We are grateful to the many people and organizations who contributed to this project, starting with the Bellsters (details at http://thebigbelltest.org). We thank the Departament d’Ensenyament de la Generalitat de Catalunya, Ministerio de Educación, Cultura y Deporte of Spain, CosmoCaixa, Fundación Bancaria “la Caixa”, INTEF, Optical Society of America, European Centers for Outreach in Photonics (ECOP), Muncyt-Museo de Ciencia y Tecnología de Madrid, Investigación y Ciéncia, Big Van, Crea Ciència, Tencent news, Micius Salon, Politecnico di Milano, University of Waterloo–Institute for Quantum Computing, Universidad Autónoma de Barcelona, Universidad Complutense de Madrid, Università degli Studi di Milano, Toptica, EPS Young Minds, Real Sociedad Española de Física, Ajuntament de Barcelona, Ajuntament de Castelldefels, Università degli studi di Padova, Università degli studi del l’Insubria, CNRIFN Istituto di Fotonica e Nanotecnologia, Istituto d’Istruzione Superiore Carlo Livi, Webbile, and Kaitos Games. We are especially thankful for the recruitment efforts of the outreach departments at our institutions. We acknowledge financial support from CONICET; ANPCyT (Argentina), Australian Research Council Centre for Quantum Computation and Communication Technology (CE110001027, CE170100012); Australian Research Council and the University of Queensland (UQ) Centre for Engineered Quantum Systems (CE110001013, CE170100009). A.G.W. acknowledges the University of Queensland Vice-Chancellor’s Research and Teaching Fellowship (Australia); Austrian Academy of Sciences (OEAW), the Austrian Science Fund (FWF) (SFB F40 (FoQuS); CoQuS No. W1210-N16), the Austrian Federal Ministry of Education, Science and Research (BMBWF) and the University of Vienna (project QUESS) (Austria), MEC; MCTIC (Brazil), Barcelona City Hall; Generalitat de Catalunya (SGR 874 and 2014-SGR-1295; CERCA programme) (Catalonia), PIA CONICYT (grants PFB0824 and PAI79160083); FONDECYT (grants 1140635, 1150101, 1160400, 3170596 and 11150325; Becas Chile); the Millennium Institute for Research in Optics (MIRO); Becas CONICYT (Chile), the National Fundamental Research Program (grant 2013CB336800); the National Natural Science Foundation of China (grants 91121022, 61401441 and 61401443); the Chinese Academy of Science (Strategic Priority Research Program (B) XDB04010200); the 1000 Youth Fellowship programme; the National Natural Science Foundation of China (grant 11674193); the Science and Technology Commission of Shanghai Municipality (grant 16JC1400402) (China); ERC (grant agreements AQUMET 280169, 3DQUEST 307783, OSYRIS 339106, ERIDIAN 713682, QITBOX, QUOLAPS, QuLIMA and SuperQuNet 339871); ESA (contract number 4000112591/14/NL/US); FEDER; H2020 (QUIC 641122) and the Marie Skłodowska-Curie programme (grant agreement 748549) (European Commission); German Federal Ministry of Education and Research (projects QuOReP and Q.com-Q) (Germany); CONACyT graduate fellowship programme (Mexico), MINECO (FIS2014-60843-P, FIS2014-62181-EXP, SEV-2015-0522, FIS2015-68039-P, FIS2015-69535-R and FIS2016-79508-P; Ramon y Cajal fellowship programme; TEC2016-75080-R); the ICFOnest + international postdoctoral fellowship programme (Spain); the Knut and Alice Wallenberg Foundation (project ‘Photonic Quantum Information’) (Sweden); NIST (USA), AXA Chair in Quantum Information Science; FQXi Fund; Fundació Privada CELLEX; Fundació Privada MIR-PUIG; the CELLEX-ICFO-MPQ programme; Fundació Catalunya-La Pedrera; and the International PhD-fellowship programme ‘la Caixa’-Severo Ochoa.

Reviewer information

Nature thanks S. Maniscalco (with F. Cosco, S. Hamedani Raja, H. Lyyra, J. Nokkala, B. Sokolov, N. Talarico and J. Teittinen), J. Sherson and the other anonymous reviewer(s) for their contribution to the peer review of this work.