On real-valued classical probability as a special case of complex-valued quantum probability. More generally, non-commutative probability.
Chaitanya Rao, Notes on von Neumann’s algebra formulation of Quantum Mechanics has a side-by-side comparison table and a reading list for getting up to speed fast.
David Ellerman On Classical and Quantum Logical Entropy: The analysis of measurement advertises an article on this theme.
Terry Tao, maximally general: Notes on Free probability.
Nonlocality and statistical inference.
Peter Woit has just made the final draft (dated 10/25/16) of his new textbook Quantum Theory, Groups and Representations: An Introduction available for free download.
1 References
Allen, Barrett, Horsman, et al. 2017. “Quantum Common Causes and Quantum Causal Models.” Physical Review X.
Baez, and Biamonte. 2012. “A Course on Quantum Techniques for Stochastic Mechanics.” arXiv:1209.3632.
Carmi, and Moskovich. 2015. “Statistics Limits Nonlocality.” arXiv:1507.07514 [Quant-Ph].