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/9708017 · Talk given at

Exponential Moments of Canonical Phase: Homodyne Measurements

Tomáš Opatrný, Mohammed Dakna, D. -G. Welsch

Published Aug 9, 1997• 0 citations
arXivHTMLPDF

Abstract

A method for direct sampling of the exponential moments of canonical phase from the data recorded in balanced homodyne detection is presented. Analytical expressions for the sampling functions are shown which are valid for arbitrary states. A numerical simulation illustrates the applicability of the method and compares it with the direct measurement of phase by means of double homodyning.

DOI
10.48550/arxiv.quant-ph/9708017

Related papers

Direct sampling of exponential phase moments of smoothed Wigner functions

Jaromı́r Fiurášek

We investigate exponential phase moments of the s-parametrized quasidistributions (smoothed Wigner functions). We show that the knowledge of these moments as functions of s provides, together with photon-number statistics, a complete description of the quantum state. We demonstrate that the exponential phase moments can be directly sampled from the data recorded in balanced homodyne detection and we present simple expressions for the sampling kernels. The phase moments are Fourier coefficients of phase distributions obtained from the quasidistributions via integration over the radial variable in polar coordinates. We performed Monte Carlo simulations of the homodyne detection and we demonstrate the feasibility of direct sampling of the moments and subsequent reconstruction of the phase distribution.

arXiv:quant-ph/0005120•Physical Review A•Jun 16, 2000•2 citations

Homodyne measurement of exponential phase moments for quantum-phase reconstruction

Mohammed Dakna, Gerd Breitenbach, J. Mlynek +3 more

We directly sample the exponential moments of the canonical phase for various quantum states from the homodyne output. The method enables us to study the phase properties experimentally, without making the detour via reconstructing the density matrix or the Wigner function and calculating the phase statistics from them. In particular, combing the measurement with a measurement of the photon-number variance, we verify fundamental number-phase uncertainty.

arXiv:quant-ph/9802023•Feb 9, 1998•0 citations

Sampling the canonical phase from phase-space functions

Jaromı́r Fiurášek, Mohammed Dakna, Tomáš Opatrný +1 more

We discuss the possibility of sampling exponential moments of the canonical phase from the s-parametrized phase-space functions. We show that the sampling kernels exist and are well-behaved for any $s>\ensuremath{-}1,$ whereas for $s=\ensuremath{-}1$ the kernels diverge in the origin. In spite of that, we show that the phase-space moments can be sampled with any predefined accuracy from the Q function measured in the double-homodyne scheme with perfect detectors. We discuss the effect of imperfect detection and address sampling schemes using other measurable phase-space functions. Finally, we discuss the problem of sampling the canonical phase distribution itself.

arXiv:quant-ph/0004059•Physical Review A•Nov 14, 2000•2 citations

Homodyning the exponential phase moments of smoothed Wigner functions

Thomas Richter, Matteo G. A. Paris

We show that the exponential phase moments associated with the s-ordered generalized Wigner function can be sampled from homodyne data for s 0. The tomographic sampling functions are evaluated for non-unit homodyne quantum efficiency, and the statistical reliability of the reconstruction is tested by Monte Carlo simulated experiments. The reconstruction of the s-ordered phase distribution from sampled moments is discussed, and the reduction of statistical fluctuations by adaptive techniques is also analysed.

Journal of Optics B Quantum and Semiclassical Optics•Feb 1, 2001•1 citation

Homodyne detection for direct sampling of the London phase distribution

Mohammed Dakna, L. Knöll, D.‐G. Welsch

The problem of direct sampling of the London phase distribution in balanced homodyning is studied. For this purpose a continuous sequence of parametrized phase distributions tending to the London phase distribution as the sequence parameter goes to zero is considered. From the integral relation of the parametrized phase distributions to the field-strength distributions measurable in homodyne detection, it is seen that for any non-vanishing sequence parameter the associated phase distribution can be obtained by direct sampling from the measured data. This offers a possibility of asymptotically measuring the London phase distribution. Numerical simulations show that it can be obtained with sufficiently high accuracy.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Jun 1, 1997•3 citations

Homodyne detection for measuring coherent phase state distributions

Mohammed Dakna, L. Knöll, D.‐G. Welsch

Using coherent phase states, parameterized phase state distributions for a single-mode radiation field are introduced and their integral relation to the phase-parameterized field-strength distributions is studied. The integral kernel is evaluated and the problem of direct sampling of the coherent phase state distributions using balanced homodyne detection is considered. Numerical simulations show that when the value of the smoothing parameter is not too small the coherent phase state distributions can be obtained with sufficiently well accuracy. With decreasing value of the smoothing parameter the determination of the coherent phase state distributions may be an effort, because both the numerical calculation of the sampling function and the measurement of the field-strength distributions are required to be performed with drastically increasing accuracy.

arXiv:quant-ph/9603027•Mar 25, 1996•0 citations
A method for direct sampling of the exponential moments of canonical phase from the data recorded in balanced homodyne detection is presented. Analytical expressions for the sampling functions are shown which are valid for arbitrary states. A numerical simulation illustrates the applicability of the method and compares it with the direct measurement of phase by means of double homodyning.
We investigate exponential phase moments of the s-parametrized quasidistributions (smoothed Wigner functions). We show that the knowledge of these moments as functions of s provides, together with photon-number statistics, a complete description of the quantum state. We demonstrate that the exponential phase moments can be directly sampled from the data recorded in balanced homodyne detection and we present simple expressions for the sampling kernels. The phase moments are Fourier coefficients of phase distributions obtained from the quasidistributions via integration over the radial variable in polar coordinates. We performed Monte Carlo simulations of the homodyne detection and we demonstrate the feasibility of direct sampling of the moments and subsequent reconstruction of the phase distribution.
We discuss the possibility of sampling exponential moments of the canonical phase from the s-parametrized phase-space functions. We show that the sampling kernels exist and are well-behaved for any $s>\ensuremath{-}1,$ whereas for $s=\ensuremath{-}1$ the kernels diverge in the origin. In spite of that, we show that the phase-space moments can be sampled with any predefined accuracy from the Q function measured in the double-homodyne scheme with perfect detectors. We discuss the effect of imperfect detection and address sampling schemes using other measurable phase-space functions. Finally, we discuss the problem of sampling the canonical phase distribution itself.
We show that the exponential phase moments associated with the s-ordered generalized Wigner function can be sampled from homodyne data for s 0. The tomographic sampling functions are evaluated for non-unit homodyne quantum efficiency, and the statistical reliability of the reconstruction is tested by Monte Carlo simulated experiments. The reconstruction of the s-ordered phase distribution from sampled moments is discussed, and the reduction of statistical fluctuations by adaptive techniques is also analysed.
The problem of direct sampling of the London phase distribution in balanced homodyning is studied. For this purpose a continuous sequence of parametrized phase distributions tending to the London phase distribution as the sequence parameter goes to zero is considered. From the integral relation of the parametrized phase distributions to the field-strength distributions measurable in homodyne detection, it is seen that for any non-vanishing sequence parameter the associated phase distribution can be obtained by direct sampling from the measured data. This offers a possibility of asymptotically measuring the London phase distribution. Numerical simulations show that it can be obtained with sufficiently high accuracy.
Using coherent phase states, parameterized phase state distributions for a single-mode radiation field are introduced and their integral relation to the phase-parameterized field-strength distributions is studied. The integral kernel is evaluated and the problem of direct sampling of the coherent phase state distributions using balanced homodyne detection is considered. Numerical simulations show that when the value of the smoothing parameter is not too small the coherent phase state distributions can be obtained with sufficiently well accuracy. With decreasing value of the smoothing parameter the determination of the coherent phase state distributions may be an effort, because both the numerical calculation of the sampling function and the measurement of the field-strength distributions are required to be performed with drastically increasing accuracy.