Mathematical Modeling of Linear Dynamical Quantum Systems

Hendra I. Nurdin, Naoki Yamamoto

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter provides a review of the mathematical theory of linear quantum systems, which is based on the Hudson–Parthasarathy quantum stochastic calculus as a mathematical tool for describing Markov open quantum systems interacting with external propagating quantum fields. A precise definition of linear quantum systems is given as well as quantum stochastic differential equations representing their linear equation of motion in the Heisenberg picture. The important notion of physical realizability for linear quantum stochastic differential equations is introduced, and necessary and sufficient conditions for physical realizability reviewed. Complete parameterizations for linear quantum systems are given, and transfer functions defined. Also, the special class of completely passive linear quantum systems is introduced and the notion of stability for linear quantum systems is developed.

Original languageEnglish
Title of host publicationCommunications and Control Engineering
PublisherSpringer International Publishing
Pages35-71
Number of pages37
Edition9783319551999
DOIs
Publication statusPublished - 2017 Jan 1

Publication series

NameCommunications and Control Engineering
Number9783319551999
ISSN (Print)0178-5354
ISSN (Electronic)2197-7119

Fingerprint

Mathematical Modeling
Quantum Systems
Differential equations
Linear Systems
Quantum Stochastic Differential Equation
Parameterization
Linear equations
Realizability
Equations of motion
Transfer functions
Open Quantum Systems
Stochastic Calculus
Quantum Fields
Linear differential equation
Transfer Function
External Field
Equations of Motion
Linear equation
Necessary Conditions
Sufficient Conditions

Keywords

  • Covariance
  • Shale

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Control and Systems Engineering
  • Control and Optimization

Cite this

Nurdin, H. I., & Yamamoto, N. (2017). Mathematical Modeling of Linear Dynamical Quantum Systems. In Communications and Control Engineering (9783319551999 ed., pp. 35-71). (Communications and Control Engineering; No. 9783319551999). Springer International Publishing. https://doi.org/10.1007/978-3-319-55201-9_2

Mathematical Modeling of Linear Dynamical Quantum Systems. / Nurdin, Hendra I.; Yamamoto, Naoki.

Communications and Control Engineering. 9783319551999. ed. Springer International Publishing, 2017. p. 35-71 (Communications and Control Engineering; No. 9783319551999).

Research output: Chapter in Book/Report/Conference proceedingChapter

Nurdin, HI & Yamamoto, N 2017, Mathematical Modeling of Linear Dynamical Quantum Systems. in Communications and Control Engineering. 9783319551999 edn, Communications and Control Engineering, no. 9783319551999, Springer International Publishing, pp. 35-71. https://doi.org/10.1007/978-3-319-55201-9_2
Nurdin HI, Yamamoto N. Mathematical Modeling of Linear Dynamical Quantum Systems. In Communications and Control Engineering. 9783319551999 ed. Springer International Publishing. 2017. p. 35-71. (Communications and Control Engineering; 9783319551999). https://doi.org/10.1007/978-3-319-55201-9_2
Nurdin, Hendra I. ; Yamamoto, Naoki. / Mathematical Modeling of Linear Dynamical Quantum Systems. Communications and Control Engineering. 9783319551999. ed. Springer International Publishing, 2017. pp. 35-71 (Communications and Control Engineering; 9783319551999).
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