Partial ordering of weak mutually unbiased bases

A quantum system with variables in , where (with prime numbers), is considered. The non-near-linear geometry of the phase space , is studied. The lines through the origin are factorized in terms of 'prime factor lines' in . Weak mutually unbiased bases (WMUB) which are products of the mutu...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 47; no. 48; pp. 485204 - 485215
Main Authors Oladejo, S O, Lei, C, Vourdas, A
Format Journal Article
LanguageEnglish
Published IOP Publishing 05.12.2014
Subjects
finite geometry
partial ordering
weak mutually unbiased bases
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Summary:A quantum system with variables in , where (with prime numbers), is considered. The non-near-linear geometry of the phase space , is studied. The lines through the origin are factorized in terms of 'prime factor lines' in . Weak mutually unbiased bases (WMUB) which are products of the mutually unbiased bases in the 'prime factor Hilbert spaces' , are also considered. The factorization of both lines and WMUB is analogous to the factorization of integers in terms of prime numbers. The duality between lines and WMUB is discussed. It is shown that there is a partial order in the set of subgeometries of , isomorphic to the partial order in the set of subsystems of .
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/47/48/485204