Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes?

Preprint

25 November 2004

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.quant-ph/0409184

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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All Related Versions

Version 1, 2004-09-27, ArXiv
Version 2, 2004-11-25, ArXiv
Published version: Chaos, Solitons, and Fractals, 26 (5), 1267.

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