A theoretical analysis of experimental open quantum dynamics
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In recent years there has been a significant development of the dynamical map formalism for initially correlated states of a system and its environment. Based on some of these results, we study quantum process tomography for initially correlated states of the system and the environment. This is beyond the usual assumption that the state of the system and the environment are initially uncorrelated. Since quantum process tomography is an experimental procedure, we wind up having to study the role of preparation of input states for open quantum experiments. We work out a theory for the general preparation procedure, and study two preparation procedures in detail. In specific, we study the stochastic preparation procedure and the projective preparation procedure and apply them to quantum process tomography. The two preparation procedures describe the ways to uncorrelate the state of the system and the environment. However the specifics of how this is implemented plays a role on the outcomes of the experiment. When the stochastic preparation procedure is applied properly, quantum process tomography yields a linear process maps. We point out what it means to apply the stochastic preparation procedure properly by constructing several simple examples where inconsistencies in preparations leads to errors. When the projective preparation procedure is applied, quantum process tomography leads to a non-linear process map. We show that these processes can only be consistently described by a general dynamical map, which we call M-map. The M-map contains all of the dynamical information for the state of the system without the affects of a preparation procedure. By carefully extracting some of this dynamical information, we construct a quantitative measure for the memory effect due to the initial correlations with the environment.