Here’s something I was planning to make ages ago, as part of the Bloch Sphere project, but it slipped my mind.

It’s a visual demonstration of how the Born Rule, which describes how complex ‘probability amplitudes’ are related to probability.

Say we have a single quantum bit, represented as a point on the surface of the Bloch sphere. (Note: depending on how our qubit is implemented, the 3 dimensions of the Bloch sphere aren’t necessarily the same 3 dimensions of ordinary space, but let’s ignore that for now).

Let’s say we’ve recently measured the state of our qubit, so we know which way it’s pointing (the pink arrow in the model), which we’ll call ‘1’.

If we measure the state again at the same angle,  there’s 100% chance of measuring  a ‘1’. Dead certain, no ambiguity about it. 

If we rotate our qubit so it’s pointing down, we have a perfect 0% chance of measuring a ‘1’. Again, dead certain, with no ambiguity:

But if we rotate it so it’s pointing to the side, we will have a 50% chance of measuring a ‘1’:

Another way to say this is that if we measure it at right angles to the way we measured it last time, there’s absolutely no correlation between the previous measurement and the next.

And any other angle in between those will be slightly correlated to the last result, and become more correlated as the old and new angles of measurement become closer.

Here’s the files for people that want to make their own:

Born Ruler: https://www.thingiverse.com/thing:3235423

Bloch Sphere: https://www.thingiverse.com/thing:3053421