2006/11/30 by Rong Wu, Alexander Pechen, Constantin Brif +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Laser-Matter Interactions and Applications #Mechanical and Optical Resonators #Stability and Controllability of Differential Equations #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/21/015
published as J. Phys. A: Math. Theor. 40, 5681 (2007) · 16 pages
openalex publication_date 2007/05/08 · arxiv created 2007/05/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
This paper presents a constructive proof of complete kinematic state controllability of finite-dimensional open quantum systems whose dynamics are represented by Kraus maps. For any pair of states (pure or mixed) on the Hilbert space of the system, we explicitly show how to construct a Kraus map that transforms one state into another. Moreover, we prove by construction the existence of a Kraus map that transforms all initial states into a predefined target state (such a process may be used, for example, in quantum information dilution). Thus, in sharp contrast to unitary control, Kraus-map dynamics allows for the design of controls which are robust to variations in the initial state of the system. The capabilities of non-unitary control for population transfer between pure states illustrated for an example of a two-level system by constructing a family of non-unitary Kraus maps to transform one pure state into another. The problem of dynamic state controllability of open quantum systems (i.e., controllability of state-to-state transformations, given a set of available dynamical resources such as coherent controls, incoherent interactions with the environment, and measurements) is also discussed.