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Title: Heisenberg picture approach to the stability of quantum Markov systems

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.
Authors:
;  [1] ;  [2] ;  [3] ;  [4] ;  [5]
  1. Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia)
  2. Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305 (United States)
  3. Institute of Mathematics and Physics, Aberystwyth University, SY23 3BZ Wales (United Kingdom)
  4. School of Engineering and Information Technology, University of New South Wales at ADFA, Canberra, ACT 2600 (Australia)
  5. ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia)
Publication Date:
OSTI Identifier:
22306186
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFERENTIAL EQUATIONS; HEISENBERG PICTURE; LYAPUNOV METHOD; MARKOV PROCESS; NONLINEAR PROBLEMS; QUANTUM MECHANICS; QUANTUM STATES