Abstract
Theory of feasible quantum phase mesurement is formulated within the framework of quantum estimation theory. Phase detection is linked to the measurement of a pair of commuting Hermitian operators. The ideal phase concepts are distinguished, among all the possible realizations as the representations of the Euclidean algebra on Hermitian operators. Possible representations of the rotational subgroup correspond to measurements with indefinite phase. Traditional “quantum phase difficulties”, ascribed sometimes to the lack of uniqueness of the Hermitian phase operator, are related to the classical attempt to distinguish between quantum effect and measurement itself. In realistic quantum phase measurement, the phase statistics should be estimated using counted discrete data. Possible interferometric measurements of phase-so called operationally defined quantum phase models-are included as special realizations of presented theory.
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
P. A. M. Dirac, Proc. R. Soc. London Ser. A 114, 243 (1927).
L. Susskind and J. Glogower, Physics 1, 49 (1964).
P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40, 411 (1968).
D. T. Pegg and S. M. Barnett, Phys. Rev. A 39, 1665 (1989).
M. J. Hall, Quantum Opt. 3, 7 (1991).
A. Bandilla and H. Paul, Ann. Phys., (Lpz)23, 323 (1969).
C. M. Caves, Phys. Rev. D 23, 1693 (1981).
J. H. Shapiro and S. M. Wagner, IEEE J. Quantum Electron. QE-20, 803 (1984).
B. Yurke, Samuel L. McCall and J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
S. L. Braunstein and C. M. Caves, Phys. Rev. A 42, 4115 (1990).
J. W. Noh, A. Fougères and L. Mandel, Phys. Rev. A 45, 424 (1992).
Physica Scripta, Vol. T48, (1993).
A. Luks, V. Pefinovâ, Quantum Opt. 6, 125 (1994).
C. W. Helstrom, Quantum Detection and Estimation Theory (Academic Press 1974, New York) chap. 8.
H. P. Yuen, Phys. Lett. 91A, 101 (1982).
R. C. Rao, Linear Statistical Inference and Its Applications ( New York, Wiley, 1973 ) p. 175.
Z. Hradil, A 47, 4532 (1993).
N. J. Vilenkin, Special Functions and Theory of Group Representation ( Moscow, Nauka 1965 ); in Russian.
Y. S. Kim and M. E. Noz, Phase Space Picture of Quantum Mechanics: Group Theoretical Approach ( Singapore, World Scientific 1991 ).
A. Vourdas, Phys. Rev. A 41, 1653 (1990).
M. Ban, J. Math. Phys. 32, 3077 (1991).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Hradill, Z. (1995). Quantum Phase Measurement. In: Belavkin, V.P., Hirota, O., Hudson, R.L. (eds) Quantum Communications and Measurement. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1391-3_15
Download citation
DOI: https://doi.org/10.1007/978-1-4899-1391-3_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1393-7
Online ISBN: 978-1-4899-1391-3
eBook Packages: Springer Book Archive