I\'m currently trying to find my way into the geometric description of Quantum M

Question

I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading:

Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et al., eds.). Lecture Notes in Physics 768, Springer Verlag, Berlin, New York, 2009, 1-60.

A document that can also be found as a manuscript via: http://www.physik.uni-leipzig.de/~uhlmann/PDF/UC07.pdf

Even though I thought that I have a solid background in abstract algebra I somewhat got lost in Chapter 2 when he's trying to classify all the *-algebras that represent actual physical systems (starting at page 24 in the document).

Do you have some recommendations for texts that introduce the *-algebra language in Quantum Mechanics in a more 'detailed' way. Because I kind of have the feeling that at a certain point Uhlmann just keeps skipping steps and I also lack some of the physical intuition concerning partial traces, canonical traces, purification and all that. From time to time I'd also be happy to see a concrete example.

I'm looking forward to your responses.

Best regards.

Explanation / Answer

OP wrote(v2):

I also lack some of the physical intuition concerning partial traces, canonical traces, purification and all that.

Apart from the mathematical subject of *-algebras, I get the impression that OP really wants to study quantum information rather than quantum mechanics. If this hunch is correct, then I can recommend for starters from the physics side, the textbook

M. Nielsen and I.L Chuang, Quantum Computation and Quantum Information, Cambridge University Pres (2000).

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