Quantum theory based on real numbers can be experimentally falsified

TL;DR

This paper demonstrates that real-number based quantum theory can be experimentally distinguished from complex-number based quantum theory through specific network scenarios, challenging the necessity of complex numbers in quantum physics.

Contribution

It proves that real and complex quantum theories make different predictions in certain network experiments, enabling experimental falsification of real quantum theory.

Findings

Real and complex quantum theories differ in predictions for network scenarios.

A Bell-like experiment can disprove real quantum theory.

Complex numbers are essential in the quantum formalism.

Abstract

While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through theories. While most theories of physics are based on real numbers, quantum theory was the first to be formulated in terms of operators acting on complex Hilbert spaces. This has puzzled countless physicists, including the fathers of the theory, for whom a real version of quantum theory, in terms of real operators, seemed much more natural. In fact, previous works showed that such "real quantum theory" can reproduce the outcomes of any multipartite experiment, as long as the parts share arbitrary real quantum states. Thus, are complex numbers really needed in the quantum formalism? Here, we show this to be case by proving that real and complex quantum theory make different predictions in network scenarios comprising independent states and measurements. This allows us to devise a Bell-like experiment whose successful realization would disprove real quantum theory, in the same way as standard Bell experiments disproved local physics.