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 International Crisis and Risk Communication Research

Bell’s Measure as a Quantitative Tool in Classical Optical Coherence of Electromagnetic Fields

Kumel H. Kagalwala, Giovanni Di Giuseppe, Ayman F. Abouraddy, Bahaa E. A. Saleh

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We demonstrate an experimental measurement of Bell’s inequality for a classical optical beam with two binary degrees of freedom: polarization and spatial parity; and illustrate the usefulness of this measure as a quantitative tool in classical optical coherence theory.
DOI
10.1364/cleo_qels.2013.qth1e.6

Related papers

Classical Entanglement in Electromagnetic Beams

Kumel H. Kagalwala, Giovanni Di Giuseppe, Ayman F. Abouraddy +1 more

We study classical entanglement for an optical beam with two binary degrees of freedom: polarization and spatial parity; and demonstrate experimentally a measurement of Bell’s inequality and show its usefulness as a quantitative tool in classical optical coherence theory.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2013•0 citations

Bell’s Inequality in Classical Optical Coherence

Kumel H. Kagalwala, Giovanni Di Giuseppe, Ayman F. Abouraddy +1 more

We experimentally test Bell’s inequality using two correlated binary degrees of freedom (DOFs) of an optical beam: polarization and spatial parity; and show that this measure may be used to distinguish between intrinsic incoherence and acquired incoherence.

Frontiers in Optics•Jan 1, 2012•0 citations

Experimental violation of the Leggett-Garg inequality using the polarization of classical light

Wenlei Zhang, Ravi K. Saripalli, Jacob M. Leamer +2 more

In contrast to Bell's inequalities, which test the correlations between multiple spatially separated systems, the Leggett-Garg inequalities test the temporal correlations between measurements of a single system. We experimentally demonstrate the violation of the Leggett-Garg inequality in a classical optical system using only the polarization degree of freedom of a laser beam. Our results show maximal violations of the Leggett-Garg inequality.

arXiv:2012.03940•Physical Review A•Oct 28, 2021•6 citations

Entanglement and Coherence in Classical and Quantum Optics

Kumel H. Kagalwala

We explore the concepts of coherence and entanglement as they apply to both the classical and quantum natures of light. In the classical domain, we take inspiration from the tools and concepts developed in foundational quantum mechanics and quantum information science to gain a better understanding of classical coherence theory of light with multiple degrees of freedom (DoFs). First, we use polarization and spatial parity DoFs to demonstrate the notion of classical entanglement, and show that Bell's measure can serve as a useful tool in distinguishing between classical optical coherence theory. Second, we establish a methodical yet versatile approach called 'optical coherency matrix tomography' for reconstructing the coherency matrix of an electromagnetic beam with multiple DoFs. This technique exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. Third, we report the first experimental measurements of the 4 x 4 coherency matrix associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young's double slit to spatial parity and orbital angular momentum modes. In the quantum domain, we use the modal structure of classical fields to develop qubits and structure Hilbert spaces for use in quantum information processing. Advancing to three-qubit logic gates is an important step towards the success of optical schemes for quantum computing. We experimentally implement a variety of two- and three- qubit, linear and deterministic, single-photon, controlled, quantum logic gates using polarization and spatial parity qubits. Lastly, we demonstrate the implementation of two-qubit single-photon logic using polarization and orbital angular momentum qubits.

Journal of International Crisis and Risk Communication Research•Jan 1, 2015•0 citations

Quantum Tools for Classical Coherence

Ayman F. Abouraddy

The statistical description of optical fields in coherence theory is based on underlying fluctuations originating at the source or during propagation through a random medium. We show that uncertainty (partial coherence) also stems from the act of ignoring a degree of freedom of a beam when observing another degree of freedom classically entangled with it. Specifically, we demonstrate that Bells measure, commonly used in tests of quantum non-locality, is as a quantitative tool that delineates intrinsic incoherence associated with statistical fluctuations from classical entanglement-based incoherence. This demonstrates, more generally, the applicability of concepts from quantum information processing to classical optical coherence theory and optical signal processing.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2013•0 citations

Experimental Bell violations with classical, non-entangled optical fields

J. Gonzales, P. Sánchez, Diego Barberena +3 more

Abstract We report experiments in which the Bell parameter S that enters the Clauser–Horne–Shimony–Holt inequality: ∣ S ∣ ≤ 2 , attains values ∣ S ∣ > 2 . In our experiments, we used two spatially separated optical beams, the electric fields of which were correlated to one another. The amount of correlation was quantified by the spectral degree of coherence η ( α , β ) . This quantity measures the correlation between fields that exist at two distant locations and whose respective polarizations are given in terms of angles α and β , which can be set independently from one another. Such a correlation qualifies for the construction of the Bell parameter S . By changing the amount of field correlation, we could cover a range that goes from ∣ S ∣ < 2 to ∣ S ∣ > 2 . Our experimental findings should provide useful material for the ongoing, theoretical discussions about the quantum–classical border.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 13, 2017•3 citations
We explore the concepts of coherence and entanglement as they apply to both the classical and quantum natures of light. In the classical domain, we take inspiration from the tools and concepts developed in foundational quantum mechanics and quantum information science to gain a better understanding of classical coherence theory of light with multiple degrees of freedom (DoFs). First, we use polarization and spatial parity DoFs to demonstrate the notion of classical entanglement, and show that Bell's measure can serve as a useful tool in distinguishing between classical optical coherence theory. Second, we establish a methodical yet versatile approach called 'optical coherency matrix tomography' for reconstructing the coherency matrix of an electromagnetic beam with multiple DoFs. This technique exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. Third, we report the first experimental measurements of the 4 x 4 coherency matrix associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young's double slit to spatial parity and orbital angular momentum modes. In the quantum domain, we use the modal structure of classical fields to develop qubits and structure Hilbert spaces for use in quantum information processing. Advancing to three-qubit logic gates is an important step towards the success of optical schemes for quantum computing. We experimentally implement a variety of two- and three- qubit, linear and deterministic, single-photon, controlled, quantum logic gates using polarization and spatial parity qubits. Lastly, we demonstrate the implementation of two-qubit single-photon logic using polarization and orbital angular momentum qubits.
The statistical description of optical fields in coherence theory is based on underlying fluctuations originating at the source or during propagation through a random medium. We show that uncertainty (partial coherence) also stems from the act of ignoring a degree of freedom of a beam when observing another degree of freedom classically entangled with it. Specifically, we demonstrate that Bells measure, commonly used in tests of quantum non-locality, is as a quantitative tool that delineates intrinsic incoherence associated with statistical fluctuations from classical entanglement-based incoherence. This demonstrates, more generally, the applicability of concepts from quantum information processing to classical optical coherence theory and optical signal processing.
Abstract We report experiments in which the Bell parameter S that enters the Clauser–Horne–Shimony–Holt inequality: ∣ S ∣ ≤ 2 , attains values ∣ S ∣ > 2 . In our experiments, we used two spatially separated optical beams, the electric fields of which were correlated to one another. The amount of correlation was quantified by the spectral degree of coherence η ( α , β ) . This quantity measures the correlation between fields that exist at two distant locations and whose respective polarizations are given in terms of angles α and β , which can be set independently from one another. Such a correlation qualifies for the construction of the Bell parameter S . By changing the amount of field correlation, we could cover a range that goes from ∣ S ∣ < 2 to ∣ S ∣ > 2 . Our experimental findings should provide useful material for the ongoing, theoretical discussions about the quantum–classical border.