© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1506.07112

Quantifying classical entanglement using polarimetry: Spatially-inhomogeneously polarized beams

Samlan Chandran Thodika, Nirmal K. Viswanathan

Published Jun 21, 2015• 6 citations

Abstract

Generation of spatially inhomogeneously polarized (SIP) beams due to polarization spatial mode nonseparability is demonstrated using a polarization Sagnac interferometer. Counter propagating horizontal (H) and vertical (V) polarized Laguerre Gaussian beams of opposite topological charges(LG01)corresponding to the two binary degrees of freedom (DoF) are coherently superposed in the interferometer. Quantum inspired entanglement witness and quantification such as Bell state measurement, violation of CHSH form of Bells inequality and concurrence measurements are experimentally measured to establish nonseparability between the two DoF. As the SIP beams are equivalent to bipartite pure states, point wise Stokes polarimetry measurements are used to calculate the reduced coherency matrix corresponding to polarization DoF. Using these we calculate the linear entropy and maximized Bells measure to quantify the degree of entanglement of the SIP beams.

DOI: 10.48550/arxiv.1506.07112

Related papers

Entanglement and classical nonseparability convertible from orthogonal polarizations

Minghui Li, Wei Wang, Zikang Tang +1 more

The nonclassicality of a macroscopic single-mode optical superposition state is potentially convertible into entanglement, when the state is mixed with the vacuum on a beam splitter. Considering light beams with polarization degree of freedom in Euclidean space as coherent product states in a bipartite Hilbert space, we propose a method to convert the two orthogonal polarizations into simultaneous entanglement and classical nonseparability through nonclassicality in the superpositions of coherent and displaced Fock states. Equivalent Bell state emerges from the resulted superpositions and the proportion of mixed entanglement and nonseparablity is determined by the displacement amplitudes along the polarization directions. We characterize the state nonclassicality via features in Wigner distributions and propose an experimental method for generating these states and measuring them via homodyne tomography.

arXiv:2310.04065•Oct 6, 2023•0 citations

Entanglement and classical nonseparability convertible from orthogonal polarizations

Minghui Li, Wei Wang, Zikang Tang +1 more

The nonclassicality of a macroscopic single-mode optical superposition state is potentially convertible into entanglement, when the state is mixed with the vacuum on a beam splitter. Considering light beams with polarization degree of freedom in Euclidean space as coherent product states in a bipartite Hilbert space, we propose a method to convert the two orthogonal polarizations into simultaneous entanglement and classical nonseparability through nonclassicality in the superpositions of coherent and displaced Fock states. Equivalent Bell state emerges from the resulted superpositions and the proportion of mixed entanglement and nonseparablity is determined by the displacement amplitudes along the polarization directions. We characterize the state nonclassicality via features in Wigner distributions and propose an experimental method for generating these states and measuring them via homodyne tomography.

Optics Express•Jul 25, 2024•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

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

Measuring the nonseparability of vector vortex beams

Melanie G. McLaren, Thomas Konrad, Andrew Forbes

Vector beams have the defining property of nonseparable spatial and polarization degrees of freedom and are now routinely generated in the laboratory and used in a myriad of applications. Here we exploit the nonseparability of such beams, akin to entanglement of quantum states, to apply tools traditionally associated with quantum measurements to these classical fields. We find that the entanglement entropy is a proxy for the average degree of polarization and thus provides a single number for the vector nature of such beams. In addition to providing tools for the analysis of vector beams, we also explore the concept of classical entanglement to explain why these tools are appropriate in the first place.

Physical Review A•Aug 18, 2015•209 citations

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

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

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.

Journal of International Crisis and Risk Communication Research•Jan 1, 2013•0 citations

Generation of spatially inhomogeneously polarized (SIP) beams due to polarization spatial mode nonseparability is demonstrated using a polarization Sagnac interferometer. Counter propagating horizontal (H) and vertical (V) polarized Laguerre Gaussian beams of opposite topological charges(LG01)corresponding to the two binary degrees of freedom (DoF) are coherently superposed in the interferometer. Quantum inspired entanglement witness and quantification such as Bell state measurement, violation of CHSH form of Bells inequality and concurrence measurements are experimentally measured to establish nonseparability between the two DoF. As the SIP beams are equivalent to bipartite pure states, point wise Stokes polarimetry measurements are used to calculate the reduced coherency matrix corresponding to polarization DoF. Using these we calculate the linear entropy and maximized Bells measure to quantify the degree of entanglement of the SIP beams.

The nonclassicality of a macroscopic single-mode optical superposition state is potentially convertible into entanglement, when the state is mixed with the vacuum on a beam splitter. Considering light beams with polarization degree of freedom in Euclidean space as coherent product states in a bipartite Hilbert space, we propose a method to convert the two orthogonal polarizations into simultaneous entanglement and classical nonseparability through nonclassicality in the superpositions of coherent and displaced Fock states. Equivalent Bell state emerges from the resulted superpositions and the proportion of mixed entanglement and nonseparablity is determined by the displacement amplitudes along the polarization directions. We characterize the state nonclassicality via features in Wigner distributions and propose an experimental method for generating these states and measuring them via homodyne tomography.

The nonclassicality of a macroscopic single-mode optical superposition state is potentially convertible into entanglement, when the state is mixed with the vacuum on a beam splitter. Considering light beams with polarization degree of freedom in Euclidean space as coherent product states in a bipartite Hilbert space, we propose a method to convert the two orthogonal polarizations into simultaneous entanglement and classical nonseparability through nonclassicality in the superpositions of coherent and displaced Fock states. Equivalent Bell state emerges from the resulted superpositions and the proportion of mixed entanglement and nonseparablity is determined by the displacement amplitudes along the polarization directions. We characterize the state nonclassicality via features in Wigner distributions and propose an experimental method for generating these states and measuring them via homodyne tomography.

Vector beams have the defining property of nonseparable spatial and polarization degrees of freedom and are now routinely generated in the laboratory and used in a myriad of applications. Here we exploit the nonseparability of such beams, akin to entanglement of quantum states, to apply tools traditionally associated with quantum measurements to these classical fields. We find that the entanglement entropy is a proxy for the average degree of polarization and thus provides a single number for the vector nature of such beams. In addition to providing tools for the analysis of vector beams, we also explore the concept of classical entanglement to explain why these tools are appropriate in the first place.