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I needed some references which involves, the basic definition and motivation for Entanglement Entropy, and its one or two applications to many-body physics/black holes.

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    $\begingroup$ What do you mean by QM1 and QM2? $\endgroup$ – Emilio Pisanty Oct 16 '12 at 14:17
  • $\begingroup$ I mean that which is based on the basic quantum mechanics and advanced quantum mechanics, and doesn't involve much of many body theory and quantum field theory $\endgroup$ – Jaswin Oct 16 '12 at 14:22
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    $\begingroup$ But condensed matter is all about many body problems...? $\endgroup$ – genneth Oct 16 '12 at 14:23
  • $\begingroup$ I am preparing for a presentation on "Entanglement Entropy from Condensed Matter Physics to Black Holes" hence I was looking for useful resources. $\endgroup$ – Jaswin Oct 16 '12 at 14:23
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    $\begingroup$ Hi Jaswin - it's better to ask about what you want to know directly, rather than asking for a reference. People will still point you to relevant books and papers as needed. Could you edit your question along those lines? $\endgroup$ – David Z Oct 16 '12 at 20:58
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The standard reference for quantum information is Nielsen and Chuang, Quantum Computation and Quantum Information. Here is the Google books preview.

On the free side, I strongly recomment the "Quantum Entanglement" review by Horodecki brothers (they are quite famous in quantum information). It contains almost anything you'd want to know about entanglement and references to the rest. You can download it freely from arXiv: http://arxiv.org/abs/quant-ph/0702225

None of these require you to learn either many body theory or quantum field theory. But for many body theory and QFT, this is usually a good choice Quantum Field Theory of Many Body Systems. I'm afraid when it comes to quantum many body theory, basic QFT is a must and you will not be able to do without it.

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I don't know the subject, but I found interesting resources below, I hope it will help you :

Entanglement Entropy in QFT, Holographic Entanglement Entropy

Entanglement entropy from a holographic viewpoint

Entanglement Entropy in Many-Body Systems

Area laws for the entanglement entropy

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