Abstract
If quantum gravity does not lead to a breakdown of predictability, then Almheiri-Marolf-Polchinski-Sully (AMPS) have argued that an observer falling into a black hole can perform an experiment which verifies a violation of entanglement monogamy — that late time Hawking radiation is maximally entangled with early time Hawking radiation and also with in-falling radiation — something impossible in quantum field theory. However, as pointed out by Hayden and Harlow, this experiment is infeasible, as the time required to perform the experiment is almost certainly longer than the lifetime of the black hole. Here we propose an alternative firewall experiment which could actually be performed within the black hole’s lifetime. The alternative experiment involves forming an entangled black hole in which the unscrambling of information is precomputed on a quantum memory prior to the creation of the black hole and without acting on the matter which forms the black hole or emerges from it. This would allow an observer near a black hole to signal faster than light. As another application of our precomputing strategy, we show how one can produce entangled black holes which acts like “flat mirrors”, in the sense that information comes out almost instantly (as in the Hayden-Preskill scenario), but also emerge unscrambled, so that it can actually be observed instantly as well. Finally, we prove that a black hole in thermal equilibrium with its own radiation, is uncorrelated with this radiation.
Highlights
Number of photons forming a black hole in an initially pure quantum state, and after it has radiated half its photons thermally, the remaining photons must be entangled with the previous one, in order to preserve the purity of the full state
If quantum gravity does not lead to a breakdown of predictability, Almheiri-Marolf-Polchinski-Sully (AMPS) have argued that an observer falling into a black hole can perform an experiment which verifies a violation of entanglement monogamy — that late time Hawking radiation is maximally entangled with early time Hawking radiation and with in-falling radiation — something impossible in quantum field theory
This is because Alice needs to perform a quantum computation on the Hawking radiation in order to decode entanglement between the zone and the early Hawking radiation, and the time that it would take to perform the quantum computation is longer than the time it takes for the black hole to evaporate
Summary
The important ingredient we needed was that the state of the black hole is maximally mixed on its full Hilbert space, so we require that the black hole has maximum entropy for a given mass. The box is opened, delivering the box’s entropy to the black hole with minimal mass increase to the black hole During this process, the black hole will be emitting Hawking radiation, and the question is whether we can grow the black hole faster than it’s evaporating. The mining process has been studied recently, via a process of lowering many ropes to the horizon of the black hole [43] This allows radiation to more escape the angular momentum potential barrier of the black hole.
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