Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9712032

Direct and indirect strategies for phase measurement

Márcia T. Fontenelle, Samuel L. Braunstein, Wolfgang P. Schleich, Mark S. Hillery

Published Dec 16, 1997• 1 citation
arXivHTMLPDF

Abstract

Recently, Torgerson and Mandel [Phys. Rev. Lett. 76, 3939 (1996)] have reported a disagreement between two schemes for measuring the phase difference of a pair of optical fields. We analyze these schemes and derive their associated phase-difference probability distributions, including both their strong and weak field limits. Our calculation confirms the main point of Torgerson and Mandel of the non-uniqueness of an operational definition of the phase distribution. We further discuss the role of postselection of data and argue that it cannot meaningfully improve the sensitivity.

DOI
10.48550/arxiv.quant-ph/9712032

Related papers

Is There a Unique Operator for the Phase Difference of Two Quantum Fields?

J. R. Torgerson, L. Mandeļ

The recent operational approach to the phase operator of a quantized electromagnetic field is applied to the problem of determining the phase difference between two weak coherent fields in two different ways. The phase difference is determined directly, and indirectly by measuring each field in turn against the field of a strong local oscillator. We show by measurements with an eight-port interferometer that these two different schemes lead to quite different outcomes for the probability distribution of the phase difference, in agreement with our theory, but in disagreement with most other theoretical approaches.

Physical Review Letters•May 20, 1996•46 citations

Phase measurement andQfunction

Ulf Leonhardt, Henryk Paul

Generalizing a recent theoretical result obtained by Freyberger and Schleich [Phys. Rev. A 47, R30 (1993)], we show that the phase-measurement scheme proposed and realized by Noh, Foug\`eres, and Mandel [Phys. Rev. Lett. 67, 1426 (1991); Phys. Rev. A 45, 424 (1992)] amounts to measuring the Q function for the light under investigation, provided the reference beam (used for homodyne detection) is a very strong coherent field so that it can be described classically. The desired phase distribution follows from the Q function by averaging over the field amplitude. Since an analysis of an earlier proposal by Bandilla and Paul [Ann. Phys. (Leipzig) 23, 323 (1969)] to measure phase distributions via amplification led to just the same result, a perfect physical equivalence of those two approaches has thus been established.

Physical Review A•Apr 1, 1993•131 citations

Phase measurements

Stephen Mark Barnett, David Thomas Pegg

We address the problem of identifying an operational prescription for quantum phase measurements. As is known, different experiments can lead to different measured phase operators. However, we show that ambiguities of interpretation can arise even if a single experiment, such as that of Noh, Foug\`eres, and Mandel [Phys. Rev. Lett. 67, 1426 (1991)], is chosen as defining a phase measurement. We show by reference to a simple but fundamental example that it is not possible to deduce a unique phase difference from the measurements.

Physical Review A•May 1, 1993•17 citations

Photon counting, quantum phase, and phase-space distributions

Matthias Freyberger, Wolfgang P. Schleich

We analyze a recent proposal for a new phase operator along with the experiment [J. W. Noh, A. Foug\`eres, and L. Mandel, Phys. Rev. Lett. 67, 1426 (1991)] using phase-space functions. We show that the measured dispersion in phase results from a phase distribution given by the appropriate Wigner function integrated over radius. We relate this experiment to a different phase operator [H. Paul, Fortschr. Phys. 22, 657 (1974)] and the integrated Q function.

Physical Review A•Jan 1, 1993•107 citations

Operational approach in the weak-field measurement of polarization fluctuations

Tugrul Hakioglu

The operational approach to the measurement of phase studied by Noh, Fouger\`es, and Mandel [Phys. Rev. A 45, 424 (1992); 46, 2840 (1992); Phys. Rev. Lett. 71, 2579 (1993); Phys. Rev. A 47, 4535 (1993)] is applied to the measurement of the state of polarization of fully polarized light. Operational counterparts of the quantum Stokes parameters are introduced and their fluctuations are examined. It is shown that if the polarized field is weak, the measured fluctuations are influenced not only by the quantum properties of the source field but also that of the measurement. This character is reflected on the measured probability distributions of the parameters of polarization, which are also investigated independently for the fully polarized coherent states and the Fock states as the initial field strength is varied. Finally, connection between the operational approach to the measurement of polarization and the su(2) interferometry is examined.

arXiv:physics/9903018•Physical Review A•Feb 1, 1999•7 citations

Comment on ‘‘Operational approach to the phase of a quantum field’’

Z. Hradil

Interpretational difficulties of a quantum measurement [J. W. Noh, A. Foug\`eres, and L. Mandel, Phys. Rev. A 45, 424 (1992)] are pointed out. The nonunitarity of the respective exponential phase operator reflects an enhanced noise, which can be reduced by discarding ambiguous output data. Consequently, dispersion of such measurements does not represent a meaningful performance measure relevant to the input state. Moreover, the proposed model of quantum phase measurements provides a discrete spectrum of the quantum phase operator, whereas the phase-shift parameter is continuous.

Physical Review A•May 1, 1993•33 citations
Recently, Torgerson and Mandel [Phys. Rev. Lett. 76, 3939 (1996)] have reported a disagreement between two schemes for measuring the phase difference of a pair of optical fields. We analyze these schemes and derive their associated phase-difference probability distributions, including both their strong and weak field limits. Our calculation confirms the main point of Torgerson and Mandel of the non-uniqueness of an operational definition of the phase distribution. We further discuss the role of postselection of data and argue that it cannot meaningfully improve the sensitivity.
The recent operational approach to the phase operator of a quantized electromagnetic field is applied to the problem of determining the phase difference between two weak coherent fields in two different ways. The phase difference is determined directly, and indirectly by measuring each field in turn against the field of a strong local oscillator. We show by measurements with an eight-port interferometer that these two different schemes lead to quite different outcomes for the probability distribution of the phase difference, in agreement with our theory, but in disagreement with most other theoretical approaches.
Generalizing a recent theoretical result obtained by Freyberger and Schleich [Phys. Rev. A 47, R30 (1993)], we show that the phase-measurement scheme proposed and realized by Noh, Foug\`eres, and Mandel [Phys. Rev. Lett. 67, 1426 (1991); Phys. Rev. A 45, 424 (1992)] amounts to measuring the Q function for the light under investigation, provided the reference beam (used for homodyne detection) is a very strong coherent field so that it can be described classically. The desired phase distribution follows from the Q function by averaging over the field amplitude. Since an analysis of an earlier proposal by Bandilla and Paul [Ann. Phys. (Leipzig) 23, 323 (1969)] to measure phase distributions via amplification led to just the same result, a perfect physical equivalence of those two approaches has thus been established.
We address the problem of identifying an operational prescription for quantum phase measurements. As is known, different experiments can lead to different measured phase operators. However, we show that ambiguities of interpretation can arise even if a single experiment, such as that of Noh, Foug\`eres, and Mandel [Phys. Rev. Lett. 67, 1426 (1991)], is chosen as defining a phase measurement. We show by reference to a simple but fundamental example that it is not possible to deduce a unique phase difference from the measurements.
The operational approach to the measurement of phase studied by Noh, Fouger\`es, and Mandel [Phys. Rev. A 45, 424 (1992); 46, 2840 (1992); Phys. Rev. Lett. 71, 2579 (1993); Phys. Rev. A 47, 4535 (1993)] is applied to the measurement of the state of polarization of fully polarized light. Operational counterparts of the quantum Stokes parameters are introduced and their fluctuations are examined. It is shown that if the polarized field is weak, the measured fluctuations are influenced not only by the quantum properties of the source field but also that of the measurement. This character is reflected on the measured probability distributions of the parameters of polarization, which are also investigated independently for the fully polarized coherent states and the Fock states as the initial field strength is varied. Finally, connection between the operational approach to the measurement of polarization and the su(2) interferometry is examined.
Interpretational difficulties of a quantum measurement [J. W. Noh, A. Foug\`eres, and L. Mandel, Phys. Rev. A 45, 424 (1992)] are pointed out. The nonunitarity of the respective exponential phase operator reflects an enhanced noise, which can be reduced by discarding ambiguous output data. Consequently, dispersion of such measurements does not represent a meaningful performance measure relevant to the input state. Moreover, the proposed model of quantum phase measurements provides a discrete spectrum of the quantum phase operator, whereas the phase-shift parameter is continuous.