The sticky elactic in the Bloch sphere

[naima]

I found a funny model of the qubit written by Aerts in
Foundations of quantum physics: a general
realistic and operational realistic and operational approach.

At the beginning the qubit is at the point P on the Bloch sphere. It will be measured along another direction (two opposite points on the sphere). There is an elastic between these points. A and B. P falls orthogonally on AB at Q and then the elastic breaks somewhere between A and B. So Q is projected to up (A) or down (B) according to the probability formula of QM!

 

[Strilanc]

Yes; as far as the probabilities go, measurement is like a projection. This is true even for complicated measurements involving many qubits, though there's not a nice sphere-based visualization of those.

Here's a circuit diagram showing it happening. Notice how the probability of a wire being measured as On (+Z instead of -Z) closely tracks the vertical position on the Bloch sphere representation of the wire's state, and how the measured wire's state is pinned along the Z axis: