Person:

Rodriguez-Rosario, Cesar

Assignment maps are mathematical operators that describe initial system-environment states for open quantum systems. We re-examine the notion of assignments that account for correlations between the system and the environment and show that these maps can be made linear at the expense of giving up positivity or consistency of the map. We study the role of positivity and consistency of the map and show the effects of relaxing these. Finally, we establish a connection between the violation of the positivity of linear assignments and the no-broadcasting theorem.

We establish the necessary and sufficient conditions for a quantum system to be stable under any general system-environment interaction. Quantum systems are stable when the time-derivative of their purity is zero. This stability provides a dynamical explanation of the classicality of measurement apparatus. We also propose a protocol to detect global quantum correlations using only local dynamical information. We show how quantum correlations to the environment provide bounds to the purity rate, which in turn can be used to estimate dissipation rates for general non-Markovian open quantum systems.