Linear quantum systems: A tutorial

The purpose of this tutorial is to give a brief introduction linear quantum control systems. mathematical model systems presented first, then some fundamental control-theoretic notions such as stability, controllability and observability are given, which closely related several important concepts in information science decoherence-free subsystems, non-demolition variables, back-action evasion measurements. After that, Gaussian states introduced, particular, an information-theoretic uncertainty relation often gives better bound for mixed than the well-known Heisenberg relation. Kalman filter systems, analogy classical (namely, non-quantum-mechanical) canonical decomposition recorded, its application illustrated by means recent experiment. As single- multi-photon useful resources technology, response these types input presented. Finally, coherent feedback briefly experiment used demonstrate effectiveness networks theory.