Extreme Test of Quantum Theory with Black Holes

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.