CHSH inequality

The Clauser–Horne–Shimony–Holt inequality bounds correlations between two parties’ binary measurement outcomes. Its quantum violation conflicts with local hidden-variable theories under assumptions including measurement independence.

Bell state: A maximally entangled two-qubit state with correlations that cannot be reproduced by separable states. Measurements on this state attain the maximum quantum violation of the inequality.
Bell inequality: A constraint on correlations that any theory satisfying specified locality and hidden-variable assumptions must obey. CHSH is a particular experimentally accessible Bell inequality.
John Clauser: An American physicist whose experiments and theoretical work helped establish tests of Bell inequalities. Clauser co-authored the inequality and led an early experimental test.
Bell test: An experiment that tests whether observed correlations violate a Bell inequality. A CHSH Bell test compares measured correlations with the local bound.
CH inequality: A Bell inequality formulated directly with detection probabilities rather than only outcome correlations. It can treat detector losses differently from the usual CHSH correlation form.
Quantum entanglement: A quantum relationship in which a joint state cannot be described as independent states of its parts. Entanglement supplies the correlations that can surpass the local bound.
Locality (physics): The principle that events cannot be causally influenced by signals traveling faster than light. Locality is one of the assumptions behind the bound for hidden-variable models.
Michael Horne: An American physicist who co-authored the CHSH inequality and contributed to quantum foundations. His collaboration gave the inequality its Horne initial.
Aspect's experiment: A 1982 experiment by Alain Aspect and collaborators that tested Bell inequalities using rapidly switched analyzer settings. It demonstrated a prominent CHSH violation while addressing a locality loophole.
Mermin inequality: A multipartite Bell inequality that exposes strong nonlocal correlations in GHZ states. It extends Bell-inequality tests beyond the two-party structure of CHSH.

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