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Quantum Optics and the Spectroscopy of Solids pp 139–174Cite as

Quantum Estimation Theory and Optical Detection

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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 83))

Abstract

In quantum mechanics we call “observable” any physical quantity that can be represented by numbers. An observable is associated in a one-to-one way with a selfadjoint operator \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{X} \) acting on the Hilbert space H S of the quantum system S, and the spectrum of \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{X} \) represents the set of all possible readings from the measurement. Let us consider, for example, an observable with spectrum equal to whole real line R, and with spectral decomposition

$$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{X} = \int {xd\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{E} (x)} $$
((1))

.

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Author information

Authors and Affiliations

  1. Dipartimento di Fisica “A. Volta”, via Bassi 6, I-27100, Pavia, Italy

    G. M. D’ariano

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  1. G. M. D’ariano
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Editors and Affiliations

  1. Physics Department, Bilkent University, Ankara, Turkey

    T. Hakioğlu  & A. S. Shumovsky  & 

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© 1997 Springer Science+Business Media Dordrecht

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D’ariano, G.M. (1997). Quantum Estimation Theory and Optical Detection. In: Hakioğlu, T., Shumovsky, A.S. (eds) Quantum Optics and the Spectroscopy of Solids. Fundamental Theories of Physics, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8796-9_8

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  • DOI: https://doi.org/10.1007/978-94-015-8796-9_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4797-7

  • Online ISBN: 978-94-015-8796-9

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