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

Tomographic reconstruction of completely unpolarized light

Th. Richter

Published Jun 1, 1997• 7 citations
Publisher

Abstract

We reconsider the state reconstruction of a completely unpolarized light beam from measured homodyne data. We show that the measurement of the quadrature distribution of any linearly polarized component of the light field is sufficient to determine the quantum state of completely unpolarized light. As a result we reveal the close connection to the reconstruction algorithm in the single-mode case.

DOI
10.1103/physreva.55.4629

Related papers

Optical homodyne tomography of unpolarized light

D. S. Krähmer, Ulf Leonhardt

We show how to reconstruct the quantum state of completely unpolarized light of type I [J. Lehner, U. Leonhardt, and H. Paul, Phys. Rev. A 53, 2727 (1996)] via optical homodyne tomography. Our analysis can be extended to any two-mode situation with complete two-mode randomization and, moreover, to any two-dimensional harmonic oscillator with SU(2) symmetric states. Interestingly, we have shown that the Laplace operator applied to the quadrature distribution of unpolarized photons is orthogonal on the set of these distributions.

Physical Review A•Apr 1, 1997•10 citations

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

Complete characterization of the quantum state of a light mode by using optical homodyne tomography

Michael G. Raymer, D. T. Smithey, M. Beck +1 more

This paper reviews recent experiments in which the density matrix, wavefunction, Wigner distribution, and quantum distributions of optical phase of a light mode were determined by performing tomographic inversion of a set of measured probability distributions for quadrature amplitudes.1

Annual Meeting Optical Society of America•Jan 1, 1993•0 citations

Tomographic reconstruction of the density matrix via pattern functions

Ulf Leonhardt, Henryk Paul, Giacomo Mauro D’Ariano

We propose a general method for reconstructing directly the density matrix of a single light mode in optical homodyne tomography. In our scheme the density matrix 〈a\ensuremath{\Vert}\ensuremath{\rho}^\ensuremath{\Vert}${\mathit{a}}^{\ensuremath{'}}$〉 is obtained by averaging a set of pattern functions ${\mathit{F}}_{\mathit{aa}}^{\ensuremath{'}}$(${\mathit{x}}_{\mathrm{\ensuremath{\theta}}}$,\ensuremath{\theta}) with respect to the homodyne data ${\mathit{x}}_{\mathrm{\ensuremath{\theta}}}$. The functions show the typical features of the quadrature distributions for the corresponding density-matrix elements. It is also possible to compensate the effect of detection losses which requires, however, extra effort in both experimental and numerical precision. We calculate the pattern functions for the coherent-state and Fock representations and study their properties. We believe that our method is the most efficient way for reconstructing the density matrix from homodyne measurements.

Physical Review A•Dec 1, 1995•130 citations

Homodyne Tomography and the Reconstruction of Quantum States of Light

Giacomo Mauro D’Ariano, Lorenzo Maccone, Massimiliano Federico Sacchi

Quantum tomography is a procedure to determine the quantum state of a physical system, or equivalently, to estimate the expectation value of any operator. It consists in appropriately averaging the outcomes of the measurement results of different observables, obtained on identical copies of the same system. Alternatively, it consists in maximizing an appropriate likelihood function defined on the same data. The procedure can be also used to completely characterize an unknown apparatus. Here we focus on the electromagnetic field, where the tomographic observables are obtained from homodyne detection.

arXiv:quant-ph/0507078•IMPERIAL COLLEGE PRESS eBooks•Feb 1, 2007•8 citations

Quantum state reconstruction: a comparison of maximum likelihood and tomographic schemes

Daniel F. V. James, Paul G. Kwiat, Z. Hradil +2 more

Summary form only given. Experimental techniques for measurement of the quantum state of light have been the subject of intensive investigation for some time. Tomographic techniques have been applied to experiments such as the homodyne measurement of the Wigner function of a single mode of light and of the density matrix of the polarization degrees of freedom of a pair of entangled photons. In this technique, the density matrix (or Wigner function) which characterizes the quantum state of the system being measured is found from a linear transformation of experimental data. There are a number of drawbacks to the method, principally in that the recovered state might not, because of experimental noise, correspond to a physical state. For example, density matrices for any quantum state must be Hermitian, positive semi-definite matrices with unit trace. The tomographically measured matrices often fail to be positive semi-definite. To avoid this problem, the maximum likelihood approach to the estimation of quantum states has been developed. We evaluate two different approaches to the maximum likelihood technique, namely defining the likelihood function f as a weighted sum of squared variances from measured data, and defining it in terms of information content. These are compared with results of standard tomographical schemes.

Quantum Electronics and Laser Science Conference•Nov 13, 2002•2 citations
We reconsider the state reconstruction of a completely unpolarized light beam from measured homodyne data. We show that the measurement of the quadrature distribution of any linearly polarized component of the light field is sufficient to determine the quantum state of completely unpolarized light. As a result we reveal the close connection to the reconstruction algorithm in the single-mode case.
We show how to reconstruct the quantum state of completely unpolarized light of type I [J. Lehner, U. Leonhardt, and H. Paul, Phys. Rev. A 53, 2727 (1996)] via optical homodyne tomography. Our analysis can be extended to any two-mode situation with complete two-mode randomization and, moreover, to any two-dimensional harmonic oscillator with SU(2) symmetric states. Interestingly, we have shown that the Laplace operator applied to the quadrature distribution of unpolarized photons is orthogonal on the set of these distributions.
We propose a general method for reconstructing directly the density matrix of a single light mode in optical homodyne tomography. In our scheme the density matrix 〈a\ensuremath{\Vert}\ensuremath{\rho}^\ensuremath{\Vert}${\mathit{a}}^{\ensuremath{'}}$〉 is obtained by averaging a set of pattern functions ${\mathit{F}}_{\mathit{aa}}^{\ensuremath{'}}$(${\mathit{x}}_{\mathrm{\ensuremath{\theta}}}$,\ensuremath{\theta}) with respect to the homodyne data ${\mathit{x}}_{\mathrm{\ensuremath{\theta}}}$. The functions show the typical features of the quadrature distributions for the corresponding density-matrix elements. It is also possible to compensate the effect of detection losses which requires, however, extra effort in both experimental and numerical precision. We calculate the pattern functions for the coherent-state and Fock representations and study their properties. We believe that our method is the most efficient way for reconstructing the density matrix from homodyne measurements.
Quantum tomography is a procedure to determine the quantum state of a physical system, or equivalently, to estimate the expectation value of any operator. It consists in appropriately averaging the outcomes of the measurement results of different observables, obtained on identical copies of the same system. Alternatively, it consists in maximizing an appropriate likelihood function defined on the same data. The procedure can be also used to completely characterize an unknown apparatus. Here we focus on the electromagnetic field, where the tomographic observables are obtained from homodyne detection.
Summary form only given. Experimental techniques for measurement of the quantum state of light have been the subject of intensive investigation for some time. Tomographic techniques have been applied to experiments such as the homodyne measurement of the Wigner function of a single mode of light and of the density matrix of the polarization degrees of freedom of a pair of entangled photons. In this technique, the density matrix (or Wigner function) which characterizes the quantum state of the system being measured is found from a linear transformation of experimental data. There are a number of drawbacks to the method, principally in that the recovered state might not, because of experimental noise, correspond to a physical state. For example, density matrices for any quantum state must be Hermitian, positive semi-definite matrices with unit trace. The tomographically measured matrices often fail to be positive semi-definite. To avoid this problem, the maximum likelihood approach to the estimation of quantum states has been developed. We evaluate two different approaches to the maximum likelihood technique, namely defining the likelihood function f as a weighted sum of squared variances from measured data, and defining it in terms of information content. These are compared with results of standard tomographical schemes.