New Construction of Mutually Unbiased Bases in Square Dimensions

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dc.creatorWocjan, Pawel
dc.creatorBeth, Thomas
dc.date2004-07-12
dc.date.accessioned2026-07-07T06:10:15Z
dc.date.available2026-07-07T06:10:15Z
dc.descriptionWe show that k=w+2 mutually unbiased bases can be constructed in any square dimension d=s^2 provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (k,s)-nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bounds on the asymptotic growth of the number of mutually orthogonal Latin squares (based on number theoretic sieving techniques), we obtain that the number of mutually unbiased bases in dimensions d=s^2 is greater than s^1/14.8 for all s but finitely many exceptions. Furthermore, our construction gives more mutually orthogonal bases in many non-prime-power dimensions than the construction that reduces the problem to prime power dimensions.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0407081
dc.identifierhttp://arxiv.org/abs/quant-ph/0407081
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/92208
dc.subjectQuantum Physics
dc.titleNew Construction of Mutually Unbiased Bases in Square Dimensions
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