2 Probability theory2.1 Boolean algebras of events2.2 The rules of probability2.3 Random variables2.4 Convexity2.5 Independence2.6 Additional exercises2.7 Notes and further reading3 Classical channels3.1 Definition3.2 Alternate definitions3.3 Notes and further reading4 Quantum probability theory4.1 States, effects, and measurements4.2 Qubits4.3 Comparison with probability theory4.4 Composite systems4.5 Isomorphism of operators and bipartite vectors4.6 Notes and further reading5 Quantum channels5.1 Definition5.2 Everything is a channel5.3 The Choi isomorphism5.4 The Kraus representation5.5 Two further isomorphisms5.6 Notes and further reading6 Purification6.1 Purification of density operators6.2 Ensembles and purifications6.3 Dilation of channels6.4 Relationship of Choi, Kraus, and Stinespring6.5 Information disturbance6.6 Coherent classical information (?)6.7 Notes and further reading7 Quantum mysteries7.1 Complementarity7.2 Hidden variables7.3 Bell’s theorem and the CHSH inequality7.4 Notes and further reading