What's in the box?

Z shape X colour Y colour

Open one face. You only get one.

How to read the box

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

Shapes live on the vertical axis: a triangle at |0⟩, a circle at |1⟩, and anything in between shows both, each sized by its own amplitude. Colour is the phase angle read straight off the wheel painted around the equator, so opposite phases come out as opposite colours. Climb toward either pole and the colour drains to grey, because a pole has no phase to show.

Why one student can never be sure

A measurement is not a readout. Each face has only two possible answers, and those two answers are themselves two of the six states on offer. Measure a state along its own axis and it hands back its own glyph every single time. Measure it along either of the other two axes and it is a straight coin flip, because those axes know nothing about it.

Work backwards and one shot crosses off exactly one name: the pole opposite the thing you saw. Five always survive. Seeing coral does not mean the box holds |+⟩, because every state except |−⟩ can hand you coral, and four of them do it half the time. The only way through is repetition. Whichever face the room stops disagreeing on is the axis the qubit is sitting on, and which end it agrees on names the pole. That is the experiment.