Testing real quantum theory in an optical quantum network

TL;DR

This paper experimentally tests whether real quantum theory can explain quantum correlations in an optical network, providing evidence that complex numbers are essential in quantum mechanics.

Contribution

The authors adapt Bell inequality tests for photonic systems to experimentally disprove real quantum theory as a complete description of quantum phenomena.

Findings

Quantum correlations violate real quantum theory constraints by over 4.5 standard deviations.

Experimental demonstration in a three-party, two-source photonic network.

Disproves the sufficiency of real quantum theory for describing quantum correlations.

Abstract

Quantum theory is commonly formulated in complex Hilbert spaces. However, the question of whether complex numbers need to be given a fundamental role in the theory has been debated since its pioneering days. Recently it has been shown that tests in the spirit of a Bell inequality can reveal quantum predictions in entanglement swapping scenarios that cannot be modelled by the natural real-number analog of standard quantum theory. Here, we tailor such tests for implementation in state-of-the-art photonic systems. We experimentally demonstrate quantum correlations in a network of three parties and two independent EPR sources that violate the constraints of real quantum theory by over $4.5$ standard deviations, hence disproving real quantum theory as a universal physical theory.