  The two observables are complementary if they cannot be measured
simultaneously, however they become maximally complementary if their
eigenstates are mutually unbiased. Only then the measurement of one observable
gives no information about the other observable. The spin projection operators
onto three mutually orthogonal directions are maximally complementary only for
the spin 1/2. For the higher spin numbers they are no longer unbiased. In this
work we examine the properties of spin 1 Mutually Unbiased Bases (MUBs) and
look for the physical meaning of the corresponding operators. We show that if
the computational basis is chosen to be the eigenbasis of the spin projection
operator onto some direction z, the states of the other MUBs have to be
squeezed. Then, we introduce the analogs of momentum and position operators and
interpret what information about the spin vector the observer gains while
measuring them. Finally, we study the generation and the measurement of MUBs
states by introducing the Fourier like transform through spin squeezing. The
higher spin numbers are also considered.
