Mesoscopic superpositions of states (3)

The third lesson dealt with the study of transformations of the density operator of an open physical system interacting with an environment. We presented a universal formalism that applies to very general situations in physics and quantum information. We introduced the notion of super-operator, an application of the space of density operators in itself, and gave the general properties of these super-operators, presenting simple examples. We have shown that these super-operators can be put into a standard form corresponding to a decomposition into a sum of terms, each of which is generated by an operator of the system (Kraus form). The ambiguity of this decomposition, which can be realized by an infinite number of sets of equivalent generators, was highlighted. The lesson continued with the description of some simple examples of Kraus decomposition, corresponding to the most general possible evolution of a qubit. We described the mechanisms of bit switching, phase switching and decoherence, as well as the spontaneous emission of a qubit.