An introduction to quantum filtering

Luc Bouten, Ramon Van Handel, Matthew R. James

Research output: Contribution to journalArticlepeer-review

357 Scopus citations


This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum Itô calculus and its use in the modeling of physical systems. We use both reference probability and innovations methods to obtain quantum filtering equations for system-probe models from quantum optics.

Original languageEnglish (US)
Pages (from-to)2199-2241
Number of pages43
JournalSIAM Journal on Control and Optimization
Issue number6
StatePublished - 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


  • Quantum filtering
  • Quantum probability
  • Quantum stochastic processes


Dive into the research topics of 'An introduction to quantum filtering'. Together they form a unique fingerprint.

Cite this