https://doi.org/10.1140/epjd/s10053-025-01082-y
Regular Article - Quantum Optics
Characterizing the generalized Einstein–Podolsky–Rosen state and extensions
1
Department of Physics, Jamia Millia Islamia, 110025, New Delhi, India
2
Centre for Theoretical Physics, Jamia Millia Islamia, 110025, New Delhi, India
Received:
21
May
2025
Accepted:
27
September
2025
Published online:
22
October
2025
In their seminal paper, Einstein, Podolsky, and Rosen (EPR) had introduced a momentum-entangled state for two particles. That state, referred to as the EPR state, has been widely used in studies on entangled particles with continuous degrees of freedom. Later that state was generalized to a form that allows varying degree of entanglement, known as the generalized EPR state. In a suitable limit it reduces to the EPR state. The generalized EPR state is theoretically analyzed here and its entanglement quantified in terms of a recently introduced generalized entanglement measure. This state can also be applied to entangled photons produced from spontaneous parametric down-conversion (SPDC). The present analysis is then used in quantifying the entanglement of photons produced from the SPDC process, in terms of certain experimental parameters. A comparison is also made with the Schmidt number, which is normally used as an entanglement measure in such situations. A procedure for experimentally determining the entanglement of SPDC photons has also been described. Furthermore, an additional state exhibiting non-Gaussian entanglement has been examined, and its entanglement has been quantified.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
