Quantum theory based on real numbers can be experimentally falsified

Marc-Olivier Renou, David Trillo, Mirjam Weilenmann, Thinh P. Le, Armin Tavakoli, Nicolas Gisin, Antonio Acín and Miguel Navascués ()
Additional contact information
Marc-Olivier Renou: The Barcelona Institute of Science and Technology
David Trillo: Austrian Academy of Sciences
Mirjam Weilenmann: Austrian Academy of Sciences
Thinh P. Le: Austrian Academy of Sciences
Armin Tavakoli: Austrian Academy of Sciences
Nicolas Gisin: University of Geneva
Antonio Acín: The Barcelona Institute of Science and Technology
Miguel Navascués: Austrian Academy of Sciences

Nature, 2021, vol. 600, issue 7890, 625-629

Abstract: Abstract Although complex numbers are essential in mathematics, they are not needed to describe physical experiments, as those are expressed in terms of probabilities, hence real numbers. Physics, however, aims to explain, rather than describe, experiments through theories. Although 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 spaces1,2. 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 natural3. In fact, previous studies have shown that such a ‘real quantum theory’ can reproduce the outcomes of any multipartite experiment, as long as the parts share arbitrary real quantum states4. Here we investigate whether complex numbers are actually needed in the quantum formalism. We show this to be case by proving that real and complex Hilbert-space formulations of quantum theory make different predictions in network scenarios comprising independent states and measurements. This allows us to devise a Bell-like experiment, the successful realization of which would disprove real quantum theory, in the same way as standard Bell experiments disproved local physics.

Date: 2021
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://www.nature.com/articles/s41586-021-04160-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:nature:v:600:y:2021:i:7890:d:10.1038_s41586-021-04160-4

Ordering information: This journal article can be ordered from
https://www.nature.com/

DOI: 10.1038/s41586-021-04160-4

Access Statistics for this article

Nature is currently edited by Magdalena Skipper

More articles in Nature from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().