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Monday, June 22, 2026

The GHZ State: All Together, or Not at All

Two entangled qubitsThe basic unit of a quantum computer. Like a 'bit' in a normal computer, but instead of being only 0 or 1 it can be 0, 1, or a blend of both at once. are a handshake. A GHZ stateA maximally entangled state of three or more qubits: an all-or-nothing superposition of all-zeros and all-ones. If one qubit is lost or ignored, the remaining GHZ entanglement is destroyed. is the whole room agreeing at once, and falling silent the instant a single person leaves.

A cat that sharpened Bell's theorem

The Greenberger-Horne-Zeilinger state, GHZ for short, is one of the clearest and most concentrated forms of multi-qubit entanglementA quantum link where two qubits' states become tied together, so acting on or measuring one affects the other. It is a key resource for quantum computing.. Where two entangled qubits are a simple link, a GHZ state puts a whole register into a single superpositionThe quantum ability of a qubit to be in a combination of 0 and 1 simultaneously, which gives quantum computers their power. of all-zeros and all-ones, written |00…0⟩ plus |11…1⟩, with nothing in between.1 Schrödinger's cat was one macroscopic system poised between alive and dead; a GHZ state is that same poise spread across dozens of qubits, every one committed to the same two outcomes together.2 No qubit has a value of its own. The information lives only in the collective, in the shared phase that ties the all-zero and all-one branches together and lets the state interfere as no classical arrangement can.3

Not many small correlations. One enormous correlation, shared by the whole register at once.

That structure sharpened an old argument into one of its cleanest forms. Testing whether the world is locally real, whether particles carry definite properties fixed in advance, once required Bell's statistical inequalities: measure many pairs, average the outcomes, and check whether the average breaks a classical bound.1 A GHZ state gives Bell's theorem without inequalities: an all-or-nothing contradiction between the predictions of quantum mechanics and local realismThe classical assumption that things have definite properties before measurement and are influenced only by their immediate surroundings..1 Real experiments still verify the correlations statistically, but the logical clash is sharper than an ordinary Bell-inequality test. The first three-photon GHZ experiment turned the state itself into laboratory fact,4 and generalized Bell-type checks now confirm a genuine GHZ state with only a handful of measurementsReading a quantum system, which forces it out of its blend of possibilities into a single definite 0 or 1 and ends its quantum behaviour., robustly even under some noise.3

Building a GHZ state. A quantum circuit on three qubits: a Hadamard gate on the top qubit followed by a cascade of CNOT gates, producing the state (|000⟩ + |111⟩)/√2, with nothing in between.
Figure 1: Building the GHZ cat. A Hadamard followed by a cascade of CNOT gates puts the whole register into one superposition of all-zeros and all-ones, with nothing in between.

Where the fragility pays, and how big it gets

The same all-or-nothing fragility becomes the feature when you turn it around. Run N separate sensors and precision improves only as the square root of N, the standard quantum limitThe best precision from independent, unentangled probes, where error shrinks only as the square root of the number of tries. you get from averaging independent tries. Entangle those N sensors into a GHZ stateA maximally entangled state of three or more qubits: an all-or-nothing superposition of all-zeros and all-ones. If one qubit is lost or ignored, the remaining GHZ entanglement is destroyed. and they accumulate a signal's phase together, pushing precision to the Heisenberg limitThe ultimate precision limit of measurement, where error shrinks as one over the number of particles N, beating the classical square-root scaling., a scaling of one over N. That quadratic gain can be enormous, provided the entangled state can be prepared and protected.5 The same structure underpins quantum secret sharingA protocol that splits a secret among several parties so only all of them together can recover it, built on shared entanglement., where a message is split so that only the full set of parties working together can recover it.3

A big GHZ state is a stress test the whole machine has to pass at once.

It is also one of the most honest benchmarks of a quantum computer. Because a single slip anywhere ruins the whole state, a large, high-fidelity GHZ state rewards not raw qubit countThe raw number of physical qubits in a machine. A weak measure of power on its own, since quality and connectivity matter more. but the global coherence of every qubitThe basic unit of a quantum computer. Like a 'bit' in a normal computer, but instead of being only 0 or 1 it can be 0, 1, or a blend of both at once. and gate at the same instant.6 In a 2024 peer-reviewed demonstration on superconducting processors, researchers created GHZ states up to 60 qubits at a fidelity near 0.60, riding circuits of thousands of gates.6 A later 2025 preprint reported a 120-superconducting-qubit GHZ state with fidelity 0.56(3), using post-selection with a 28 percent post-selection rate.7 In the 2024 work, one recent trick was not to correct errors directly but to hide from them, sheltering the state in the stable modes of a cat-scar discrete time crystalA driven phase of matter that repeats in time in a stable, noise-resistant way. Its stable states can shelter a fragile GHZ state. to stretch its life.6 The shift worth watching is from merely observing these fragile states to building them at scale and holding them still, which is exactly the global control a useful quantum machine will demand.

Two precision curves against the number of probes N. The standard quantum limit falls as one over the square root of N, while the ideal GHZ-enabled Heisenberg limit falls faster, as one over N.
Figure 2: Why entanglement pays. Independent probes improve only as 1/√N, the standard quantum limit; an ideal GHZ state can reach 1/N, the Heisenberg limit.

Sources

  1. Greenberger, D. M., Horne, M. A. & Zeilinger, A. “Going Beyond Bell’s Theorem.” In Bell’s Theorem, Quantum Theory, and Conceptions of the Universe (ed. Kafatos, M.), 69–72 (Kluwer Academic, Dordrecht, 1989). DOI: 10.1007/978-94-017-0849-4_10.
  2. Omran, A. et al. “Generation and Manipulation of Schrödinger Cat States in Rydberg Atom Arrays.” Science 365, 570–574 (2019). DOI: 10.1126/science.aax9743. Preprint: arXiv:1905.05721.
  3. Fan, X.-Y., Zhou, J., Meng, H.-X., Wu, C., Pati, A. K. & Chen, J.-L. “Greenberger-Horne-Zeilinger States: Their Identifications and Robust Violations.” Preprint: arXiv:2106.01550 (2021).
  4. Bouwmeester, D., Pan, J.-W., Daniell, M., Weinfurter, H. & Zeilinger, A. “Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement.” Physical Review Letters 82, 1345–1349 (1999). DOI: 10.1103/PhysRevLett.82.1345. Preprint: arXiv:quant-ph/9810035.
  5. Giovannetti, V., Lloyd, S. & Maccone, L. “Advances in Quantum Metrology.” Nature Photonics 5, 222–229 (2011). DOI: 10.1038/nphoton.2011.35. Preprint: arXiv:1102.2318.
  6. Bao, Z., Xu, S. et al. “Creating and Controlling Global Greenberger-Horne-Zeilinger Entanglement on Quantum Processors.” Nature Communications 15, 8823 (2024). DOI: 10.1038/s41467-024-53140-5.
  7. Javadi-Abhari, A., Martiel, S., Seif, A., Takita, M. & Wei, K. X. “Big Cats: Entanglement in 120 Qubits and Beyond.” Preprint: arXiv:2510.09520 (2025).