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A quantum analogue of Hunt's representation theorem for the generator of convolution semigroups on Lie groups
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  • Published: June 1991

A quantum analogue of Hunt's representation theorem for the generator of convolution semigroups on Lie groups

  • A. Barchielli1,2 &
  • G. Lupieri1,2 

Probability Theory and Related Fields volume 88, pages 167–194 (1991)Cite this article

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  • 7 Citations

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Summary

In quantum mechanics certain operator-valued measures are introduced, called instruments, which are an analogue of the probability measures of classical probability theory. As in the classical case, it is interesting to study convolution semigroups of instruments on groups and the associated semigroups of probability operators. In this paper the case is considered of a finite-dimensional Hilbert space (n-level quantum system) and of instruments defined on a finite-dimensional Lie group. Then, the generator of a continuous semigroup of (quantum) probability operators is characterized. In this way a quantum analogue of Hunt's representation theorem for the generator of convolution semigroups on Lie groups is obtained.

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Authors and Affiliations

  1. Dipartimento di Fisica dell'Università di Milano, Via Celoria. 16, I-20133, Milano, Italy

    A. Barchielli & G. Lupieri

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Milano, I-20133, Milano, Italy

    A. Barchielli & G. Lupieri

Authors
  1. A. Barchielli
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  2. G. Lupieri
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Barchielli, A., Lupieri, G. A quantum analogue of Hunt's representation theorem for the generator of convolution semigroups on Lie groups. Probab. Th. Rel. Fields 88, 167–194 (1991). https://doi.org/10.1007/BF01212558

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  • Received: 16 May 1989

  • Revised: 04 October 1990

  • Issue Date: June 1991

  • DOI: https://doi.org/10.1007/BF01212558

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Keywords

  • Hilbert Space
  • Convolution
  • Quantum Mechanic
  • Probability Measure
  • Probability Theory
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