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Entanglement Certification Using Noncontextuality Inequalities

Yujie Zhang1,2,*, Jonah Spodek1, David Schmid2, Carter Reid1, Liam J. Morrison1,3, Thomas Jennewein1,4, Kevin J. Resch1, and Robert W. Spekkens2

  • *Contact author: yujie4physics@gmail.com
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Phys. Rev. X 16, 031057 – Published 1 September, 2026

DOI: https://doi.org/10.1103/dxpr-wp6l

Abstract

By combining the assumptions of Bell locality with those of generalized noncontextuality, we define classes of noncontextuality inequalities for correlations arising in a bipartite Bell circuit. These classes are distinguished by which subsets of the full set of operational identities are taken as input to the principle of noncontextuality; certain natural subsets form a hierarchy that provides a way of understanding and classifying different forms of quantum correlations, including entanglement, steering, and nonlocality. Each level of this hierarchy gives rise to a corresponding class of noncontextuality inequalities whose violation witnesses one of these forms of bipartite quantum resourcefulness, thereby yielding different sufficient conditions for entanglement. The resulting entanglement certification paradigm requires no prior characterization of the measurements, delivers a verdict independent of tomographic gauge freedom, and can certify any entangled state without auxiliary entangled sources. To illustrate the power of this paradigm, we show that noncontextuality inequalities can certify entanglement for families of two-qubit isotropic states for which certification by Bell or steering inequalities is known to be impossible. We also show that, compared with the Bell test, this approach certifies a much larger fraction of entangled states, while the associated membership problem is computationally more tractable. On the experimental side, we describe techniques to ensure nontrivial operational identities in the presence of noisy and imperfect implementations. We also identify the sufficient condition under which these techniques are valid, namely, a particular notion of tomographic completeness of the implemented Bell circuit, which ensures that the operational identities are independent of tomographic gauge. Finally, we provide an experimental demonstration of the superior performance of this entanglement certification technique using polarization-entangled photons.

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Entanglement is a central resource for quantum technologies, but certifying it experimentally often requires detailed calibration of measurement devices, whereas fully device-independent tests based on Bell inequalities can detect only a restricted subset of entangled states. We introduce an alternative approach that combines locality with generalized noncontextuality. Our protocol uses operational identities among measurement procedures—which can be inferred directly from experimental data when the implemented experiment is tomographically complete—to derive noncontextuality inequalities whose violation certifies entanglement. In principle, the resulting method requires no prior characterization of the measurements, yields conclusions independent of ambiguities in tomographic reconstruction, and can certify any entangled state without auxiliary entangled sources. We demonstrate the approach using polarization-entangled photons, showing that it can certify entanglement beyond the reach of conventional Bell- and steering-based tests. This provides a broadly applicable new route to certifying quantum resources in experiments and future quantum technologies.

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Phys. Rev. X 16, 031057– Published 1 September, 2026
  • Received 24 July 2025
  • Revised 19 March 2026
  • Accepted 21 July 2026
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