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Zhiyuan Wang, Kaden R. A. Hazzard: Particle exchange statistics beyond fermions and bosons, Nature 637 (2025) 314-318 [arXiv:2308.05203, doi:10.1038/s41586-024-08262-7]
Zhiyuan Wang: Parastatistics and a secret communication challenge [arXov:2412.13360]
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added the original references on the “first quantized” picture via irreps:
Albert M. L. Messiah, O. W. Greenberg: Symmetrization Postulate and Its Experimental Foundation, Phys. Rev. 136 (1964) B248 [doi:10.1103/PhysRev.136.B248]
(where irreps of the symmetric group are called “generalized rays”)
James B. Hartle, John R. Taylor: Quantum Mechanics of Paraparticles, Phys. Rev. 178 (1969) 2043 [doi:10.1103/PhysRev.178.2043]
Robert H. Stolt, John R. Taylor: Correspondence between the first- and second-quantized theories of paraparticles, Nuclear Physics B 19 1 (1970) 1-19 [doi:10.1016/0550-3213(70)90024-6]
James B. Hartle, Robert H. Stolt, John R. Taylor: Paraparticles of Infinite Order, Phys. Rev. D 2 (1970) 1759 [doi:10.1016/0550-3213(70)90024-6]
finally found what I felt ought to exist: discussion of quantum gates built from (parastatistical) permutation actions:
Stephen P. Jordan, pp 108 in: Quantum Computation Beyond the Circuit Model, PhD thesis, MIT (2010) [arXiv:0809.2307, pdf]
Stephen P. Jordan: Permutational Quantum Computing, Quantum Information and Computation 10 (2010) 470 [arXiv:0906.2508, doi:10.26421/QIC10.5-6-7]
Stephen P. Jordan: Permutational Quantum Computation, talk at Complexity Resources in Physical Computation, Oxford (2009) [pdf]
Michel Planat, Rukhsan Ul Haq: The Magic of Universal Quantum Computing with Permutations, Advances in Mathematical Physics 2017 287862 (2017) [doi:10.1155/2017/5287862]
I’ll give this its own entry permutational quantum computing…
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