Hardy's paradox and violation of a state-independent Bell inequality in time

TL;DR

This paper demonstrates that Hardy's paradox and a state-independent Bell inequality violation can be observed in the time domain using a photonic entangling gate, highlighting fundamental quantum nonlocality in temporal correlations.

Contribution

It experimentally extends Hardy's paradox and Bell inequality violations to the time domain with a photonic setup, showing state-independent violations including for mixed states.

Findings

Hardy's paradox is stronger in the time domain.

A temporal Bell inequality is violated independently of the quantum state.

Violations are observed even with fully mixed states.

Abstract

Tests such as Bell's inequality and Hardy's paradox show that joint probabilities and correlations between distant particles in quantum mechanics are inconsistent with local realistic theories. Here we experimentally demonstrate these concepts in the time domain, using a photonic entangling gate to perform nondestructive measurements on a single photon at different times. We show that Hardy's paradox is much stronger in time and demonstrate the violation of a temporal Bell inequality independent of the quantum state, including for fully mixed states.