- ⚖
Balance. In every row and column, each axis of the Bloch sphere has as many states at one end as at the other: as many |0⟩ as |1⟩, as many |+⟩ as |−⟩, as many |+i⟩ as |−i⟩. The row's average state is then the centre of the sphere.
- ≢
No three alike. No three identical states may sit next to each other in a row or column.
- ○
○ identical: the two neighbours are the same state, overlap |⟨a|b⟩|² = 1.
- ●
● opposite: the two ends of one axis, like |0⟩ and |1⟩, overlap 0.
- ◐
◐ unbiased: on different axes, like |0⟩ and |+⟩, overlap ½. Classical bits never have this relation: two bits are either equal or opposite.
You can measure a cell along an axis, at most 3 times per puzzle. The puzzle keeps the original state, and you measure a copy. If the state lies on that axis, you always get its own pole. If it doesn't, you get a random 50/50 result. Either way the answer only rules out the opposite pole. That's all one measurement of a qubit can tell you.