### Reading lists for topics on the interface between quantum information theory and quantum gravity

(created for/by participants at the ASPEN workshop *Quantum information in quantum gravity and condensed matter*, 2011

**Workshop lecture notes**

**Further reading on quantum information theory**

- John Preskill's lecture notes on quantum computation, Particularly good on quantum error correction, fault-tolerance and topological quantum computation
- On the quantum, classical and total amount of correlations in a quantum state, Groisman, Popescu and Winter (2004): Contains the demonstration that mutual information governs how much noise is required to eliminate correlations
- A decoupling approach to the quantum capacity, Hayden, Horodecki, Yard and Winter (2007): A demonstration that random subspaces give good quantum error correcting codes

**Entanglement**

**How fast can information leave a black hole**

- Information in Black Hole Radiation, Don Page (1993): If quantum gravity is unitary, information should come out of a black hole after half the photons have been emitted.
- Review article by John Preskill (1992)
- Information locking in black holes, Smolin and Oppenheim (2005): information can come out at the very end, without the usual difficulties associated with remnants.
- Black holes as mirrors: quantum information in random subsystems, Preskill and Hayden (2007): information can leave black holes almost instantaneously
- Fast Scramblers, Sukino and Susskind (2008): How fast can black holes scramble/thermalize information?

**Ads/CFT**

I'd enjoy some good review articles, e.g.

- The "MAGOO review". A fairly comprehensive review of the state of the art as of 1999. Includes a lot of background about the string and field theory side; I think the primary audience is probably string theory grad students.
- Holographic duality with a view toward many-body physics, by John McGreevy. A more modern discussion with the goal of discussing applications to condensed matter problems; it has some very nice conceptual discussions about the correspondence along with the applications, and is meant for a cond-mat theory audience.
- Insightful D-branes, Horowitz, Lawrence, and Silverstein. Constructs gauge theory observables which seem to capture the experience of infalling observers (for a particular black hole).

**Large N as a classical limit**

- Large N limits as classical mechanics by Laurence Yaffe. Gives a general set of criteria for a classical limit and shows how large N theories fit in this framework.
- The 1/N expansion in atomic and particle physics, Cargese lectures by Edward Witten (the web page has linked to scanned versions in various file formats).
- For a general discussion of the large N limit in QFT, the lectures "1/N" in Sidney Coleman's book "Aspects of Symmetry" is a classic and a must-read.

BLACK-HOLE/QUBIT CORRESPONDENCE

REVIEW ARTICLES

http://arxiv.org/abs/1101.3559 http://arxiv.org/abs/0809.4685 http://cerncourier.com/cws/article/cern/42328

OTHER

http://arXiv.org/abs/arXiv:1102.4857 http://arxiv.org/abs/arXiv:1003.4255 http://arXiv.org/abs/arXiv:1002.4223 http://arXiv.org/abs/arXiv:0812.3322 http://arXiv.org/abs/arXiv:0903.5517 http://arXiv.org/abs/arXiv:0802.0840 http://arXiv.org/abs/arXiv:0704.0507 http://arXiv.org/abs/hep-th/0612036 http://arXiv.org/abs/quant-ph/0609227 http://arXiv.org/abs/hep-th/0602160 http://arXiv.org/abs/hep-th/0601134 http://arXiv.org/abs/1102.1193 http://arXiv.org/abs/1011.4180 http://arxiv.org/abs/0708.2799 http://arxiv.org/abs/hep-th/0610314 http://arxiv.org/abs/hep-th/0603136 http://arxiv.org/abs/hep-th/0602061

FOUR QUBIT ENTANGLEMENT

http://arxiv.org/abs/1001.3753 http://arXiv.org/abs/1004.3639 http://arXiv.org/abs/arXiv:1005.4915 http://arxiv.org/abs/1010.4219

SUPERQUBITS

http://arxiv.org/abs/0904.2512 http://arxiv.org/abs/1001.3753 http://arXiv.org/abs/arXiv:0908.0706

**General Probabilistic Theories**

Here are some places to start:

- Gilles Brassard, Is Information the Key?, Nature Physics (2005). A non-technical survey over some ideas and (not so recent) results. Nice read.
- J. Barrett, Information Processing in General Probabilistic Theories (2005). A great introduction to the framework. On p.10, an example of a post-quantum PR-box state.
- H. Barnum et al., Entropy and Information Causality in General Probabilistic Theories (2009). These more general theories also have a notion of entropy. This paper is a bit more technical, but can be browsed quickly to get an overview.
- Papers that derive quantum theory (in this framework) from simple physical axioms can be found here (L. Hardy, 2001) and here (shorter, fewer axioms, 2010). The goal is to find simple modifications of quantum theory.

**Tensor network states**

There was a lot of interest in MERA and its relation to CFTs. There are the original papers by Vidal et al.

and one recent result how MERA in 2d is unfortunately not more powerful than PEPS.

Some more questions were related to parent hamiltonians of PEPS. There are a lot of related papers by e.g. Perez-Garcia et al. For example, see this one.