{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T11:15:28Z","timestamp":1774523728647,"version":"3.50.1"},"reference-count":54,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T00:00:00Z","timestamp":1622764800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"crossref","award":["RGF\\EA\\180093"],"award-info":[{"award-number":["RGF\\EA\\180093"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"crossref","award":["URF\\R\\201011"],"award-info":[{"award-number":["URF\\R\\201011"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000271","name":"Science and Technology Facilities Council","doi-asserted-by":"crossref","award":["ST\/P000754\/1"],"award-info":[{"award-number":["ST\/P000754\/1"]}],"id":[{"id":"10.13039\/501100000271","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We study the implications of the anyon fusion equation <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>a<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:mi>b<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>c<\/mml:mi><\/mml:math> on global properties of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>2<\/mml:mn><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>D topological quantum field theories (TQFTs). Here <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>a<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>b<\/mml:mi><\/mml:math> are anyons that fuse together to give a unique anyon, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>c<\/mml:mi><\/mml:math>. As is well known, when at least one of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>a<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>b<\/mml:mi><\/mml:math> is abelian, such equations describe aspects of the one-form symmetry of the theory. When <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>a<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>b<\/mml:mi><\/mml:math> are non-abelian, the most obvious way such fusions arise is when a TQFT can be resolved into a product of TQFTs with trivial mutual braiding, and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>a<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>b<\/mml:mi><\/mml:math> lie in separate factors. More generally, we argue that the appearance of such fusions for non-abelian <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>a<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>b<\/mml:mi><\/mml:math> can also be an indication of zero-form symmetries in a TQFT, of what we term \"quasi-zero-form symmetries\" (as in the case of discrete gauge theories based on the largest Mathieu group, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>M<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mn>24<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>), or of the existence of non-modular fusion subcategories. We study these ideas in a variety of TQFT settings from (twisted and untwisted) discrete gauge theories to Chern-Simons theories based on continuous gauge groups and related cosets. Along the way, we prove various useful theorems.<\/jats:p>","DOI":"10.22331\/q-2021-06-04-468","type":"journal-article","created":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T12:57:28Z","timestamp":1622811448000},"page":"468","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>a<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:mi>b<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>c<\/mml:mi><\/mml:math> in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>2<\/mml:mn><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>D TQFT"],"prefix":"10.22331","volume":"5","author":[{"given":"Matthew","family":"Buican","sequence":"first","affiliation":[{"name":"CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linfeng","family":"Li","sequence":"additional","affiliation":[{"name":"CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rajath","family":"Radhakrishnan","sequence":"additional","affiliation":[{"name":"CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2021,6,4]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Gregory W. Moore and N. Read. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B, 360: 362\u2013396. 10.1016\/0550-3213(91)90407-O.","DOI":"10.1016\/0550-3213(91)90407-O"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Edward Witten. Quantum Field Theory and the Jones Polynomial. Commun. Math. Phys., 121: 351\u2013399, 1989. 10.1007\/BF01217730. [233(1988)].","DOI":"10.1007\/BF01217730"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Zhenghan Wang. Topological quantum computation. Number 112. American Mathematical Soc., 2010. 10.1090\/cbms\/112.","DOI":"10.1090\/cbms\/112"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Gregory W. Moore and Nathan Seiberg. LECTURES ON RCFT. In 1989 Banff NATO ASI: Physics, Geometry and Topology Banff, Canada, August 14-25, 1989, pages 1\u2013129, 1989. 10.1007\/978-1-4615-3802-8_8. [,1(1989)].","DOI":"10.1007\/978-1-4615-3802-8_8"},{"key":"4","doi-asserted-by":"publisher","unstructured":"Bojko Bakalov and Alexander A Kirillov. Lectures on tensor categories and modular functors, volume 21. American Mathematical Soc., 2001. 10.1090\/ulect\/021.","DOI":"10.1090\/ulect\/021"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Alexei Kitaev. Anyons in an exactly solved model and beyond. Annals of Physics, 321 (1): 2\u2013111, 2006. 10.1016\/j.aop.2005.10.005.","DOI":"10.1016\/j.aop.2005.10.005"},{"key":"6","doi-asserted-by":"publisher","unstructured":"Eric Rowell, Richard Stong, and Zhenghan Wang. On classification of modular tensor categories. Communications in Mathematical Physics, 292 (2): 343\u2013389, 2009. 10.1007\/s00220-009-0908-z.","DOI":"10.1007\/s00220-009-0908-z"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Paul Bruillard, Julia Plavnik, and Eric Rowell. Modular categories of dimension $p^3m$ with $m$ square-free. Proceedings of the American Mathematical Society, 147 (1): 21\u201334, 2019. doi.org\/10.1090\/proc\/13776.","DOI":"10.1090\/proc\/13776"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Gil Young Cho, Dongmin Gang, and Hee-Cheol Kim. M-theoretic Genesis of Topological Phases. JHEP, 11: 115, 2020. 10.1007\/JHEP11(2020)115.","DOI":"10.1007\/JHEP11(2020)115"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Michael M\u00fcger. On the structure of modular categories. Proceedings of the London Mathematical Society, 87 (2): 291\u2013308, 2003. 10.1112\/S0024611503014187.","DOI":"10.1112\/S0024611503014187"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Davide Gaiotto, Anton Kapustin, Nathan Seiberg, and Brian Willett. Generalized Global Symmetries. JHEP, 02: 172, 2015. 10.1007\/JHEP02(2015)172.","DOI":"10.1007\/JHEP02(2015)172"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Po-Shen Hsin, Ho Tat Lam, and Nathan Seiberg. Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d. 2018. 10.21468\/SciPostPhys.6.3.039.","DOI":"10.21468\/SciPostPhys.6.3.039"},{"key":"12","doi-asserted-by":"publisher","unstructured":"FA Bais and JK Slingerland. Condensate-induced transitions between topologically ordered phases. Physical Review B, 79 (4): 045316, 2009. 10.1103\/PhysRevB.79.045316.","DOI":"10.1103\/PhysRevB.79.045316"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Kenneth A. Intriligator. Bonus Symmetry in Conformal Field Theory. Nucl. Phys. B, 332: 541\u2013565, 1990. 10.1016\/0550-3213(90)90001-T.","DOI":"10.1016\/0550-3213(90)90001-T"},{"key":"14","doi-asserted-by":"publisher","unstructured":"A.N. Schellekens and S. Yankielowicz. Simple Currents, Modular Invariants and Fixed Points. Int. J. Mod. Phys. A, 5: 2903\u20132952, 1990a. 10.1142\/S0217751X90001367.","DOI":"10.1142\/S0217751X90001367"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Robbert Dijkgraaf and Edward Witten. Topological Gauge Theories and Group Cohomology. Commun. Math. Phys., 129: 393, 1990. 10.1007\/BF02096988.","DOI":"10.1007\/BF02096988"},{"key":"16","doi-asserted-by":"publisher","unstructured":"P. Roche, V. Pasquier, and R. Dijkgraaf. QuasiHopf algebras, group cohomology and orbifold models. Nucl. Phys. B Proc. Suppl., 18: 60\u201372, 1990. 10.1016\/0920-5632(91)90123-V.","DOI":"10.1016\/0920-5632(91)90123-V"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Dmitri Nikshych and Brianna Riepel. Categorical lagrangian grassmannians and brauer\u2013picard groups of pointed fusion categories. Journal of Algebra, 411: 191\u2013214, 2014. 10.1016\/j.jalgebra.2014.04.013.","DOI":"10.1016\/j.jalgebra.2014.04.013"},{"key":"18","doi-asserted-by":"publisher","unstructured":"Salman Beigi, Peter W Shor, and Daniel Whalen. The quantum double model with boundary: condensations and symmetries. Communications in mathematical physics, 306 (3): 663\u2013694, 2011. 10.1007\/s00220-011-1294-x.","DOI":"10.1007\/s00220-011-1294-x"},{"key":"19","doi-asserted-by":"publisher","unstructured":"Maissam Barkeshli, Parsa Bonderson, Meng Cheng, and Zhenghan Wang. Symmetry Fractionalization, Defects, and Gauging of Topological Phases. Phys. Rev. B, 100 (11): 115147, 2019. 10.1103\/PhysRevB.100.115147.","DOI":"10.1103\/PhysRevB.100.115147"},{"key":"20","doi-asserted-by":"crossref","unstructured":"Matthew Buican, Linfeng Li, and Rajath Radhakrishnan. Non-Abelian Anyons and Some Cousins of the Arad-Herzog Conjecture. 12 2020. URL https:\/\/arxiv.org\/abs\/2012.03394v2.","DOI":"10.1007\/JHEP12(2020)045"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Deepak Naidu. Categorical morita equivalence for group-theoretical categories. Communications in Algebra, 35 (11): 3544\u20133565, 2007. 10.1080\/00927870701511996.","DOI":"10.1080\/00927870701511996"},{"key":"22","doi-asserted-by":"publisher","unstructured":"Yuting Hu, Yidun Wan, and Yong-Shi Wu. Twisted quantum double model of topological phases in two dimensions. Phys. Rev. B, 87 (12): 125114, 2013. 10.1103\/PhysRevB.87.125114.","DOI":"10.1103\/PhysRevB.87.125114"},{"key":"23","doi-asserted-by":"crossref","unstructured":"Pierre Deligne. Cat\u00e9gories tensorielles. Moscow Mathematical Journal, 2 (2): 227\u2013248, 2002. URL https:\/\/publications.ias.edu\/book\/export\/html\/434.","DOI":"10.17323\/1609-4514-2002-2-2-227-248"},{"key":"24","doi-asserted-by":"publisher","unstructured":"Ilan Zisser. Irreducible products of characters in $a_n$. Israel Journal of Mathematics, 84 (1-2): 147\u2013151, 1993. 10.1007\/BF02761696.","DOI":"10.1007\/BF02761696"},{"key":"25","doi-asserted-by":"publisher","unstructured":"Deepak Naidu, Dmitri Nikshych, and Sarah Witherspoon. Fusion subcategories of representation categories of twisted quantum doubles of finite groups. International Mathematics Research Notices, 2009 (22): 4183\u20134219, 2009. 10.1093\/imrn\/rnp084.","DOI":"10.1093\/imrn\/rnp084"},{"key":"26","doi-asserted-by":"publisher","unstructured":"Shawn X Cui, C\u00e9sar Galindo, Julia Yael Plavnik, and Zhenghan Wang. On gauging symmetry of modular categories. Communications in Mathematical Physics, 348 (3): 1043\u20131064, 2016. 10.1007\/s00220-016-2633-8.","DOI":"10.1007\/s00220-016-2633-8"},{"key":"27","doi-asserted-by":"publisher","unstructured":"Tom Rudelius and Shu-Heng Shao. Topological Operators and Completeness of Spectrum in Discrete Gauge Theories. 6 2020. 10.1007\/JHEP12(2020)172.","DOI":"10.1007\/JHEP12(2020)172"},{"key":"28","doi-asserted-by":"publisher","unstructured":"I Martin Isaacs. Character theory of finite groups, volume 69. Courier Corporation, 1994. 10.1090\/chel\/359.","DOI":"10.1090\/chel\/359"},{"key":"29","doi-asserted-by":"publisher","unstructured":"W. Burnside. Theory of groups of finite order (2nd Ed.). Dover Publications, Inc., New York, 1955. 10.1017\/CBO9781139237253.","DOI":"10.1017\/CBO9781139237253"},{"key":"30","doi-asserted-by":"publisher","unstructured":"Dilip Gajendragadkar. A characteristic class of characters of finite $\\pi$-separable groups. Journal of algebra, 59 (2): 237\u2013259, 1979. 10.1016\/0021-8693(79)90124-8.","DOI":"10.1016\/0021-8693(79)90124-8"},{"key":"31","doi-asserted-by":"publisher","unstructured":"Gabriel Navarro. New properties of the $\\pi$-special characters. Journal of Algebra, 187 (1): 203 \u2013 213, 1997. ISSN 0021-8693. 10.1006\/jabr.1997.6798.","DOI":"10.1006\/jabr.1997.6798"},{"key":"32","doi-asserted-by":"publisher","unstructured":"Peter Brooksbank and Matthew Mizuhara. On groups with a class-preserving outer automorphism. Involve, a Journal of Mathematics, 7 (2): 171\u2013179, 2013. 10.2140\/involve.2014.7.171.","DOI":"10.2140\/involve.2014.7.171"},{"key":"33","doi-asserted-by":"publisher","unstructured":"Shawn X. Cui, Dawei Ding, Xizhi Han, Geoffrey Penington, Daniel Ranard, Brandon C. Rayhaun, and Zhou Shangnan. Kitaev's quantum double model as an error correcting code. 8 2019. 10.22331\/q-2020-09-24-331.","DOI":"10.22331\/q-2020-09-24-331"},{"key":"34","doi-asserted-by":"publisher","unstructured":"Yuting Hu and Yidun Wan. Electric-magnetic duality in twisted quantum double model of topological orders. arXiv preprint arXiv:2007.15636, 2020. 10.1007\/JHEP11(2020)170.","DOI":"10.1007\/JHEP11(2020)170"},{"key":"35","doi-asserted-by":"publisher","unstructured":"Matthew Buican and Rajath Radhakrishnan. Galois conjugation and multiboundary entanglement entropy. JHEP, 12: 045, 2020. 10.1007\/JHEP12(2020)045.","DOI":"10.1007\/JHEP12(2020)045"},{"key":"36","doi-asserted-by":"publisher","unstructured":"Micha\u00ebl Mignard and Peter Schauenburg. Modular categories are not determined by their modular data. arXiv preprint arXiv:1708.02796, 2017. 10.1007\/s11005-021-01395-0.","DOI":"10.1007\/s11005-021-01395-0"},{"key":"37","doi-asserted-by":"publisher","unstructured":"Alexei Davydov. Unphysical diagonal modular invariants. Journal of Algebra, 446: 1\u201318, 2016. 10.1016\/j.jalgebra.2015.09.007.","DOI":"10.1016\/j.jalgebra.2015.09.007"},{"key":"38","doi-asserted-by":"publisher","unstructured":"Tohru Eguchi, Hirosi Ooguri, and Yuji Tachikawa. Notes on the K3 Surface and the Mathieu group $M_{24}$. Exper. Math., 20: 91\u201396, 2011. 10.1080\/10586458.2011.544585.","DOI":"10.1080\/10586458.2011.544585"},{"key":"39","doi-asserted-by":"publisher","unstructured":"Miranda C.N. Cheng, John F.R. Duncan, and Jeffrey A. Harvey. Umbral Moonshine. Commun. Num. Theor. Phys., 08: 101\u2013242, 2014. 10.4310\/CNTP.2014.v8.n2.a1.","DOI":"10.4310\/CNTP.2014.v8.n2.a1"},{"key":"40","doi-asserted-by":"publisher","unstructured":"Terry Gannon. Much ado about Mathieu. Adv. Math., 301: 322\u2013358, 2016. 10.1016\/j.aim.2016.06.014.","DOI":"10.1016\/j.aim.2016.06.014"},{"key":"41","unstructured":"GAP. GAP group: GAP-groups, algorithms, and programming, Version 4.4 (2004). URL http:\/\/www.gap-system.org."},{"key":"42","doi-asserted-by":"publisher","unstructured":"A.D. Berenstein and A.V. Zelevinsky. Tensor Product Multiplicities and Convex Polytopes in Partition Space. J. Geom. Phys., 5: 453, 1989. 10.1016\/0393-0440(88)90033-2.","DOI":"10.1016\/0393-0440(88)90033-2"},{"key":"43","doi-asserted-by":"publisher","unstructured":"Doron Gepner and Edward Witten. String Theory on Group Manifolds. Nucl. Phys., B278: 493\u2013549, 1986. 10.1016\/0550-3213(86)90051-9.","DOI":"10.1016\/0550-3213(86)90051-9"},{"key":"44","doi-asserted-by":"publisher","unstructured":"P. Di Francesco, P. Mathieu, and D. Senechal. Conformal Field Theory. Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 1997. ISBN 9780387947853, 9781461274759. 10.1007\/978-1-4612-2256-9.","DOI":"10.1007\/978-1-4612-2256-9"},{"key":"45","doi-asserted-by":"publisher","unstructured":"A.N. Kirillov, P. Mathieu, D. Senechal, and M.A. Walton. Can fusion coefficients be calculated from the depth rule? Nucl. Phys. B, 391: 651\u2013674, 1993. 10.1016\/0550-3213(93)90087-6.","DOI":"10.1016\/0550-3213(93)90087-6"},{"key":"46","unstructured":"A.N. Kirillov, P. Mathieu, D. Senechal, and M.A. Walton. Crystallizing the depth rule for WZNW fusion coefficients. In 19th International Colloquium on Group Theoretical Methods in Physics, 9 1992. URL https:\/\/arxiv.org\/abs\/hep-th\/9209114."},{"key":"47","doi-asserted-by":"publisher","unstructured":"Alex J. Feingold and Stefan Fredenhagen. A New perspective on the Frenkel-Zhu fusion rule theorem. J. Algebra, 320: 2079\u20132100, 2008. 10.1016\/j.jalgebra.2008.05.026.","DOI":"10.1016\/j.jalgebra.2008.05.026"},{"key":"48","doi-asserted-by":"publisher","unstructured":"Andrew Urichuk and Mark A. Walton. Adjoint affine fusion and tadpoles. J. Math. Phys., 57 (6): 061702, 2016. 10.1063\/1.4954909.","DOI":"10.1063\/1.4954909"},{"key":"49","doi-asserted-by":"publisher","unstructured":"J.M. Isidro, J.M.F. Labastida, and A.V. Ramallo. Coset constructions in Chern-Simons gauge theory. Phys. Lett. B, 282: 63\u201372, 1992. 10.1016\/0370-2693(92)90480-R.","DOI":"10.1016\/0370-2693(92)90480-R"},{"key":"50","doi-asserted-by":"publisher","unstructured":"P. Goddard, A. Kent, and David I. Olive. Virasoro Algebras and Coset Space Models. Phys. Lett. B, 152: 88\u201392, 1985. 10.1016\/0370-2693(85)91145-1.","DOI":"10.1016\/0370-2693(85)91145-1"},{"key":"51","doi-asserted-by":"publisher","unstructured":"P. Ramadevi, T.R. Govindarajan, and R.K. Kaul. Knot invariants from rational conformal field theories. Nucl. Phys. B, 422: 291\u2013306, 1994. 10.1016\/0550-3213(94)00102-2.","DOI":"10.1016\/0550-3213(94)00102-2"},{"key":"52","doi-asserted-by":"publisher","unstructured":"P. Goddard, A. Kent, and David I. Olive. Unitary Representations of the Virasoro and Supervirasoro Algebras. Commun. Math. Phys., 103: 105\u2013119, 1986. 10.1007\/BF01464283.","DOI":"10.1007\/BF01464283"},{"key":"53","doi-asserted-by":"publisher","unstructured":"A.N. Schellekens and S. Yankielowicz. Field Identification Fixed Points in the Coset Construction. Nucl. Phys. B, 334: 67\u2013102, 1990b. 10.1016\/0550-3213(90)90657-Y.","DOI":"10.1016\/0550-3213(90)90657-Y"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2021-06-04-468\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T12:57:33Z","timestamp":1622811453000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2021-06-04-468\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,4]]},"references-count":54,"URL":"https:\/\/doi.org\/10.22331\/q-2021-06-04-468","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,4]]},"article-number":"468"}}