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

Physical Review A

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

Z. Hradil

Published May 1, 1993• 33 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.47.4532

Related papers

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

Comment on ‘‘Further investigations of the operationally defined quantum phase’’

Z. Hradil, J. Bajer

The normalization of the phase experiment of the scheme 1 in the paper of Noh, Foug\`eres, and Mandel [Phys. Rev. A 46, 2840 (1992)] is inappropriate. The correct treatment of this measurement tends to the same result as in their scheme 2.

Physical Review A•Aug 1, 1993•6 citations

Operational Phase Operators and Hermitian Phase Operators

K. Kakazu

It is shown that there exist two kinds of operational (or measured) phase operators, those of the Hradil type [Phys. Rev. A 47 (1993), 4532], defined on the entire Hilbert space, and those of the Noh-Fougères-Mandel type [Phys. Rev. A 45 (1992), 424], defined only on a subspace. As a consequence, strictly speaking, the Noh-Fougères-Mandel measured phase cannot be defined in the case of, for example, coherent states, squeezed states and the vacuum. The difference between these operators is made clear by using the concept of the Bargmann distance between a quantum state and its “reduced” state. Since Noh et al. did not use the correct variances of the Susskind-Glogower and Pegg-Barnett phase operators when they compared their data with the results predicted through use of these operators, the correct expressions in that case are presented. Comparing the measured operators with the Hermitian phase operator in the extended Susskind-Glogower formalism, we show that the quantum phase given by the Hermitian phase operator is more appropriate than the measured phases. The variance of the Hermitian operator in the vacuum is consistent with the complementarity of the photon number and phase, which implies that the vacuum has a uniform phase distribution. Hradil's measured operator does not have such a property. Although the Noh-Fougères-Mandel operator has such a property in a particular limit, this operator does not represent, in principle, a meaningful measure of the phase measurement in a typical quantum region, because the Bargmann distance becomes large in such a region.

Progress of Theoretical Physics•Oct 1, 2003•0 citations

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

J. W. Noh, A. Fougères, L. Mandeļ

In response to Hradil's Comment [preceding Comment, Phys. Rev. A 47, 4532 (1993)], we point out that his prescription for putting both the cosine and sine equal to zero when the data yield ${\mathit{n}}_{3}$=${\mathit{n}}_{4}$ and ${\mathit{n}}_{5}$=${\mathit{n}}_{6}$ can lead to meaningless results. Moreover, Hradil's Eq. (5) for obtaining ${\mathit{D}}^{2}$ from the measured variance leads to disagreement with experiment. Finally, it is possible to obtain a continuous spectrum of phases with our technique.

Physical Review A•May 1, 1993•16 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

Comment on ‘‘Phase-difference operator’’

David Thomas Pegg, John A. Vaccaro

We examine the operator \ensuremath{\Phi}${\mathrm{^}}_{12}$ proposed by Luis and S\'anchez-Soto [Phys. Rev. A 48, 4702 (1993)] as a possible description of the phase difference between two electromagnetic fields. We show that there is a difficulty in directly representing the phase difference between arbitrary fields by this operator, but conclude that the incorporation of the operator into an alternative definition of phase difference constitutes a valuable alternative approach to the quantum description of phase.

Physical Review A•Jan 1, 1995•14 citations
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.
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.
It is shown that there exist two kinds of operational (or measured) phase operators, those of the Hradil type [Phys. Rev. A 47 (1993), 4532], defined on the entire Hilbert space, and those of the Noh-Fougères-Mandel type [Phys. Rev. A 45 (1992), 424], defined only on a subspace. As a consequence, strictly speaking, the Noh-Fougères-Mandel measured phase cannot be defined in the case of, for example, coherent states, squeezed states and the vacuum. The difference between these operators is made clear by using the concept of the Bargmann distance between a quantum state and its “reduced” state. Since Noh et al. did not use the correct variances of the Susskind-Glogower and Pegg-Barnett phase operators when they compared their data with the results predicted through use of these operators, the correct expressions in that case are presented. Comparing the measured operators with the Hermitian phase operator in the extended Susskind-Glogower formalism, we show that the quantum phase given by the Hermitian phase operator is more appropriate than the measured phases. The variance of the Hermitian operator in the vacuum is consistent with the complementarity of the photon number and phase, which implies that the vacuum has a uniform phase distribution. Hradil's measured operator does not have such a property. Although the Noh-Fougères-Mandel operator has such a property in a particular limit, this operator does not represent, in principle, a meaningful measure of the phase measurement in a typical quantum region, because the Bargmann distance becomes large in such a region.
In response to Hradil's Comment [preceding Comment, Phys. Rev. A 47, 4532 (1993)], we point out that his prescription for putting both the cosine and sine equal to zero when the data yield n3{\mathit{n}}_{3}n3​=n4{\mathit{n}}_{4}n4​ and n5{\mathit{n}}_{5}n5​=n6{\mathit{n}}_{6}n6​ can lead to meaningless results. Moreover, Hradil's Eq. (5) for obtaining D2{\mathit{D}}^{2}D2 from the measured variance leads to disagreement with experiment. Finally, it is possible to obtain a continuous spectrum of phases with our technique.
We examine the operator \ensuremath{\Phi}${\mathrm{^}}_{12}$ proposed by Luis and S\'anchez-Soto [Phys. Rev. A 48, 4702 (1993)] as a possible description of the phase difference between two electromagnetic fields. We show that there is a difficulty in directly representing the phase difference between arbitrary fields by this operator, but conclude that the incorporation of the operator into an alternative definition of phase difference constitutes a valuable alternative approach to the quantum description of phase.