Feynman's path integral and mutually unbiased bases

Our previous work on quantum mechanics in Hilbert spaces of finite dimension N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G Svetlichny. He speculated that the secret of the Feynman path integral may lie in the property of mutual unbiasedness of temporally proximal bases. We confirm the corresponding property of the short-time propagator by using a specially devised N x N approximation of quantum mechanics in L2 (R) applied to our finite-dimensional analogue of a free quantum particle