  We show that the amount of complementarity that a quantum system can exhibit
depends on which complementary properties one is considering. Consider a set of
mutually unbiased bases (MUBs) which corresponds to the spectral decomposition
of some maximally complementary properties: The perfect knowledge of one, i.e.
the state of the system is one of the basis states, implies that all the others
are completely unknown, namely the measurement of another property will find
any of its possible outcomes with uniform probability. We show that, depending
on which three of the MUBs we choose, a 5-dimensional system can have different
degrees of complementarity, measured using the minimum over all the system
states of the sum of the entropies and of the variances of the measurement
outcomes related to the three chosen observables. This property was first found
experimentally, and demonstrates that an experimental discovery can disclose
quantum information effects.
