Leggett–Garg inequality

The Leggett–Garg inequality is a bound on correlations between measurements made at different times. Its violation challenges the joint assumptions of macrorealism and noninvasive measurability.

Temporal correlation: A statistical relationship between values of a quantity measured at different times. The inequality constrains correlations between successive measurements, rather than correlations across space.
Superconducting qubit: A controllable quantum two-level system built from superconducting electrical circuits. Qubit experiments test Leggett–Garg violations with controlled measurements at successive times.
Bell inequality: A constraint on correlations between spatially separated measurements under local hidden-variable assumptions. Bell inequalities concern spatially separated systems, whereas Leggett–Garg inequalities concern measurements at different times.
Clumsiness loophole: The possibility that measurement disturbance, rather than nonclassical behavior, accounts for an apparent inequality violation. It directly questions whether an experiment has established noninvasive measurability well enough.
Macrorealism: The view that a system has definite properties at all times, whether or not those properties are measured. This is the assumption that makes the Leggett–Garg bound a classical constraint.
Neutrino oscillation: The periodic change in a neutrino’s flavor as it propagates through space and time. Flavor measurements at different times provide temporal correlations for inequality tests.
Clauser–Horne–Shimony–Holt inequality: A Bell inequality involving two observers, two measurement settings each, and binary outcomes. Its familiar spatial correlation bound is often compared with the temporal Leggett–Garg bound.
Ideal negative-result measurement: A measurement designed to infer a system’s property from the absence of an interaction with a detector. Leggett and Garg proposed it as a way to support the noninvasiveness assumption.
Noninvasive measurability: The assumption that a system’s properties can be measured without disturbing its subsequent behavior. Together with macrorealism, it permits the correlations to be combined into an inequality.
Photon polarization: The orientation of a photon’s polarization state, which can be measured using optical apparatus. Photon experiments use polarization as a convenient two-valued quantity for temporal tests.

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