing to measure the expectation value of a physical variable on a single particle, namely, the polarisation of a single protected photon. This is the first realisation of quantum protective measurements.