### Abstract

This is the first of two papers concerned with the formulation of a continuous-time quantum-mechanical filter. Efforts focus on a quantum system with Hamiltonian of the form H_{0}+u(t)H_{1}, where H_{0} is the Hamiltonian of the undisturbed system, H_{1} is a system observable which couples to an external classical field, and u(t) represents the time-varying signal impressed by this field. An important problem is to determine when and how the signal u(t) can be extracted from the time-development of the measured value of a suitable system observable C (invertibility problem). There exist certain quasiclassical observables such that the expected value and the measured value can be made to coincide. These are called quantum nondemolition observables. The invertibility problem is posed and solved for such observables. Since the physical quantum-mechanical system must be modelled as an infinite-dimensional bilinear system, the domain issue for the operators H_{0}, H_{1}, and C becomes nontrivial. This technical matter is dealt with by invoking the concept of an analytic domain. An additional complication is that the output observable C is in general time-dependent.

Original language | English |
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Pages (from-to) | 335-350 |

Number of pages | 16 |

Journal | Mathematical Systems Theory |

Volume | 17 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Dec 1984 |

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*,

*17*(1), 335-350. https://doi.org/10.1007/BF01744448