Reference request: a guide through quantum probability Could you point out a comprehensive reference book (or more than one, if it is the case) on Quantum Probability that introduces the subject and then gradually builds up to the edges of contemporary research?
 A: These notes are excellent:


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*Greg Kuperberg, A concise introduction to quantum probability, quantum mechanics, and quantum computation, 2005 (pdf)

A: I find the way
Michael Dickson. 1998. Quantum Chance and Nonlocality. Cambridge University Press. 
introduces the material very nicely and completely in the way you requested, in the first several chapters. It's quite comprehensive.
A: If you are interested in quantum probability from mathematical perspective, these two books will be helpful:
http://www.springer.com/mathematics/probability/book/978-3-540-60270-5 (Quantum Probability for Probabilists, by P.A. Meyer).
http://www.amazon.com/Quantum-Probability-Mathematical-Statistics/dp/0123053404 (Quantum Probability (Probability and Mathematical Statistics), by S.P. Gudder).
This textbook is very good, but the focus is on quantum information and quantum computing:
http://www.amazon.com/Quantum-Computation-Information-Anniversary-Edition/dp/1107002176 (Quantum Computation and Quantum Information, by Michael A. Nielsen and Isaac L. Chuang).
