{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T00:59:54Z","timestamp":1774054794093,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T00:00:00Z","timestamp":1741305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An analytical exploration of the phase decoherence equation of two qubits interacting with a coherent field with dipole\u2013dipole interaction is introduced. The study examines the tradeoff relationships between intrinsic concurrence and first-order coherence in the qubits\u2013cavity system while considering the impacts of decoherence and the interactions among the qubits. We affirm that the relationship between intrinsic concurrence and first-order coherence is valid. Additionally, we demonstrate that the minimum limit of intrinsic concurrence is universally applicable, although the upper limit is typically not. These connections in Heisenberg models can provide a means by which to investigate how quantum resources are allocated in spins, potentially leading to future applications in quantum information processing. It is partially but not completely possible to control the tradeoff relations between intrinsic concurrence and first-order coherence of the two-qubit cavity system; this control might involve actions that influence the system and are reflected in intrinsic concurrence and first-order coherence.<\/jats:p>","DOI":"10.3390\/sym17030400","type":"journal-article","created":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T04:29:59Z","timestamp":1741321799000},"page":"400","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Tradeoff Relations Between Intrinsic Concurrence and First-Order Coherence of Two-Qubit Cavity System: Qubit\u2013Dipole Coupling and Decoherence Effects"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3574-825X","authenticated-orcid":false,"given":"Mostafa","family":"Hashem","sequence":"first","affiliation":[{"name":"Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman"},{"name":"Department of Mathematics, Faculty of Science, Assiut University,  Assiut 71516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7497-8579","authenticated-orcid":false,"given":"A.-B. A.","family":"Mohamed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj 11942, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Assiut University,  Assiut 71516, Egypt"}]},{"given":"H. A.","family":"Hessian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha 1988, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Assiut University,  Assiut 71516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0095-1346","authenticated-orcid":false,"given":"Daniel","family":"Breaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9287-7704","authenticated-orcid":false,"given":"Ala","family":"Amourah","sequence":"additional","affiliation":[{"name":"Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman"},{"name":"Applied Science Research Center, Applied Science Private University, Amman 11937, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4052-391X","authenticated-orcid":false,"given":"Sheza M.","family":"El-Deeb","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,7]]},"reference":[{"key":"ref_1","unstructured":"Nielsen, M.A., and Chuang, I.L. 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