Triumvira: GHZ State

Quantum Foundations arc, page 9 of 193. Back to The Pixelated Physics Universe

Who they are

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

Triumvira is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.

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

$$ \begin{gathered} |\mathrm{GHZ}\rangle = \frac{|000\rangle + |111\rangle}{\sqrt{2}} \\ XYY = YXY = YYX = -1, \qquad XXX = +1 \end{gathered} $$

Symbol Meaning SI unit
$X,\ Y$ Pauli spin or polarisation measurements on one qubit, outcomes ±1 1
$XYY$ X on qubit 1, Y on qubits 2 and 3; the product of the three outcomes 1

Sources

Crossovers

Triumvira meets Quavo & Lia (Entangled Twins / Quantum Connection). Quavo and Lia need statistics, many runs of a Bell test, to beat a local theory. Triumvira's three sisters, sharing a GHZ state, can make the point with a single kind of perfect correlation that no local assignment of answers can match.

Triumvira meets Kochenspek (Kochen–Specker Theorem). Triumvira's three-qubit test and Kochenspek's coloured vectors attack the same idea: that every measurement result is fixed in advance. Each finds a set of quantum predictions that no fixed list of answers can reproduce.

Wear the lore

Concept keywords: GHZ State, Triumvira, Quantum Foundations, physics lore, Pixelated Physics