Triumvira

Three sisters, palms together, each holding an X or Y rune. One run, and the hidden variables have nowhere to hide.

The Physics

Three qubits are entangled in a GHZ state. Quantum mechanics says certain products of X and Y measurements are −1 with certainty. If each result were a pre-set local value of ±1, multiplying those three products would force XXX = −1, but quantum mechanics says XXX = +1. This is Bell's theorem without inequalities.

|GHZ⟩ = (|000⟩ + |111⟩)/√2

• |000⟩, |111⟩: all three qubits in state 0, or all in state 1
• X, Y: Pauli spin or polarisation measurements on each qubit, outcomes ±1 (dimensionless)

Greenberger, Horne and Zeilinger introduced it in 1989; Pan et al. tested it with three photons (Nature, 2000).

On the shirt

Front: Triumvira, the pixel-art character, with the title. Back: the GHZ state, the three certain results, the hidden-variable contradiction and both sources. Printed on a unisex tee.