Proof-of-Principle Direct Measurement of Particle Statistical Phase

The symmetrization postulate in quantum mechanics is formally reflected in the appearance of an exchange phase governing the symmetry of identical-particle global states under particle swapping. Many indirect measurements of this fundamental phase have been reported thus far, but a direct observation has been achieved only recently for photons. Here, we propose a general scheme capable of directly measur-ing the exchange phase of any type of particle (bosons, fermions, or anyons), exploiting the operational framework of spatially localized operations and classical communication. We experimentally implement it on an all-optical platform, providing a proof of principle for different simulated exchange phases. As a by-product, we supply a direct measurement of the real bosonic exchange phase of photons. Additionally, we analyze the performance of the proposed scheme when mixtures of particles of different nature are injected. Our results confirm the symmetrization tenet and provide a tool to explore it in various scenarios. Finally, we show that the proposed setup is suited to generating indistinguishability-driven NOON states useful for quantum-enhanced phase estimation.

Automated summary

This study proposes a general scheme for directly measuring the exchange phase of any type of particle. Experimental verification on an all-optical platform confirms the symmetrization tenet and provides a tool for exploring symmetrization in various scenarios.