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Entanglement types mirror states, GHZ stronger than W

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October 22, 2026 by Ivy Delaney

Szilárd Szalay has constructed a new polynomial measure of filling a gap in the established toolkit for quantifying how three quantum bits become linked. This work establishes a clear ordering among entanglement types; researchers found that the measure of bipartite entanglement is larger than the W measure, which in turn is larger than the GHZ measure. The paper demonstrates a parallel between the ordering of these entanglement measures and the ordering of the equivalence classes of entangled three-qubit states, where bipartite entanglement is the weakest and GHZ the strongest.

Polynomial Measures Define Three Entanglement Types

A newly constructed polynomial measure quantifies W-entanglement in three-qubit systems, completing a toolkit alongside existing measures for GHZ-entanglement and bipartite entanglement. This measure addresses a gap in the established methods for characterizing the complex relationships between entangled quantum bits, providing a consistent framework for comparison. The development of this W-entanglement measure allows for a direct assessment of its strength relative to other common entanglement types.

These entanglement measures are ordered, with the bipartite measure being the largest, followed by the W measure and then the GHZ measure. Szilárd Szalay constructed this measure to provide a more complete picture of entanglement in multi-qubit systems.

GHZ and W Entanglement: Ordering of Measures

The relationship between three distinct forms of quantum entanglement, bipartite, W, and GHZ, now has a defined order, with implications for understanding how entanglement manifests in multi-particle systems. The work builds upon earlier investigations by Coffman, Kundu and Wootters into distributed entanglement, extending their framework to encompass a more complete picture of three-qubit entanglement.

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Bipartite Entanglement as a Baseline for Comparison

The newly developed polynomial measure of W-entanglement establishes a clear ranking alongside existing metrics for quantifying entanglement, such as the three-tangle for GHZ-entanglement and bipartite concurrence. Szilárd Szalay’s work extends beyond simply adding another measure. It reveals a consistent ordering among these three entanglement types.

Bipartite entanglement is demonstrably the weakest, followed by W-entanglement, with GHZ-entanglement representing the strongest form. These findings also connect to research by Ignacio Cirac, Duff and Ebrahim, who previously explored the inequivalent ways three qubits can be entangled and the Freudenthal construction for classifying entanglement, and to the foundational understanding of entanglement properties provided by Wootters’ work on entanglement of formation and distributed entanglement.

👉 More information
🗞 The three kinds of three-qubit entanglement
✍️ Szilárd Szalay
🧠 DOI: https://quantum-journal.org/papers/q-2026-10-22-2242/

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Ivy Delaney

Ivy Delaney has been working with neural networks and machine learning since the mid-nineties, back when a couple of hidden layers and a long afternoon of training counted as ambitious. She has watched the field go from academic curiosity to the thing quietly running underneath everything, and she brings that long view to quantum computing. For Quantum Zeitgeist she covers the ground where the two fields meet. That means quantum machine learning and the variational algorithms it leans on, and it also means the less glamorous but more interesting story of classical machine learning already doing real work inside quantum machines, decoding error-correcting codes, calibrating noisy hardware and learning the error models that simulators depend on. She writes about the hardware those algorithms have to run on too, and about the post-quantum cryptography scramble that the same hardware has set off. Her stories typically start with the paper, whether that is peer-reviewed work, conference proceedings or an arXiv preprint, with the source linked so you can hold a claim up against the research it came from. She is unimpressed by benchmarks that will not say what they beat, and by demonstrations that only work in the press release.

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