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

Journal of Modern Optics

Determination of photon statistics and density matrix from double homodyne detection measurements

Th. Richter

Published Aug 1, 1998• 13 citations
Publisher

Abstract

We consider double balanced homodyne detection schemes with and without (local oscillator) phase-randomized detection. We discuss the reconstruction of the photon statistics from phase-randomized measurements. We show how the Wigner function of a photon-number state can be synthesized from phase-randomized double homodyne measurements of two properly prepared field states. Moreover we propose a new procedure to determine the whole density matrix from the Q function. Finally we express the Q function in terms of normally ordered moments and discuss their reconstruction.

DOI
10.1080/09500349808230666

Related papers

On tomographic reconstruction of the quantum state of a two-mode light field

Th. Richter

We consider the state reconstruction of an optical two-mode light field from sum quadrature distributions measured with a single balanced homodyne detector. New explicit formulas for the pattern functions necessary to reconstruct the density matrix of the two-mode field in the photon-number basis are derived. Moreover, an expression of the measured quadature distribution in terms of the two-mode normally ordered moments is given and the determination of the moments from it is discussed.

Journal of Modern Optics•Nov 1, 1997•14 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

Characterizing photon number statistics using conjugate optical homodyne detection

Bing Qi, Pavel Lougovski, Brian P. Williams

We study the problem of determining the photon number statistics of an unknown quantum state using conjugate optical homodyne detection. We quantify the information gain in a single-shot measurement and show that the photon number statistics can be recovered in repeated measurements on an ensemble of identical input states without scanning the phase of the input state or randomizing the phase of the local oscillator used in homodyne detection. We demonstrate how the expectation maximization algorithm and Bayesian inference can be utilized to facilitate the reconstruction and illustrate our approach by conducting experiments to study the photon number distributions of a weak coherent state and a thermal state source.

arXiv:1702.02558•Optics Express•Jan 6, 2020•30 citations

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

Correlation and joint density matrix of two spatial-temporal modes from balanced-homodyne sampling

D. F. McAlister, Michael G. Raymer

A theoretical treatment is given which establishes dual-mode balanced-homodyne detection as a practical and well characterized technique for measuring optical field correlations, photon-number correlations, or the full quantum state of a pair of optical modes. The definition of modes used includes temporal wave packets, Gaussian or other beam profiles, or two-frequency fields. The proposed method allows the measurement of two-time correlations on sub-picosecond scales, the disentangling of the statistics of signal light in two spatially overlapping modes, and the measurement of field correlations, such as squeezing, over 100 THz bandwidths. We show how to estimate from the data the statistical errors on the measured correlations and the density matrix arising from finite data sets, and the errors introduced by using finite numbers of phases and relative amplitudes of the two local oscillator fields.

Journal of Modern Optics•Nov 1, 1997•13 citations

Local sampling of phase-space distributions by cascaded optical homodyning

Z. Kis, T. Kiss, József Janszky +3 more

We propose the determination of phase-space distributions of optical fields by cascaded optical homodyning, where phase-randomized balanced homodyning is used for measuring the output photon-number statistics of an unbalanced homodyne detection scheme. The phase-space point of interest is controlled by the complex amplitude of the local oscillator and a universal sampling function is sufficient for mapping the measured quadrature statistics onto the phase-space distribution.

Physical Review A•Jan 1, 1999•30 citations
We consider double balanced homodyne detection schemes with and without (local oscillator) phase-randomized detection. We discuss the reconstruction of the photon statistics from phase-randomized measurements. We show how the Wigner function of a photon-number state can be synthesized from phase-randomized double homodyne measurements of two properly prepared field states. Moreover we propose a new procedure to determine the whole density matrix from the Q function. Finally we express the Q function in terms of normally ordered moments and discuss their reconstruction.
We study the problem of determining the photon number statistics of an unknown quantum state using conjugate optical homodyne detection. We quantify the information gain in a single-shot measurement and show that the photon number statistics can be recovered in repeated measurements on an ensemble of identical input states without scanning the phase of the input state or randomizing the phase of the local oscillator used in homodyne detection. We demonstrate how the expectation maximization algorithm and Bayesian inference can be utilized to facilitate the reconstruction and illustrate our approach by conducting experiments to study the photon number distributions of a weak coherent state and a thermal state source.
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.
A theoretical treatment is given which establishes dual-mode balanced-homodyne detection as a practical and well characterized technique for measuring optical field correlations, photon-number correlations, or the full quantum state of a pair of optical modes. The definition of modes used includes temporal wave packets, Gaussian or other beam profiles, or two-frequency fields. The proposed method allows the measurement of two-time correlations on sub-picosecond scales, the disentangling of the statistics of signal light in two spatially overlapping modes, and the measurement of field correlations, such as squeezing, over 100 THz bandwidths. We show how to estimate from the data the statistical errors on the measured correlations and the density matrix arising from finite data sets, and the errors introduced by using finite numbers of phases and relative amplitudes of the two local oscillator fields.