Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements

TL;DR

This paper extends Leggett-Garg inequalities to more complex experimental scenarios, demonstrating their violation using entangled photons and semi-weak measurements, revealing new links to weak values.

Contribution

It generalizes Leggett-Garg inequalities to include multi-particle correlations and ambiguous measurements, and experimentally demonstrates their violation with entangled photons.

Findings

Violations of two-particle Leggett-Garg inequalities observed

Semi-weak measurements enable simultaneous testing of multiple inequalities

Connection established between inequality violations and strange weak values

Abstract

We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multi-particle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semi-weak polarization measurement based on Fresnel reflection. We also point out a non- trivial connection between specific two-party Leggett-Garg inequality violations and convex sums of strange weak values.