  We propose an extreme test of quantum theory using astrophysical black holes
and entangled photons from atomic cascades. The identification of a cascade
emission close to a black-hole event horizon would allow us to observe photons
entangled with partners that have fallen behind the horizon. The experiment
involves testing the characteristic cos^2(theta) modulation of photon
transmission through a pair of polarisers at relative angle theta (Malus' law).
For single photons, Malus' law is a remarkable feature of quantum theory: it is
equivalent to expectation additivity for incompatible observables, and is
generically violated for hidden-variables theories with nonstandard probability
distributions. An experiment with entangled states straddling an event horizon
is motivated by the Hawking information loss puzzle, as well as on general
grounds. In principle, one could test the currently observed X-ray photons in
iron lines from black-hole accretion discs. However, only a small fraction
(~0.6%) have cascade partners, and current X-ray polarimetry does not permit
successive measurements on a single X-ray photon. A realisable experiment
requires the identification of an appropriate cascade in a more convenient
frequency band.
