Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions

Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity. An alternative proof of existence of a maximal collection of N+1 mutually unbiased bases in Hilbert spaces of prime dimension N is given by exploiting the finite Heisenberg gr...

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Bibliographic Details
Published in:arXiv.org 2007-11
Main Authors: Sulc, P, Tolar, J
Format: Article
Language:English
Subjects:
Fields (mathematics)
Hilbert space
Quantum theory
Online Access:Get full text
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Summary:Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity. An alternative proof of existence of a maximal collection of N+1 mutually unbiased bases in Hilbert spaces of prime dimension N is given by exploiting the finite Heisenberg group (also called the Pauli group) and the action of SL(2,Z_N) on finite phase space Z_N x Z_N implemented by unitary operators in the Hilbert space. Crucial for the proof is that, for prime N, Z_N is also a finite field.
ISSN:2331-8422
DOI:10.48550/arxiv.0708.4114