dorsal/arxiv
View SchemaSets of Mutually Unbiased Bases as Arcs in Finite Projective Planes?
| Authors | Metod Saniga, Michel Planat |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409184 |
| URL | https://arxiv.org/abs/quant-ph/0409184 |
| DOI | 10.1016/j.chaos.2005.03.008 |
| Journal | Chaos, Solitons and Fractals 26 (2005) 1267 - 1270 |
Abstract
This note is a short elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as an analogue of an arc in a (Desarguesian) projective plane of order d. Complete sets of MUBs thus correspond to (d+1)-arcs, i.e., ovals. The existence of two principally distinct kinds of ovals for d even and greater than four, viz. conics and non-conics, implies the existence of two qualitatively different groups of the complete sets of MUBs for the Hilbert spaces of corresponding dimensions.
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"abstract": "This note is a short elaboration of the conjecture of Saniga et al (J. Opt.\nB: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased\nbases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as\nan analogue of an arc in a (Desarguesian) projective plane of order d. Complete\nsets of MUBs thus correspond to (d+1)-arcs, i.e., ovals. The existence of two\nprincipally distinct kinds of ovals for d even and greater than four, viz.\nconics and non-conics, implies the existence of two qualitatively different\ngroups of the complete sets of MUBs for the Hilbert spaces of corresponding\ndimensions.",
"arxiv_id": "quant-ph/0409184",
"authors": [
"Metod Saniga",
"Michel Planat"
],
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"quant-ph"
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"doi": "10.1016/j.chaos.2005.03.008",
"journal_ref": "Chaos, Solitons and Fractals 26 (2005) 1267 - 1270",
"title": "Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes?",
"url": "https://arxiv.org/abs/quant-ph/0409184"
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