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In one of L. Susskind's talks he said something along the line of "some people [including me] think that quantum error-correction is of importance [in quantum gravity or qft in curved spacetime]". He didn't elaborated on it. Hence the question:
Why is quantum error-correction in quantum gravity according to some scientists a 'big deal'?
Thank you for your responses! :-)
Disclaimer: This response to the question is not an answer, but although I would prefer to put it in the comment box, it's too large. It is my hope that it leads to an answer from the references cited.
Also, I feel the excerpt that occupies the bulk of this answer may genuinely be of help to the OP.
Abstract: Over the last few years it has become increasingly clear that there is a deep connection between fundamental physics and quantum information. The connection goes back to the remarkable discovery that black holes carry entropy with an amount given by the horizon area. I will present new evidence that this is only the tip of the iceberg, and prove that a similar area law applies to more general Renyi entanglement entropies. To demonstrate the simplicity of my prescription, I will use it to calculate for the first time the mutual Renyi information between two disks in a holographic conformal field theory (CFT) of arbitrary dimension. I will briefly comment on the prospect of verifying this area law experimentally in light of recent advances in measuring Renyi entropies. Furthermore, I will provide quantum corrections to the area law and use it to solve a long-standing problem in quantum gravity: what region of the dual spacetime is described by a subregion in a holographic CFT?
The answer to this question lies in a new perspective that I will advocate: holography is a quantum error correction code. [My Emphasis]
I hope you get a real answer, but I feel if you follow on from the highlighted statement above, it may be of some use.
Other, more newbie friendly sources (I mean myself here) include pdfs, such as Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence and Is spacetime a quantum error-correcting code? Pastawski, Yoshida, Harlow, Preskill = HaPPY arXiv:1503.06237 which has lots of pictures (always good) and may be easier to follow.
My apologies: a Google search will be needed to find these, as my tablets has issues with copying pdf URLs.
This question can't be answered definitively. There are some indications that this is the case, The paper by Verlinde and Verlinde discusses this and makes an interesting point. The entropy removed by a quantum error correction is not perfect. There is then a as V & V point out some open system; there must be something else. We can think of it as a Hamming distance problem. Once a black hole or quantum gravity system has emitted so much quanta the remaining quantum information is more scrambled and the Hamming distance too large for effective quantum error correction coding. Interestingly this occurs at around the Page time in the decay of a black hole. The firewall is proving to be a stubborn obstruction.
This is not to say I think quantum error correction is wrong. The QECC is governed by some algebraic system, such as what computes sphere packing as the distance between letters in a code. This is probably central to the dynamics of quantum gravity. It may however not be the final answer. In effect the quantum universe may compute on the "cosmic cloud," to use an analogue with the internet. There may be some open structure quantum gravity is coupled to which perform the necessary accounting.
I hope this helps a little bit. Do a search on arxiv for quantum error correction and you will find a lot of hits! There are a lot of people in pursuit of this type of physics.
This paper https://arxiv.org/abs/1411.7041 was the first (pretty sure) to point out similarities between the AdS/CFT correspondence and quantum error correcting codes. Thinking of the correspondence in this way has been very useful in shedding some light on how the gravitational system encodes CFT data. Some people think understanding exactly how this happens is a route for understanding quantum gravity.
There was also much discussion of this question at this summer school: https://www.perimeterinstitute.ca/conferences/it-qubit-summer-school
