Volume 86, Number 6, June 2009
Article Number 60005
Number of page(s) 3
Section General
Published online 10 July 2009
EPL, 86 (2009) 60005
DOI: 10.1209/0295-5075/86/60005

The geometry of generalized Pauli operators of N-qudit Hilbert space, and an application to MUBs

K. Thas

Department of Pure Mathematics and Computer Algebra, Ghent University - Krijgslaan 281, S25, B-9000 Ghent, Belgium, EU

received 4 February 2009; accepted in final form 3 June 2009; published June 2009
published online 10 July 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 ${\mathcal{W}}_{2N - 1}(d) $ 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 d = 2). 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).

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