Qubit state on the unit circle

A one-qubit state (with real amplitudes) is an arrow of length 1. Drag the tip, or use the angle. Its projections onto the axes are the amplitudes; their squares are the probabilities.

|0> |1>
α (amp of |0>) = 1.00
β (amp of |1>) = 0.00
Probabilities = amplitude²
P(|0>)1.00
P(|1>)0.00
Measure — collapses the arrow to one axis, chosen by the squared-projection probabilities
tally: |0> = 0, |1> = 0
0°

The arrow is the state; its length is always 1, so its tip lives on the circle. The dashed lines drop to each axis: those are the amplitudes α and β. Square them and you get the probability of measuring |0> or |1>. Hit Measure and the arrow snaps to one axis, chosen with those squared-projection probabilities; over many shots the tally converges to them.