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

K. Thas
2009 Europhysics letters  
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 W2N−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
more » ... sion (also including the prime case).
doi:10.1209/0295-5075/86/60005 fatcat:rwwefdimhrc6diipjfcvlhxtyy