  It is shown that 'non-quantum systems', with anomalous statistical
properties, would carry a distinctive experimental signature. Such systems can
exist in deterministic hidden-variables theories (such as the pilot-wave theory
of de Broglie and Bohm). The signature consists of non-additive expectations
for non-commuting observables, breaking the sinusoidal modulation of quantum
probabilities for two-state systems. This effect is independent of the quantum
state (pure or mixed), or of the details of the hidden-variables model.
Experiments are proposed, testing polarisation probabilities for single
photons.
