Frontiers in Mathematical Sciences

Open Quantum Systems, Measurement and Control

Mazyar Mirrahimi


We live today the second quantum revolution, where the quantum properties such as coherent superposition and entanglement are used in a controlled and reproducible manner to develop new technological tools in computation, communication and high-precision measurement. After a brief discussion on particular features of quantum systems with respect to classical ones (composite systems modeled by tensor products, and the irreversible and unpredictable nature of quantum measurements), I will overview the main mathematical models behind these systems and some of their properties. These models include the discrete Markov chain models for quantum systems under measurement, the continuous-time stochastic master equations, and the Lindblad-type master equation modeling the average evolution. I will also briefly discuss some control and stabilization problems which are at the center of the current developments for instance in the area of quantum error correction.