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

Direct measurement of the Wigner distribution of a traveling field

Celso J. Villas-Bôas, Gilberto Aparecido Prataviera, M. H. Y. Moussa

Published Nov 13, 2001• 9 citations
Publisher

Abstract

We present a technique for direct measurement of the Wigner distribution function of a traveling field, based on a Mach-Zehnder interferometer with a phase-sensitive element. In our scheme, the problem arising from the non-unity efficiency of the photodetectors is circumvented by the optical intensity of the input field for interferometry.

DOI
10.1103/physreva.64.065801

Related papers

The Phase-sensitivity of a Mach-Zehnder Interferometer for Coherent Light

Jong-Tae Shin, Heonoh Kim, Goo-Dong Park +1 more

We have studied the sensitivity of four different phase shift measurement schemes with a Mach-Zehnder interferometer. The input light is considered to be in a coherent state and the detectors are assumed to be ideal with the quantum efficiency of unity. It is shown by direct calculation of the operators corresponding to the measurement schemes that the uncertainty of the phase-shift measurement is limited to the classical one $\frac{1}{\sqrt{m}}$ (m is the average number of the photons in the input state) regardless of the phase-shift measurement schemes.

Journal of the Optical Society of Korea•Mar 1, 1999•10 citations

Phase sensitivity of a quantum Mach-Zehnder interferometer for a coherent state input

Taesoo Kim, Heonoh Kim

The phase sensitivity of a Mach-Zehnder interferometer utilizing quantum entanglement is analyzed for a coherent state input. The results show that the Heisenberg limit in the measurement of the phase shift is obtainable with a coherent input. Moreover, the scheme turns out to be immune to the imperfect detector efficiencies. This suggests another promising route for implementing sub-shot-noise measurement schemes.

Journal of the Optical Society of America B•Mar 12, 2009•5 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

Wigner function of pulsed fields by direct detection

Maria Bondani, Alessia Allevi, Alessandra Andreoni

We present the reconstruction of the Wigner function of some classical pulsed optical states obtained by direct measurement of the detected-photon probability distributions of the state displaced by a coherent field. We use a photodetector endowed with internal gain, which is operated in the non-photon-resolving regime. The measurements are performed up to mesoscopic intensities (up to more than 30 photons per pulse). The method can be applied to characterize nonclassical continuous-variable states.

arXiv:0903.2336•Optics Letters•Apr 27, 2009•31 citations

Robust phase sensitivity in Mach-Zehnder interferometer using photon added and subtracted squeezed coherent state

Shivani Singh, Priya Malpani, Anirban Pathak

For the precision-based measurements, Mach-Zehnder interferometry is a widely used technique. There are various ways to enhance the precision of Mach-Zehnder interferometer (MZI), e.g., having a non-classical input state is one of the ways to enhance the precision of the phase estimation performed by MZI. The phase estimation performed by MZI is investigated here by considering that the input states of MZI are different combinations of photon added and subtracted squeezed coherent states (PASCS and PSSCS). Using quantum Fisher information, it is shown that the use of PASCS in both the input modes of MZI, provides the most precise estimate of the unknown phase. This system is also analyzed in two different measurement scenarios -- single intensity detection (SID) and intensity difference detection (IDD). Systematic analysis has established that the intensity measurement might not be an optimal measurement scheme for phase estimation in MZI as phase and intensity correspond to non-commuting observables. The impact of the photon loss on the MZI-based phase estimation setup is also studied and it is found that PASCS is robust against photon loss, when the loss in MZI is low.

quant-pharXiv:2607.02984•Jul 6, 2026•0 citations

ON THE MEASUREMENT OF THE PHASE DISTRIBUTION OF FIELD STATES

Clodoaldo Valverde, B. Baseia, J. M. C. Malbouisson

A proposal for measuring the phase distribution P(θ) of certain families of field states is presented. This method is based on establishing the connection between the phase distribution and the visibility of the (single-photon) interference in a Mach–Zehnder device. Such a scheme can also be applied to determine relative phases of superposed states.

Modern Physics Letters B•Aug 20, 2002•5 citations
We present a technique for direct measurement of the Wigner distribution function of a traveling field, based on a Mach-Zehnder interferometer with a phase-sensitive element. In our scheme, the problem arising from the non-unity efficiency of the photodetectors is circumvented by the optical intensity of the input field for interferometry.
We have studied the sensitivity of four different phase shift measurement schemes with a Mach-Zehnder interferometer. The input light is considered to be in a coherent state and the detectors are assumed to be ideal with the quantum efficiency of unity. It is shown by direct calculation of the operators corresponding to the measurement schemes that the uncertainty of the phase-shift measurement is limited to the classical one 1m\frac{1}{\sqrt{m}}m​1​ (m is the average number of the photons in the input state) regardless of the phase-shift measurement schemes.
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.
We present the reconstruction of the Wigner function of some classical pulsed optical states obtained by direct measurement of the detected-photon probability distributions of the state displaced by a coherent field. We use a photodetector endowed with internal gain, which is operated in the non-photon-resolving regime. The measurements are performed up to mesoscopic intensities (up to more than 30 photons per pulse). The method can be applied to characterize nonclassical continuous-variable states.
For the precision-based measurements, Mach-Zehnder interferometry is a widely used technique. There are various ways to enhance the precision of Mach-Zehnder interferometer (MZI), e.g., having a non-classical input state is one of the ways to enhance the precision of the phase estimation performed by MZI. The phase estimation performed by MZI is investigated here by considering that the input states of MZI are different combinations of photon added and subtracted squeezed coherent states (PASCS and PSSCS). Using quantum Fisher information, it is shown that the use of PASCS in both the input modes of MZI, provides the most precise estimate of the unknown phase. This system is also analyzed in two different measurement scenarios -- single intensity detection (SID) and intensity difference detection (IDD). Systematic analysis has established that the intensity measurement might not be an optimal measurement scheme for phase estimation in MZI as phase and intensity correspond to non-commuting observables. The impact of the photon loss on the MZI-based phase estimation setup is also studied and it is found that PASCS is robust against photon loss, when the loss in MZI is low.