What's in the box?

Z 0 or 1 X colour Y colour

Open one face. You only get one.

How to read the box

Three faces, six answers. Every answer is also one of the six states the box can hold. That is why seeing one does not mean you have found it.

|0⟩ sits at the top of the sphere, |1⟩ at the bottom. Colour is the phase angle, read off the wheel painted around the equator, so opposite phases are opposite colours. The colour fades to grey toward either pole, because a pole has no phase.

Why one shot is never enough

Measure a state along its own axis and it gives the same answer every time. Measure it along either of the other two and it is a 50/50 coin flip.

So one shot rules out exactly one of the six: the pole opposite what you saw. Five are still possible. Coral does not mean the box holds |+⟩ — every state except |−⟩ can give you coral, and four of them do it half the time.

The way through is repetition. The face the room stops disagreeing on is the axis the qubit is on, and the end it agrees on names the pole.