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=== Quantum mechanics === Beginning with the work of [[Hugh Lowell Montgomery|Hugh Montgomery]] and [[Freeman Dyson]] in the 1970s, mathematicians and physicists have speculated that the zeros of the Riemann zeta function are connected to the energy levels of [[quantum system]]s.<ref>{{cite web|first=Ivars|last=Peterson|author-link=Ivars Peterson |work=MAA Online |url=http://www.maa.org/mathland/mathtrek_6_28_99.html |title=The Return of Zeta |date=June 28, 1999 |access-date=2008-03-14 |url-status=dead |archive-url=https://web.archive.org/web/20071020141624/http://maa.org/mathland/mathtrek_6_28_99.html |archive-date=October 20, 2007 }}</ref><ref>{{Cite journal|last=Hayes|first=Brian|author-link=Brian Hayes (scientist)|date=2003|title=Computing science: The spectrum of Riemannium|jstor=27858239|journal=[[American Scientist]]|volume=91|issue=4|pages=296–300|doi=10.1511/2003.26.3349|s2cid=16785858 }}</ref> Prime numbers are also significant in [[quantum information science]], thanks to mathematical structures such as [[mutually unbiased bases]] and [[SIC-POVM|symmetric informationally complete positive-operator-valued measures]].<ref>{{cite book |title=Geometry of quantum states: an introduction to quantum entanglement |title-link=Geometry of Quantum States |last1=Bengtsson |first1=Ingemar |last2=Życzkowski |first2=Karol |publisher=[[Cambridge University Press]] |year=2017 |isbn=978-1-107-02625-4 |edition=Second |location=Cambridge |pages=313–354 |oclc=967938939 |author-link2=Karol Życzkowski }}</ref><ref>{{cite journal |last=Zhu |first=Huangjun |title=SIC POVMs and Clifford groups in prime dimensions |url=http://stacks.iop.org/1751-8121/43/i=30/a=305305?key=crossref.45cb006b9f3c7e510461594ea8dfa7f7 |journal=Journal of Physics A: Mathematical and Theoretical |volume=43 |issue=30 |pages=305305 |arxiv=1003.3591 |doi=10.1088/1751-8113/43/30/305305 |bibcode=2010JPhA...43D5305Z |year=2010 |s2cid=118363843 }}</ref>
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