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

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Phase estimation in quantum optics

Jaroslav Řeháček, Z. Hradil, Miloslav Dušek, Ondřej Haderka, Martin Hendrych

Published Mar 7, 2001• 0 citations
Publisher

Abstract

An experimental comparison of several operational phase concepts is presented. In particular, it is shown that statistically motivated evaluation of experimental data may lead to a significant improvement in phase fitting upon the conventional Noh, Fourgeres and Mandel procedure. The analysis is extended to the asymptotic limit of large intensities, where a strong evidence in favor of multi- dimensional procedures has been found.

DOI
10.1117/12.417812

Related papers

Testing operational phase concepts in quantum optics

Jaroslav Řeháček, Z. Hradil, Miloslav Dušek +2 more

An experimental comparison of several operational phase concepts is presented. In particular, it is shown that statistically motivated evaluation of experimental data may lead to a significant improvement in phase fitting upon the conventional procedure of Noh et al (1993 Phys. Rev. Lett. 71 2579). The analysis is extended to the asymptotic limit of large intensities, where a strong evidence in favour of multi-dimensional estimation procedures has been found.

arXiv:quant-ph/9910092•Journal of Optics B Quantum and Semiclassical Optics•May 11, 2000•9 citations

Testing of quantum phase in matter-wave optics

Jaroslav Řeháček, Z. Hradil, Michael Zawisky +3 more

Various phase concepts may be treated as special cases of the maximum likelihood estimation. For example, the discrete Fourier estimation that actually coincides with the operational phase of Noh, Foug\`eres, and Mandel is obtained for continuous Gaussian signals with phase modulated mean. Since signals in quantum theory are discrete, a prediction different from that given by the Gaussian hypothesis should be obtained as the best fit assuming a discrete Poissonian statistics of the signal. Although the Gaussian estimation gives a satisfactory approximation for fitting the phase distribution of almost any state, the optimal phase estimation offers in certain cases a measurably better performance. This has been demonstrated in a neutron-optical experiment.

arXiv:quant-ph/9904047•Physical Review A•Jul 1, 1999•24 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

Measurement of very small phase fluctuations by means of the operational approach

A. Bandilla

Recently Noh, Fourgeres and Mandel (NFM) have improved the operational approach to the quantum phase problem substantially and measured the phase dispersion of coherent light down to very small means photon numbers of the order of 10(exp -2). This has prompted many other investigations and clarified some important questions in relation to what is actually measured. Although their treatment is rather general, we confine ourselves here to the case of a strong local oscillator (LO) and reproduce their measurement scheme. Surprisingly enough, this simultaneous measurement of the sine and the cosine of the phase difference is completely equivalent to an old proposal to measure the phase after strong linear amplification realized experimentally by the Welling group. The reason for this rests on the fact, that in both cases the results are determined by the Q function of the signal. This was shown for amplification in and for the measurement after beam splitting by Lai and Haus.

•May 1, 1994•0 citations

On the Quantum Phase Operator for Coherent States

Bo-Sture Skagerstam, Bjørn Å Bergsjordet

In papers by Lynch [ Phys. Rev. A 41 2841 (1990)] and Gerry and Urbanski [ Phys. Rev. A 42 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, Büchler and Lifkin [ Phys. Lett. 49A 119 (1974)] are in good agreement with the variance of the Pegg–Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase ϕ 0 of the Pegg–Barnett phase operator. This off-set phase is replaced with the phase of a reference beam in an actual experiment and we show that several choices of such a relative phase can be fitted to the experimental data. We also discuss the Noh, Fougères and Mandel [ Phys. Rev. A 46 2840 (1992)] relative phase experiment in terms of the Pegg–Barnett phase taking post-selection conditions into account.

arXiv:quant-ph/0307156•Physica Scripta•Jan 1, 2004•7 citations

Experimental investigation of Bayesian bounds in multiparameter estimation

Simone Evaldo D’Aurelio, Mauro Valeri, Emanuele Polino +8 more

Abstract Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact and relevance, too. In this respect, Bayesian methods have emerged as an effective and elegant solution, with the perk of incorporating naturally the availability of a priori information. In this article we present an evaluation of Bayesian methods for multiple phase estimation, assessed based on bounds that work beyond the usual limit of large samples assumed in parameter estimation. Importantly, such methods are applied to experimental data generated from the output statistics of a three-arm interferometer seeded by single photons. Our studies provide a blueprint for a more comprehensive data analysis in quantum metrology.

arXiv:2304.06405•Quantum Science and Technology•Feb 2, 2022•5 citations
An experimental comparison of several operational phase concepts is presented. In particular, it is shown that statistically motivated evaluation of experimental data may lead to a significant improvement in phase fitting upon the conventional Noh, Fourgeres and Mandel procedure. The analysis is extended to the asymptotic limit of large intensities, where a strong evidence in favor of multi- dimensional procedures has been found.
Various phase concepts may be treated as special cases of the maximum likelihood estimation. For example, the discrete Fourier estimation that actually coincides with the operational phase of Noh, Foug\`eres, and Mandel is obtained for continuous Gaussian signals with phase modulated mean. Since signals in quantum theory are discrete, a prediction different from that given by the Gaussian hypothesis should be obtained as the best fit assuming a discrete Poissonian statistics of the signal. Although the Gaussian estimation gives a satisfactory approximation for fitting the phase distribution of almost any state, the optimal phase estimation offers in certain cases a measurably better performance. This has been demonstrated in a neutron-optical experiment.
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.
Recently Noh, Fourgeres and Mandel (NFM) have improved the operational approach to the quantum phase problem substantially and measured the phase dispersion of coherent light down to very small means photon numbers of the order of 10(exp -2). This has prompted many other investigations and clarified some important questions in relation to what is actually measured. Although their treatment is rather general, we confine ourselves here to the case of a strong local oscillator (LO) and reproduce their measurement scheme. Surprisingly enough, this simultaneous measurement of the sine and the cosine of the phase difference is completely equivalent to an old proposal to measure the phase after strong linear amplification realized experimentally by the Welling group. The reason for this rests on the fact, that in both cases the results are determined by the Q function of the signal. This was shown for amplification in and for the measurement after beam splitting by Lai and Haus.
In papers by Lynch [ Phys. Rev. A 41 2841 (1990)] and Gerry and Urbanski [ Phys. Rev. A 42 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, Büchler and Lifkin [ Phys. Lett. 49A 119 (1974)] are in good agreement with the variance of the Pegg–Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase ϕ 0 of the Pegg–Barnett phase operator. This off-set phase is replaced with the phase of a reference beam in an actual experiment and we show that several choices of such a relative phase can be fitted to the experimental data. We also discuss the Noh, Fougères and Mandel [ Phys. Rev. A 46 2840 (1992)] relative phase experiment in terms of the Pegg–Barnett phase taking post-selection conditions into account.
Abstract Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact and relevance, too. In this respect, Bayesian methods have emerged as an effective and elegant solution, with the perk of incorporating naturally the availability of a priori information. In this article we present an evaluation of Bayesian methods for multiple phase estimation, assessed based on bounds that work beyond the usual limit of large samples assumed in parameter estimation. Importantly, such methods are applied to experimental data generated from the output statistics of a three-arm interferometer seeded by single photons. Our studies provide a blueprint for a more comprehensive data analysis in quantum metrology.