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A control problem for gaussian states

  • Part C Modeling, Identification And Estimation
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Learning, control and hybrid systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 241))

Abstract

This paper is concerned with an analysis of physical limitations of macroscopic control due to the laws of quantum mechanics. A control problem for a class of quantum states, called Gaussian, which are widely used in quantum optics is considered. Our interest is focused on controlling the mean value and the variance of two obsevables, coordinate and momentum, with respect to Gaussian states. A necessary and sufficient condition for the mean value to be controllable is obtained. Furthermore it is shown that a problem to attain the smallest possible variance under the condition that its mean value is stable is reduced to an optimal regulator problem.

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Author information

Authors and Affiliations

  1. Department of Mathematical Engineering and Information Physics, The University of Tokyo, Bunkyo-ku, 113-8656, Tokyo, Japan

    Hidenori Kimura

Authors
  1. Masahiro Yanagisawa
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  2. Hidenori Kimura
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Editor information

Yutaka Yamamoto PhD Shinji Hara PhD

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© 1999 Springer-Verlag London Limited

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Yanagisawa, M., Kimura, H. (1999). A control problem for gaussian states. In: Yamamoto, Y., Hara, S. (eds) Learning, control and hybrid systems. Lecture Notes in Control and Information Sciences, vol 241. Springer, London. https://doi.org/10.1007/BFb0109736

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  • DOI: https://doi.org/10.1007/BFb0109736

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-076-7

  • Online ISBN: 978-1-84628-533-2

  • eBook Packages: Springer Book Archive

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