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I noticed that there was already a post discussing the fast scrambling property of black holes. But it seems no satisfactory answer was given.

As mentioned by L. Susskind et. al, the fast scrambling property of BHs seems to say BHs are infinite dimensional systems so that every pair of qubits can directly interact 'locally' so that the fast scrambling can be implemented by BHs. He also mentioned that this is due to the effect of gravity during the collapse procedure.

I am wondering, how such a gravitational collapse can lead to such an 'infinite dimensional' geometry? If the geometry is related with tensor networks, then what's the correspondent tensor network of BHs? It sounds very strange for me.

An alternative is that maybe we do not need such an 'infinite dimensional' geometry, instead if the internal geometry of BHs is a manifold with a vanishing geodesic distance as discussed here, then the fast scrambling assumption may also be valid. But still, how such a geometry can be built inside a BH? Also, it seems that such a vanishing geodesic manifold should be an infinite dimensional manifold too.

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    $\begingroup$ This sounds a lot more like fundamental physics than quantum computation, to me. Perhaps more appropriate for the Physics StackExchange? $\endgroup$ – Niel de Beaudrap Oct 29 '18 at 20:25
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    $\begingroup$ @Niel de Beaudrap While my understanding is that the geometry is built by quantum states, or the information pattern in quantum states, so it's a quantum information problem. During the collapsing gravity evolve the system and the system runs into a certain state and this state generates the strange geometry of BHs. $\endgroup$ – XXDD Oct 30 '18 at 1:53
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    $\begingroup$ Black hole holography is certainly (a niche subject) within the mainstream of QIP, but is gravitational dynamics? Just because the question relates to tensor networks (or the information pattern in quantum states), does not make it a problem that can be tackled by the methods of quantum information theory. As soon as you ask "how such a gravitational collapse can lead to" some phenomenon, it sounds to me as though you're asking for a dynamical mechanism which lies outside of quantum information theory (unless someone's saving a mature theory of quantum gravity for a rainy day). $\endgroup$ – Niel de Beaudrap Oct 30 '18 at 16:58
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    $\begingroup$ @Niel de Beaudrap Yes, you are absolutely right that a complete picture need a dynamical mechanism. But if for the time being we are less ambitious and we only check 'what kind of quantum state corresponds to a geometry that may support a fast scrambler', then this might be answered by QIP if the geometry is really built by a tensor network, since now we only check a specific time slice but not the complete dynamics. $\endgroup$ – XXDD Oct 30 '18 at 17:12
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    $\begingroup$ I do think this is something that would be tackled by Quantum Information Theory. Even though black holes are not the first thing you think about when thinking about quantum computers, the scrambling time of black holes is a topic which in recent years, I have only seen quantum information theorists talk about. A recent example is Peter Shor's paper in July 2018. The most classic paper in the field is this paper by Patrick Hayden and Johnny Preskill. $\endgroup$ – user5019 Nov 5 '18 at 18:37

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