1. The problem statement, all variables and given/known data Say I have two incompatible observables A and B. A has a finite number of base states say 4. How many base states should B have? 2. Relevant equations Heisenberg's uncertainty AB - BA <> 0 3. The attempt at a solution I guess the answer is 4 as A and B basis states should form basis in the same space, but not very sure.