There is no generalization of known formulas for mutually unbiased bases

dc.creatorarcher, Claude
dc.date2003-12-26
dc.date.accessioned2026-07-07T06:08:42Z
dc.date.available2026-07-07T06:08:42Z
dc.descriptionIn a quantum system having a finite number $N$ of orthogonal states, two orthonormal bases $\{a_i\}$ and $\{b_j\}$ are called mutually unbiased if all inner products $<a_i|b_j>$ have the same modulus $1/\sqrt{N}$. This concept appears in several quantum information problems. The number of pairwise mutually unbiased bases is at most $N+1$ and various constructions of $N+1$ such bases have been found when $N$ is a power of a prime number. We study families of formulas that generalize these constructions to arbitrary dimensions using finite rings.We then prove that there exists a set of $N+1$ mutually unbiased bases described by such formulas, if and only if $N$ is a power of a prime number.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0312204
dc.identifierhttp://arxiv.org/abs/quant-ph/0312204
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/91718
dc.subjectQuantum Physics
dc.titleThere is no generalization of known formulas for mutually unbiased bases
dc.typetext

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