Heisenberg Picture Approach to the Stability of Quantum Markov Systems

Yu Pan, Hadis Amini, Zibo Miao, John Edward Gough, Valery Ugrinovskii, Matthew R. James

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

31 Dyfyniadau(SciVal)
154 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

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.
Iaith wreiddiolSaesneg
Rhif yr erthygl062701
CyfnodolynJournal of Mathematical Physics
Cyfrol55
Rhif cyhoeddi6
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - Meh 2014

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