Structure of the sets of mutually unbiased bases with cyclic symmetry
Ulrich Seyfarth, Luis Lorenzo Sánchez-Soto, Gerd Leuchs · Journal of Physics A Mathematical and Theoretical · 2014
Mutually unbiased bases that can be cyclically generated by a single unitary operator are of special interest, for they can be readily implemented in practice. We show that, for a system of qubits, finding such a generator can be cast as the problem of finding a symmetric matrix over the field 2 equipped with an irreducible characteristic polynomial of a given Fibonacci index. The entanglement structure of the resulting complete sets is determined by two additive matrices of the same size.