On mutually unbiased bases: Passing from $d$ to $d^2$

Maurice Robert Kibler (1)

1 IPNL - Institut de Physique Nucléaire de Lyon

We show how to transform the problem of finding d+1 mutually unbiased bases in the d-dimensional Hilbert space into the one of finding d(d+1) vectors in the N-dimensional Hilbert space with N=d**2. The transformation formulas admit a solution when d is a prime number.

Mots clés: finite-dimensional quantum mechanics; mutually unbiased bases; projection operators; quadratic discrete Fourier transform; Gauss sums

Domaines: Physique Quantique [quant-ph]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Maurice Robert Kibler. On mutually unbiased bases: Passing from $d$ to $d^2$. 2013. ⟨in2p3-00747123v2⟩