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
.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. W. Helstrom, Quantum Detection and Estimation Theory, Academic Press, (New York, 1976). The reader is also addressed to the original papers:
C. W. Helstrom, Found. Phys. 4, 453 (1974);
C. W. Helstrom, Int. J. Theor. Phys. 11, 357 (1974).
M. A. Naimark, Iza. Akad. Nauk USSR, Ser. Mat. 4 277 (1940).
N. I. Akhierzer and I. M. Glezman, Theory of Linear Operators in the Hilbert Space, (two volumes bound as one), Dover Publ. Inc. N.Y 1993, pag. 121 of Vol. 2.
A. Peres, Quantum Theory: Concepts and Methods, vol. 57 of Fundamental Theories of Physics, Kluwer Academic Publisers (Dordrecht, Boston, London 1993)
G. M. D’Ariano, Measuring Quantum States, in this volume.
L. Mandel, Proc. Phys. Soc. 72 1037 (1958);
L. Mandel, ibid. 74 233 (1959)
P. L. Kelley, and W. H. Kleiner, Phys. Rev. A 30 844 (1964)
H. Carmichael, An Open System Approach to Quantum Optics, Cap. 1 e 2, Springer-Verlag, Heidelberg (1993).
G. M. D’Ariano, Int. J. Mod. Phvs. B 6 1291 (1992)
G. M. D’Ariano, Nuovo Cimento 107B 643 (1992).
H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory, 24 657 (1978);
H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory, 25 179 (1979);
H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory, 26 78 (1980).
H. P. Yuen, Phys. Lett. 91A, 101 (1982).
E. Arthurs and M. S. Goodman, Phys. Rev. Lett. 60 2447 (1988)
A. S. Holevo. Probabilistic and statistical aspects of quantum theory, North-Holland, (Amsterdam, 1982).
G. M. D’Ariano and M. G. A. Paris, Phys. Rev. A 49 3022 (1994).
See R. Omnès, The interpretation of Quantum Mechanics, Princeton Series in Physics, Princeton University Press, (Princeton, 1994), pag. 84. The original reference is:
W. Pauli, Handbuch der Physik, 24 1 (1933)
M. Ozawa, in Squeezed States and Nonclassical Light, ed. by P. Tombesi and E. R. Pike, pag. 263, Plenum, (New York, 1989).
A. S. Holevo, in Quantum Aspects of Optical Communications, (Paris 1990), Lecture Notes in Physics 378, eds. C. Bendjaballah, O. Hirota and S. Reynaud, Springer, Berlin-New York, (1991) pag. 127
G. Ludvig, Foundations of Quantum Mechanics I and II, Springer, (Berlin, 1983).
K. Kraus, States, Effects, and Operations: fundamental notions of Quantum theory, Springer, (Berlin, 1983).
E. B. Davies, Quantum Theory of Open Systems, Academic, (London, 1976).
M. Ozawa, J. Math. Phys. 25 (1984).
J. von Neumann. Mathematical Foundations of Quantum Mechanics, Princeton UP, (Princeton, NJ, 1955).
E. Arthurs and J. L. Kelly, Bell. Syst. Tech. J., 44 725–729 (1965).
J. P. Gordon and W. H. Louisell, in Physics of Quantum Electronics, pp. 833–840, McGraw-Hill, (New York, 1966).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive