2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143745Mutually 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.13 pages; accepted in J. Phys. A: Math. TheorQuantum Physicstext