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:1508.02368 · Physical Review A

Normalized Stokes operators for polarization correlations of entangled optical fields

Marek Żukowski, Wiesław Laskowski, Marcin Wieśniak

Published Apr 10, 2017• 16 citations
arXivHTMLPDF

Abstract

Stokes parameters are a standard tool in quantum optics. They involve averaged intensities at exits of polarizers. If the overall measured intensity fluctuates, as, e.g., for states with undefined photon numbers, the instances of its increased value contribute more to the parameters. One can introduce normalized quantum Stokes operators. Operationally, for a given single run of the experiment, their values are differences of measured intensities (or photon numbers) at the two exits of a polarizer divided by their sum. Effects of intensity fluctuations are removed. Switching to normalized Stokes operators results in more sensitive entanglement conditions. We also show a general method of deriving an entanglement indicator for optical fields which use polarization correlations, which starts with any two-qubit entanglement witness. This allows one to vastly expand the family of such indicators.

DOI
10.1103/physreva.95.042113

Related papers

On entanglement of light and Stokes parameters

Marek Żukowski, Wiesław Laskowski, Marcin Wieśniak

Abstract We present a new approach to Stokes parameters, which enables one to see better non-classical properties of bright quantum light, and of undefined overall photon numbers. The crucial difference is as follows. The standard quantum optical Stokes parameters are averages of differences of intensities of light registered at the two exits of polarization analyzers, and one gets their normalized version by dividing them by the average total intensity. The new ones are averages of the registered normalized Stokes parameters, for the duration of the experiment. That is, we redefine each Stokes observable as the difference of photon number operators at the two exits of a polarizing beam splitter multiplied by the inverse of their sum. The vacuum eigenvalue of the operator is defined a zero. We show that with such an approach one can obtain more sensitive entanglement indicators based on polarization measurements.

Physica Scripta•Jul 12, 2016•4 citations

Entanglement Conditions Involving Intensity Correlations of Optical Fields: the Case of Multi-Port Interferometry

J. Ryu, Marcin Marciniak, Marcin Wieśniak +2 more

Normalized quantum Stokes operators introduced in Phys. Rev. A 95, 042113 (2017) enable one to better observe non-classical correlations of entangled states of optical fields with undefined photon numbers.For a given run of an experiment the new quantum Stokes operators are defined by the differences of the measured intensities (or photon numbers) at the exits of a polarizer divided by their sum.It is this ratio that is to be averaged, and not the numerator and the denominator separately, as it is in the conventional approach.The new approach allows to construct more robust entanglement indicators against photon-loss noise, which can detect entangled optical states in situations in which witnesses using standard Stokes operators fail.Here we show an extension of this approach beyond phenomena linked with polarization.We discuss EPR-like experiments involving correlations produced by optical beams in a multi-mode bright squeezed vacuum state.EPR-inspired entanglement conditions for all prime numbers of modes are presented.The conditions are much more resistant to noise due to photon loss than similar ones which employ standard Glauber-like intensity, correlations.

arXiv:1803.00373•Acta Physica Polonica A•Dec 1, 2017•1 citation

Stronger entanglement conditions based on redefined Stokes parameters for quantum optical fields

Marek Żukowski, Wiesław Laskowski, Marcin Wieśniak

We show that a redefined approach to Stokes parameters for quantum optical fields of varying intensities allows one to formulate more sensitive entanglement conditions. The redefined Stokes parameters characterize average measured polarization, and the effects of intensity fluctuations of the fields are removed. Thus their average values are a statistical ensemble averages of polarization, and not averages of intensity at the exits of polarization analyzers (divided by the total average intensity), as it is in the standard case. We show examples of entanglement conditions, which upon change from old to new Stokes parameters detect entanglement for a significantly broader range of states. Our working example is the (bright) squeezed vacuum.

•Aug 10, 2015•0 citations

Simplified quantum optical Stokes observables and Bell’s theorem

Konrad Schlichtholz, Bianka Wołoncewicz, Marek Żukowski

We discuss a simplified form of Stokes operators for quantum optical fields that involve the known concept of binning. Behind polarization analyzer photon numbers (more generally intensities) are measured. We have two outputs, say, for horizontal and vertical polarization. If the value obtained in horizontal output is greater than in vertical one we put 1. Otherwise, we put - 1. For equal photon numbers, we put 0. Such observables do not have all properties of the Stokes operators, but can be employed in Bell type measurements, involving polarization analyzers. They are especially handy for states of undefined number of photons, e.g. squeezed vacuum and their realisation is intuitive. We show that our observables can lead to quite robust violations of associated Bell inequalities. We formulate a strongly supported numerically conjecture that one can observe with this approach violations of local realism for the four mode squeezed vacuum for all pumping powers (i.e. gain values).

arXiv:2112.00084•Scientific Reports•Jun 16, 2022•5 citations

Stokes parameters and Stokes operators

A.S. Shumovsky, Özgür Esat Müstecaplıoğlu, Mithat Ünsal

It is shown that the description of polarization based on quantization of classical Stokes parameters is incomplete in quantum domain. For example, the polarization of the electric dipole radiation of the atomic or molecular transitions is described by nine generators of the SU(3) subalgebra in the Weyl-Heisenberg algebra of photons, in other words, by nine independent Stokes operators instead of four dependent classical Stokes parameters. Although some of the Stokes operators have one and the same averages, they describe absolutely different physical quantities with strongly different quantum fluctuations. The quantum polarization properties of the electric dipole and quadrupole radiation are examined as a function of distance for the near, intermediate, and far zones. Application of results in the near-field optics and quantum entanglement research is discussed.

Laser Physics•Jan 1, 2000•0 citations

The Quantum Polarization of the Single-Mode Excited and Photon Depleted Entangled Even and Odd Squeezed States

elnaz dibakar, Amir Karimi, Mohammad Kazem Tavassoly

In this paper, using the Stokes parameters in classical optics and generalizing them to the Stokes operators in quantum optics, we study the quantum polarization of the “single-mode excited and photon depleted entangled even and odd squeezed states” for different photon numbers of excitation and depletion separately and at last, we compare our results.

انجمن اپتیک و فوتونیک ایران•Mar 15, 2015•0 citations
Stokes parameters are a standard tool in quantum optics. They involve averaged intensities at exits of polarizers. If the overall measured intensity fluctuates, as, e.g., for states with undefined photon numbers, the instances of its increased value contribute more to the parameters. One can introduce normalized quantum Stokes operators. Operationally, for a given single run of the experiment, their values are differences of measured intensities (or photon numbers) at the two exits of a polarizer divided by their sum. Effects of intensity fluctuations are removed. Switching to normalized Stokes operators results in more sensitive entanglement conditions. We also show a general method of deriving an entanglement indicator for optical fields which use polarization correlations, which starts with any two-qubit entanglement witness. This allows one to vastly expand the family of such indicators.
Abstract We present a new approach to Stokes parameters, which enables one to see better non-classical properties of bright quantum light, and of undefined overall photon numbers. The crucial difference is as follows. The standard quantum optical Stokes parameters are averages of differences of intensities of light registered at the two exits of polarization analyzers, and one gets their normalized version by dividing them by the average total intensity. The new ones are averages of the registered normalized Stokes parameters, for the duration of the experiment. That is, we redefine each Stokes observable as the difference of photon number operators at the two exits of a polarizing beam splitter multiplied by the inverse of their sum. The vacuum eigenvalue of the operator is defined a zero. We show that with such an approach one can obtain more sensitive entanglement indicators based on polarization measurements.
Normalized quantum Stokes operators introduced in Phys. Rev. A 95, 042113 (2017) enable one to better observe non-classical correlations of entangled states of optical fields with undefined photon numbers.For a given run of an experiment the new quantum Stokes operators are defined by the differences of the measured intensities (or photon numbers) at the exits of a polarizer divided by their sum.It is this ratio that is to be averaged, and not the numerator and the denominator separately, as it is in the conventional approach.The new approach allows to construct more robust entanglement indicators against photon-loss noise, which can detect entangled optical states in situations in which witnesses using standard Stokes operators fail.Here we show an extension of this approach beyond phenomena linked with polarization.We discuss EPR-like experiments involving correlations produced by optical beams in a multi-mode bright squeezed vacuum state.EPR-inspired entanglement conditions for all prime numbers of modes are presented.The conditions are much more resistant to noise due to photon loss than similar ones which employ standard Glauber-like intensity, correlations.
We show that a redefined approach to Stokes parameters for quantum optical fields of varying intensities allows one to formulate more sensitive entanglement conditions. The redefined Stokes parameters characterize average measured polarization, and the effects of intensity fluctuations of the fields are removed. Thus their average values are a statistical ensemble averages of polarization, and not averages of intensity at the exits of polarization analyzers (divided by the total average intensity), as it is in the standard case. We show examples of entanglement conditions, which upon change from old to new Stokes parameters detect entanglement for a significantly broader range of states. Our working example is the (bright) squeezed vacuum.
We discuss a simplified form of Stokes operators for quantum optical fields that involve the known concept of binning. Behind polarization analyzer photon numbers (more generally intensities) are measured. We have two outputs, say, for horizontal and vertical polarization. If the value obtained in horizontal output is greater than in vertical one we put 1. Otherwise, we put - 1. For equal photon numbers, we put 0. Such observables do not have all properties of the Stokes operators, but can be employed in Bell type measurements, involving polarization analyzers. They are especially handy for states of undefined number of photons, e.g. squeezed vacuum and their realisation is intuitive. We show that our observables can lead to quite robust violations of associated Bell inequalities. We formulate a strongly supported numerically conjecture that one can observe with this approach violations of local realism for the four mode squeezed vacuum for all pumping powers (i.e. gain values).
It is shown that the description of polarization based on quantization of classical Stokes parameters is incomplete in quantum domain. For example, the polarization of the electric dipole radiation of the atomic or molecular transitions is described by nine generators of the SU(3) subalgebra in the Weyl-Heisenberg algebra of photons, in other words, by nine independent Stokes operators instead of four dependent classical Stokes parameters. Although some of the Stokes operators have one and the same averages, they describe absolutely different physical quantities with strongly different quantum fluctuations. The quantum polarization properties of the electric dipole and quadrupole radiation are examined as a function of distance for the near, intermediate, and far zones. Application of results in the near-field optics and quantum entanglement research is discussed.