2021/01/26 by Marc-Olivier Renou, David Trillo, Mirjam Weilenmann +8 · 2 voices · 219 citations
Computer Science · Mathematics · Medicine · Physics and Astronomy · #Biofield Effects and Biophysics #Computer science #Discrete mathematics #Hilbert space #Mathematics #Multipartite #Open quantum system #POVM #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum information #Quantum mechanics #Quantum operation #Real number #Realization (probability) #Theoretical physics #quant-ph
paper · pdf · doi:10.1038/s41586-021-04160-4
published in Nature 600(7890), 625-629 (Nature Portfolio) · 21 pages. Some typos corrected in the analytic proof, new discussion about the use of tensor products to model space-like separation in quantum field theory, short introduction to non-local real quantum models reproducing the predictions of quantum theory, compendium of theoretical arguments against real quantum theory, real quantum simulation of joint measurements of independent preparations
arxiv published 2021/01/26 · openalex publication_date 2021/12/15 · arxiv created 2021/12/27 · arxiv updated 2021/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 spaces 1,2 . 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 natural 3 . 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 states 4 . 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.