Quantum

All Bell inequalities with a quantum advantage in the minimal scenario are self-testing

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Briefings

A 2026 study on the minimal Bell scenario establishes that all Tsirelson inequalities with quantum advantage are maximized by a single extremal correlation, meaning they are self-tested. This finding characterizes self-tests for linear Bell inequalities and limits the number of inequalities maximized by a nonlocal extremal correlation to at most two dimensions, identified as polygons for qubit states of arbitrary entanglement. The study concludes that the quantum set is not self-dual.

Key points

• Every Tsirelson inequality with quantum advantage is maximized by a single extremal correlation in the minimal Bell scenario.
• At most a two-dimensional family of inequalities can be maximized by a nonlocal extremal correlation, identified as polygons for qubit states of arbitrary entanglement.

Context

This research addresses the minimal Bell scenario where all extremal quantum correlations are known but Tsirelson inequalities remain poorly understood. The findings clarify which correlations maximize specific inequalities and which inequalities are maximized by a single extremal correlation, providing a characterization of self-tests for linear Bell inequalities.

Limitations

The study is based on preprint arXiv:2611.06997v1 and does not include peer-reviewed publication or experimental validation. Results are limited to the minimal Bell scenario and rely on theoretical analysis of qubit states of arbitrary entanglement without experimental confirmation.

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