Special topic on dynamics of open quantum systems

Midhun Krishna, Parvinder Solanki, Sai Vinjanampathy

Alexander Nikolaevich Pechen

This work reviews several topics in the non-equilibrium dynamics and control of open quantum systems, including the dynamics in the weak coupling and low density regimes, incoherent control and universal Kraus maps.

Ángel S. Sanz, Salvador Miret-Artés

Gernot Schaller

Alexander Nikolaevich Pechen

This work reviews several topics in the non-equilibrium dynamics and control of open quantum systems, including the dynamics of the system and the environment in the weak coupling and low density regimes, incoherent control, production of universal Kraus maps and engineering of arbitrary pure and mixed quantum states.

I. Kurniawan, Gunther Dirr, Uwe Helmke B

Knowledge about to what extent quantum dynamical systems can be steered by coherent controls is indispensable for future developments in quantum technology. The purpose of this paper is to analyze such controllability aspects for finite dimensional bilinear quantum control systems. We use a unified approach based on Lie-algebraic methods from nonlinear control theory to revisit known and to establish new results for closed and open quantum systems. In particular, we provide a simplified characterization of different notions of controllability for closed quantum systems described by the Liouville-von Neumann equation. We derive new necessary and sufficient conditions for accessibility of open quantum systems modelled by the Lindblad-Kossakowski master equation. To this end, we exploit a well-studied topic of differential geometry, namely the classification of all matrix Lie-groups which act transitively on the Grassmann manifold or the punctured Euclidean space. For the special case of coupled spin-1/2 systems, we obtain a remarkably simple characterization of accessibility. These accessibility results correct and refine previous statements in the quantum control literature.