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Contextuality is a hallmark feature of the quantum theory that captures itsincompatibility with any noncontextual hidden-variable model. TheGreenberger--Horne--Zeilinger (GHZ)-type paradoxes are proofs of contextualitythat reveal this incompatibility with deterministic logical arguments. However,the simplest GHZ-type paradox with the fewest number of complete contexts andthe largest amount of nonclassicality remains elusive. Here, we derive aGHZ-type paradox utilizing only three complete contexts and show this numbersaturates the lower bound posed by quantum theory. We demonstrate the paradoxwith a time-domain fiber optical platform and recover all essential ingredientsin a 37-dimensional contextuality test based on high-speed modulation,convolution, and homodyne detection of time-multiplexed pulsed coherent light.By proposing and observing a strong form of contextuality in high Hilbert-spacedimensions, our results pave the way for the exploration of exotic quantumcorrelations with time-multiplexed optical systems.

Exploring the boundary of quantum correlations with a time-domain optical processor