Generation of all sets of mutually unbiased bases for three-qubit systems

Abstract

We propose a new method of finding the mutually unbiased bases for three qubits. The key element is the construction of the table of striation-generating curves in the discrete phase space. We derive a system of equations in the Galois field GF(8) and show that the solutions of these equations are sufficient for the construction of the general sets of complete mutually unbiased bases. A few examples are presented in order to show how our algorithm works in the cases: striation table with three, two axes, and one and no axis in the discrete phase space.