Quantum information in Hawking radiation

Abstract

In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate 1,2 . The problem of the fate of information in this process is known as the "black hole information paradox" 3,4 . It inspired a plethora of theoretical models which, for the most part, assume either a fundamental loss of information 5,6 or some form of quantum gravity 7,8 . At variance to the main trends, a conservative approach assuming information retrieval in quantum correlation between Hawking particles was proposed 9, 10 and recently developed within qubit toy-models [11][12][13][14][15][16][17] . Here we leverage modern quantum information to incarnate this idea in a realistic model of quantised radiation. To this end we employ the formalism of quantum Gaussian states 18 together with the continuous-variables version of the quantum marginal problem 19,20 . Using a rigorous solution to the latter 21 we show that the thermality of all Hawking particles is consistent with a global pure state of the radiation. Surprisingly, we find out that the radiation of an astrophysical black hole can be thermal until the very last particle. In contrast, the thermality of Hawking radiation originating from a microscopic black hole -which is expected to evaporate through several quanta -is not excluded, though there are constraints on modes' frequencies. Our result support the conservative resolution to the black hole information paradox. Furthermore, it suggests a systematic programme for probing the global state of Hawking radiation.

The double doors of the horizon

“…Some (unknown) unitary operator evolves an initially pure state of matter to a gravitational collapse and then onto Hawking radiation escaping to infinity. In [13,14] we considered the kinematics of such a process, where in the final state radiation will be in multi-mode entangled state. That such multi-party entanglement should be present in Hawking radiation is known already from [11], where it was pointed out that when one Hawking particle is emitted with some momentum, the remaining black hole must carry the opposite momentum.…”