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Quantum self-testing no longer relies on ideal entanglement

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October 1, 2026 by Ivy Delaney

Matthijs Vernooij of Delft Institute of Applied Mathematics and Yuming Zhao of the University of Copenhagen have removed a key limitation in quantum self-testing protocols. Published in volume 10, page 2222 of Quantum, their work demonstrates that robust self-testing for synchronous games now applies to all quantum strategies, a significant expansion from previous methods reliant on symmetric projective maximally entangled (PME) strategies.

This upgrade builds upon the MIP*=RE paper and related articles, making these results more physically relevant by eliminating the PME assumption. The researchers have also proven the Quantum Low Degree Test is now an efficient test applicable to n-qubit systems.

Lifting PME Assumptions in Synchronous Game Self-Testing

This advancement addresses a longstanding constraint in robust self-testing, a technique used to verify the performance of quantum devices by assessing the strategies players employ in non-local games. Previously, proving robust self-testing relied on restricting those strategies to symmetric projective maximally entangled (PME) states, a condition not reflective of physical reality.

Researchers have now proven that any perfect synchronous game, previously requiring PME strategies for robust self-testing, can in fact be tested against all strategies. This shift in methodology is rooted in an operator-algebraic approach, allowing for a broader range of strategies to be considered during the self-testing process, and offering a more comprehensive and realistic assessment of quantum device capabilities.

👉 More information
🗞 Lifting the maximally-entangledness assumption in robust self-testing for synchronous games
✍️ Matthijs Vernooij and Yuming Zhao
🧠 DOI: https://quantum-journal.org/papers/q-2026-10-01-2222/

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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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