Heisenberg picture approach to the stability of quantum Markov systems
Abstract
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 01, 2014
- Source ID
- 10.1063/1.4884300
Entities
People
- Hadis Amini
- John E. Gough
- Matthew R. James
- Valery Ugrinovskii
- Yu Pan
- Zibo Miao
Organizations
- Aberystwyth University
- Air Force Office of Scientific Research
- Australian National University
- Stanford University
- University of New South Wales