Volume 86, Number 6, June 2009
|Number of page(s)||3|
|Published online||10 July 2009|
The geometry of generalized Pauli operators of N-qudit Hilbert space, and an application to MUBs
Department of Pure Mathematics and Computer Algebra, Ghent University - Krijgslaan 281, S25, B-9000 Ghent, Belgium, EU
Accepted: 3 June 2009
We prove that the set of non-identity generalized Pauli operators on the Hilbert space of N d-level quantum systems, d an odd prime, naturally forms a symplectic polar space of rank N and order d. This generalizes the solution (by the author) of a recent conjecture posed by Saniga-Planat (which covers the case ). As an application, we give a new short proof for the existence of maximal sets of MUBs (mutually unbiased bases) in Hilbert spaces of prime power dimension (also including the prime case).
PACS: 02.40.Dr – Euclidean and projective geometries / 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) / 03.67.-a – Quantum information
© EPLA, 2009
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