• Triumvira GHZ State pixel-art physics T-shirt, white tee, front view

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Triumvira

The GHZ State Physics

\[|\mathrm{GHZ}\rangle = \frac{|000\rangle + |111\rangle}{\sqrt{2}}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

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.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Pour l'échelle : la taille M mesure 20 in (50.80 cm) de large, soit environ 3.143 × 1034 longueurs de Planck (lP = 1.616255 × 10−35 m). Un mètre ruban est plus rapide.

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

We are three sisters sharing one quantum state: all of us 0, or all of us 1, in equal superposition. Measure us in the right combinations and quantum mechanics is certain about the answer.

Ask one of us for X and the other two for Y, in any order, and the product of our three answers is always −1. If each answer were written in advance as +1 or −1, multiplying those three products would force our XXX answer to be −1, because every Y appears twice. Quantum mechanics says XXX is +1.

That is Bell's theorem without inequalities: one contradiction, no statistics needed in principle. Greenberger, Horne and Zeilinger found it in 1989, and in 2000 Pan and colleagues tested it with three entangled photons. The quantum prediction won. Real experiments still need counts and error bars, because no detector is perfect.

Equations

\[|\mathrm{GHZ}\rangle = \frac{|000\rangle + |111\rangle}{\sqrt{2}}\]
\[XYY = YXY = YYX = -1, \qquad XXX = +1\]
SymbolMeaningUnit
\(\) 000\rangle,\ \(\mathrm{111\rangle}\)
\(X,\ Y\) Pauli spin or polarisation measurements on one qubit, outcomes ±1 \(\mathrm{1}\)
\(XYY\) X on qubit 1, Y on qubits 2 and 3; the product of the three outcomes \(\mathrm{1}\)

Sources

  1. Greenberger, Horne, Shimony & Zeilinger (1990) Bell's theorem without inequalities, Am. J. Phys. 58, 1131
  2. Pan, Bouwmeester, Daniell, Weinfurter & Zeilinger (2000) Experimental test of quantum nonlocality in three-photon GHZ entanglement, Nature 403, 515
  3. Greenberger, Horne & Zeilinger (1989) Going Beyond Bell's Theorem, arXiv:0712.0921

Field notes

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