Heisenberg picture approach to the stability of quantum Markov systems
- Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia)
- Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305 (United States)
- Institute of Mathematics and Physics, Aberystwyth University, SY23 3BZ Wales (United Kingdom)
- School of Engineering and Information Technology, University of New South Wales at ADFA, Canberra, ACT 2600 (Australia)
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.
- OSTI ID:
- 22306186
- Journal Information:
- Journal of Mathematical Physics, Vol. 55, Issue 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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