| Issue |
EPL
Volume 86, Number 6, June 2009
|
|
|---|---|---|
| Article Number | 60005 | |
| Number of page(s) | 3 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/86/60005 | |
| 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
Received:
4
February
2009
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.