Characterization and moment stability analysis of quasilinear quantum stochastic systems with quadratic coupling to external fields

Igor G. Vladimirov; Ian R. Petersen

doi:10.1109/CDC.2012.6425876

Characterization and moment stability analysis of quasilinear quantum stochastic systems with quadratic coupling to external fields

Igor G. Vladimirov^*, Ian R. Petersen

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

3 Citations (Scopus)

Abstract

The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic polynomials of the system variables, with the latter satisfying canonical commutation relations. In combination with a cubic system Hamiltonian, this leads to quasilinear quantum stochastic systems which extend the class of linear quantum systems and yet retain algebraic closedness in the evolution of mixed moments of system variables up to any order. Although such a system is nonlinear and its quantum state is no longer Gaussian, the dynamics of the moments are amenable to exact analysis, including the computation of their steady-state values. A generalized criterion is outlined for quadratic stability of the quasilinear systems.

Original language	English
Article number	6425876
Pages (from-to)	1691-1696
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
DOIs	https://doi.org/10.1109/CDC.2012.6425876
Publication status	Published - 2012
Externally published	Yes
Event	51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: 10 Dec 2012 → 13 Dec 2012

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10.1109/CDC.2012.6425876

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title = "Characterization and moment stability analysis of quasilinear quantum stochastic systems with quadratic coupling to external fields",

abstract = "The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic polynomials of the system variables, with the latter satisfying canonical commutation relations. In combination with a cubic system Hamiltonian, this leads to quasilinear quantum stochastic systems which extend the class of linear quantum systems and yet retain algebraic closedness in the evolution of mixed moments of system variables up to any order. Although such a system is nonlinear and its quantum state is no longer Gaussian, the dynamics of the moments are amenable to exact analysis, including the computation of their steady-state values. A generalized criterion is outlined for quadratic stability of the quasilinear systems.",

author = "Vladimirov, {Igor G.} and Petersen, {Ian R.}",

year = "2012",

doi = "10.1109/CDC.2012.6425876",

language = "English",

pages = "1691--1696",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0743-1546",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "51st IEEE Conference on Decision and Control, CDC 2012 ; Conference date: 10-12-2012 Through 13-12-2012",

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T1 - Characterization and moment stability analysis of quasilinear quantum stochastic systems with quadratic coupling to external fields

AU - Vladimirov, Igor G.

AU - Petersen, Ian R.

PY - 2012

Y1 - 2012

N2 - The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic polynomials of the system variables, with the latter satisfying canonical commutation relations. In combination with a cubic system Hamiltonian, this leads to quasilinear quantum stochastic systems which extend the class of linear quantum systems and yet retain algebraic closedness in the evolution of mixed moments of system variables up to any order. Although such a system is nonlinear and its quantum state is no longer Gaussian, the dynamics of the moments are amenable to exact analysis, including the computation of their steady-state values. A generalized criterion is outlined for quadratic stability of the quasilinear systems.

AB - The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic polynomials of the system variables, with the latter satisfying canonical commutation relations. In combination with a cubic system Hamiltonian, this leads to quasilinear quantum stochastic systems which extend the class of linear quantum systems and yet retain algebraic closedness in the evolution of mixed moments of system variables up to any order. Although such a system is nonlinear and its quantum state is no longer Gaussian, the dynamics of the moments are amenable to exact analysis, including the computation of their steady-state values. A generalized criterion is outlined for quadratic stability of the quasilinear systems.

UR - http://www.scopus.com/inward/record.url?scp=84874271312&partnerID=8YFLogxK

U2 - 10.1109/CDC.2012.6425876

DO - 10.1109/CDC.2012.6425876

M3 - Conference article

AN - SCOPUS:84874271312

SN - 0743-1546

SP - 1691

EP - 1696

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

M1 - 6425876

T2 - 51st IEEE Conference on Decision and Control, CDC 2012

Y2 - 10 December 2012 through 13 December 2012

ER -

Characterization and moment stability analysis of quasilinear quantum stochastic systems with quadratic coupling to external fields

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