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

Rinton Press eBooks

Measuring the individual elements of the optical density matrix

K. L. Pregnell, David Thomas Pegg

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Most methods for experimentally reconstructing the quantum state of light involve determining a quasiprobability distribution such as the Wigner function. In this paper we present a scheme for measuring individual density matrix elements in the photon number state representation. Remarkably, the scheme is simple, involving two beam splitters and a reference field in a coherent state.

Related papers

Measuring the elements of the optical density matrix

K. L. Pregnell, David Thomas Pegg

Most methods for experimentally reconstructing the quantum state of light involve determining a quasiprobability distribution such as the Wigner function. In this paper we present a scheme for measuring individual density matrix elements in the photon number state representation. Remarkably, the scheme is simple, involving two beam splitters and a reference field in a coherent state.

arXiv:quant-ph/0209132•Physical Review A•Jul 22, 2002•12 citations

Complete experimental characterization of the quantum state of a light mode via the Wigner function and the density matrix: application to quantum phase distributions of vacuum and squeezed-vacuum states

D. T. Smithey, M. Beck, J. Cooper +2 more

We have used the recently demonstrated method of optical homodyne tomography (OHT) to measure the Wigner quasiprobability distribution (Wigner function) and the density matrix for both a squeezed-vacuum and a vacuum state of a single spatial-temporal mode of the electromagnetic field. This method consists of measuring a set of probability distributions for many different Hilbert-space representations of the field-quadrature amplitude, using balanced homodyne detection, and then using tomography to obtain the Wigner function. Once the Wigner function is obtained, one can acquire the density matrix, including its complex phase. In the case of a pure state, this technique yields an experimentally determined complex wavefunction, as demonstrated here for the vacuum. The density matrix represents a complete quantum mechanical characterization of the state. From the measured density matrix we have obtained the Pegg–Barnett optical phase distribution, and from the Wigner function, the Wigner optical phase distribution.

Physica Scripta•Jan 1, 1993•156 citations

Direct Probing of Quantum Phase Space by Photon Counting

Konrad Banaszek, K. Wódkiewicz

We propose a very simple experimental setup to measure, via photon counting, the overlap of the Wigner functions characterizing two single mode light beams. We show that this scheme can be applied to determine directly the phase space quasiprobability distribution of the single mode field and in a certain limit the Wigner function can be measured without use of tomographic reconstruction algorithms. The deleterious effects of nonunit photodetector efficiency are analyzed.

arXiv:atom-ph/9603003•Physical Review Letters•Jun 3, 1996•340 citations

Characteristic functions and quantum measurements of optical observables

Yinchieh Lai, H. A. Haus

Three characteristic functions are reviewed along with the quantum theory of linear systems and used to derive the P-representation, Wigner distribution and quasi-probability density of coherent states and squeezed states. The quasiprobability density is interpreted as the outcome of measurements utilising a beamsplitter with homodyne detection. The quasiprobability density concept is generalised and its interpretation in terms of a measurement is presented. The measurement utilises a beam splitter with one of its inputs in a squeezed state followed by two homodyne detectors.

Quantum Optics Journal of the European Optical Society Part B•Dec 1, 1989•84 citations

Measurement of number-phase uncertainty relations of optical fields

D. T. Smithey, M. Beck, J. Cooper +1 more

We have experimentally determined all of the quantities involved in the uncertainty relation for the phase and photon number of a mode of the electromagnetic field when the field mode is in a coherent state of small average photon number. This is accomplished by determining the quantum state of the field using optical homodyne tomography, which uses measured distributions of electric-field quadrature amplitude to determine the Wigner function and hence the density matrix. The measured state is then used to calculate the uncertainty product for the number and phase, as well as the expectation value of the commutator of the number and phase operators. The experimental results agree with the quantum-mechanical predictions. We also present measured phase- and photon-number distributions for these weak coherent states, as well as their measured complex wave functions.

Physical Review A•Oct 1, 1993•190 citations

Wigner function reconstruction by hybrid photodetectors in the linear regime

Maria Bondani, Alessia Allevi, Alessandra Andreoni

We present an experimental scheme for the reconstruction of the Wigner function of optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. We mix, at a beam-splitter, the signal state with a set of coherent probes of known complex amplitudes, and measure the probability distribution of the detected photons for each probe. The Wigner function is given by a suitable sum of those probability distributions. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 22, 2009•2 citations
Most methods for experimentally reconstructing the quantum state of light involve determining a quasiprobability distribution such as the Wigner function. In this paper we present a scheme for measuring individual density matrix elements in the photon number state representation. Remarkably, the scheme is simple, involving two beam splitters and a reference field in a coherent state.
We have used the recently demonstrated method of optical homodyne tomography (OHT) to measure the Wigner quasiprobability distribution (Wigner function) and the density matrix for both a squeezed-vacuum and a vacuum state of a single spatial-temporal mode of the electromagnetic field. This method consists of measuring a set of probability distributions for many different Hilbert-space representations of the field-quadrature amplitude, using balanced homodyne detection, and then using tomography to obtain the Wigner function. Once the Wigner function is obtained, one can acquire the density matrix, including its complex phase. In the case of a pure state, this technique yields an experimentally determined complex wavefunction, as demonstrated here for the vacuum. The density matrix represents a complete quantum mechanical characterization of the state. From the measured density matrix we have obtained the Pegg–Barnett optical phase distribution, and from the Wigner function, the Wigner optical phase distribution.
Three characteristic functions are reviewed along with the quantum theory of linear systems and used to derive the P-representation, Wigner distribution and quasi-probability density of coherent states and squeezed states. The quasiprobability density is interpreted as the outcome of measurements utilising a beamsplitter with homodyne detection. The quasiprobability density concept is generalised and its interpretation in terms of a measurement is presented. The measurement utilises a beam splitter with one of its inputs in a squeezed state followed by two homodyne detectors.
We have experimentally determined all of the quantities involved in the uncertainty relation for the phase and photon number of a mode of the electromagnetic field when the field mode is in a coherent state of small average photon number. This is accomplished by determining the quantum state of the field using optical homodyne tomography, which uses measured distributions of electric-field quadrature amplitude to determine the Wigner function and hence the density matrix. The measured state is then used to calculate the uncertainty product for the number and phase, as well as the expectation value of the commutator of the number and phase operators. The experimental results agree with the quantum-mechanical predictions. We also present measured phase- and photon-number distributions for these weak coherent states, as well as their measured complex wave functions.
We present an experimental scheme for the reconstruction of the Wigner function of optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. We mix, at a beam-splitter, the signal state with a set of coherent probes of known complex amplitudes, and measure the probability distribution of the detected photons for each probe. The Wigner function is given by a suitable sum of those probability distributions. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.