While I prepare the post on dimers, here is a brief one directly from a thread in physics forums. It is a talk given in Loops’07:
- Entanglement Entropy in Loop Quantum Gravity – William Donnelly
The paper seems not to be in arXiv yet. The idea is that the Bekenstein-Hawking entropy is the entanglement von Neumann entropy between the black hole and the rest of the universe. I am not an expert in black hole entropy, so if anyone would like to contribute with comments or explanations it would be very nice. For example, I could not identify in the text the connection between the entanglement entropy calculated using spin networks and the usual entropy formula for the black hole.
Reading the paper, I discovered one more thing that I don’t understand. If the black hole and the rest of the universe are entangled, a measure of the state of the universe would give complete information about the state of the black hole. Isn’t that impossible for an external observer? Well, maybe I put this question in physics forum…
Anyway, if someone wants a flash and pedagogical definition of entanglement and von Neumann entropy, this paper is a very good one:
- The physics of forgetting: Landauer’s erasure principle and information theory – Plenio, M., Vitelli, V.
It is very basic, undergraduate level I would say, but has also good references for more advanced readers.
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I’ve just noticed that BH in the title are the initials both for Black Hole or Bekenstein-Hawking, so read it the way you prefer. 
