Title :
Lyapunov stability for Quantum Markov Processes
Author :
Somaraju, Ram ; Petersen, Ian R.
Author_Institution :
Sch. of Inf. Technol. & Electr. Eng., Univ. of New South Wales at the Australian Defence Force Acad., Canberra, ACT, Australia
Abstract :
In this paper we prove some Lyapunov stability results for Quantum systems. The evolution of open quantum systems can be described using a one parameter semigroup of completely positive operators with which we can associate a minimal quantum Markov dilation. Analogous to Lyapunov stability theorems of classical Markov processes, we develop Lyapunov stability theorems for minimal Markov dilations of quantum systems. This theory depends on a quantum version of Dynkin´s formula.
Keywords :
Lyapunov methods; Markov processes; stability; Lyapunov stability; quantum Markov dilation; quantum Markov processes; quantum control; Algebra; Control systems; Extraterrestrial measurements; Lyapunov method; Markov processes; Quantum mechanics; Space technology; Stability; Stochastic processes; Stochastic systems; Lyapunov stability; Quantum Control; Quantum Markov Processes;
Conference_Titel :
American Control Conference, 2009. ACC '09.
Conference_Location :
St. Louis, MO
Print_ISBN :
978-1-4244-4523-3
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2009.5160264
