Mutually unbiased bases are orthonormal bases 
and 
of 
satisfying
 |
A family is pairwise mutually unbiased when this holds for every pair of distinct bases. Write 
for the largest size of such a family. In dimension
two, the eigenbases of the three Pauli matrices
give three mutually unbiased bases. A basis unbiased to the coordinate basis is represented
by the normalized columns of a complex Hadamard
matrix.
