### Abstract

This is the second of two papers concerned with the formulation of a continuous-time quantum-mechanical filter. In the first paper, the invertibility of a quantum system coupled to a weak time-dependent classical field was studied. The physical system is modelled as an infinite-dimensional bilinear system. Necessary and sufficient conditions for invertibility were derived under the assumption that the output observable is a quantum nondemolition observable (QNDO), characterized by the classical property that its expected value is equal to its measured value. In this paper necessary and sufficient conditions are developed for an observable to qualify as a QNDO; if in addition the criteria for invertibility are met, the given observable defines a quantum nondemolition filter (QNDF). The associated filtering algorithm thus separates cleanly into the choice of output observable (a QNDO) and the choice of procedure for processing the measurement outcomes. This approach has the advantage over previous schemes that no optimization is necessary. Applications to demodulation of optical signals and to the detection and monitoring of gravitational waves are envisioned.

Original language | English |
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Pages (from-to) | 33-55 |

Number of pages | 23 |

Journal | Mathematical Systems Theory |

Volume | 18 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Dec 1985 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Mathematics(all)
- Computational Theory and Mathematics

### Cite this

*Mathematical Systems Theory*,

*18*(1), 33-55. https://doi.org/10.1007/BF01699460