{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T10:53:34Z","timestamp":1790765614554,"version":"4.1.0"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T00:00:00Z","timestamp":1655164800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T00:00:00Z","timestamp":1655164800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-022-03540-7","type":"journal-article","created":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T21:02:51Z","timestamp":1655240571000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Generation of enhanced entanglement of directly and indirectly coupled modes in a two-cavity magnomechanical system"],"prefix":"10.1007","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8777-7928","authenticated-orcid":false,"given":"Amjad","family":"Sohail","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali","family":"Hassan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8168-6777","authenticated-orcid":false,"given":"Rizwan","family":"Ahmed","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8174-3775","authenticated-orcid":false,"given":"Chang-shui","family":"Yu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,6,14]]},"reference":[{"issue":"3","key":"3540_CR1","doi-asserted-by":"publisher","first-page":"032327","DOI":"10.1103\/PhysRevA.96.032327","volume":"96","author":"YC Su","year":"2017","unstructured":"Su, Y.C., Wu, S.T.: Entanglement enhancement through multirail noise reduction for continuous-variable measurement-based. Phys. Rev. A 96(3), 032327 (2017)","journal-title":"Phys. Rev. A"},{"key":"3540_CR2","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/aa869c","volume":"92","author":"R Ahmed","year":"2017","unstructured":"Ahmed, R., Qamar, S.: Optomechanical entanglement via non-degenerate parametric interactions. Phys. Scr. 92, 105101 (2017)","journal-title":"Phys. Scr."},{"key":"3540_CR3","doi-asserted-by":"publisher","first-page":"1391","DOI":"10.1103\/RevModPhys.86.1391","volume":"86","author":"M Aspelmeyer","year":"2014","unstructured":"Aspelmeyer, M., Kippenberg, T.J., Marquardt, F.: Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014)","journal-title":"Rev. Mod. Phys."},{"issue":"3","key":"3540_CR4","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ab4dde","volume":"95","author":"A Sohail","year":"2020","unstructured":"Sohail, A., Ahmed, R., Yu, C.S., Munir, T.: Enhanced entanglement induced by Coulomb interaction in coupled optomechanical systems. Phys. Scr. 95(3), 035108 (2020)","journal-title":"Phys. Scr."},{"issue":"23","key":"3540_CR5","doi-asserted-by":"publisher","first-page":"230504","DOI":"10.1103\/PhysRevLett.94.230504","volume":"94","author":"HK Lo","year":"2005","unstructured":"Lo, H.K., Ma, X.F., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94(23), 230504 (2005)","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"3540_CR6","doi-asserted-by":"publisher","first-page":"032312","DOI":"10.1103\/PhysRevA.97.032312","volume":"97","author":"M Pivoluska","year":"2018","unstructured":"Pivoluska, M., Huber, M., Malik, M.: Layered quantum key distribution. Phys. Rev. A 97(3), 032312 (2018)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"3540_CR7","doi-asserted-by":"publisher","first-page":"040505","DOI":"10.1103\/PhysRevLett.93.040505","volume":"93","author":"T Schaetz","year":"2004","unstructured":"Schaetz, T., et al.: Quantum dense coding with atomic qubits. Phys. Rev. Lett. 93(4), 040505 (2004)","journal-title":"Phys. Rev. Lett."},{"issue":"21","key":"3540_CR8","doi-asserted-by":"publisher","first-page":"210501","DOI":"10.1103\/PhysRevLett.93.210501","volume":"93","author":"D Bru\u00df","year":"2004","unstructured":"Bru\u00df, D., et al.: Distributed quantum dense coding. Phys. Rev. Lett. 93(21), 210501 (2004)","journal-title":"Phys. Rev. Lett."},{"issue":"7","key":"3540_CR9","doi-asserted-by":"publisher","first-page":"070505","DOI":"10.1103\/PhysRevLett.123.070505","volume":"123","author":"YH Luo","year":"2019","unstructured":"Luo, Y.H., et al.: Quantum teleportation in high dimension. Phys. Rev. Lett. 123(7), 070505 (2019)","journal-title":"Phys. Rev. Lett."},{"issue":"7","key":"3540_CR10","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1080\/09500340902767421","volume":"56","author":"R Ul-Islam","year":"2009","unstructured":"Ul-Islam, R., Ikram, M., Ahmed, R., Khosa, A.H., Saif, F.: Atomic state teleportation: from internal to external degrees of freedom. J. Mod. Opt. 56(7), 875\u2013880 (2009)","journal-title":"J. Mod. Opt."},{"key":"3540_CR11","doi-asserted-by":"publisher","first-page":"250402","DOI":"10.1103\/PhysRevLett.115.250402","volume":"115","author":"K Lynden","year":"2015","unstructured":"Lynden, K., et al.: Strong loophole-free test of local realism. Phys. Rev. Lett. 115, 250402 (2015)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR12","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1038\/nature15759","volume":"526","author":"B Hensen","year":"2015","unstructured":"Hensen, B., et al.: Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682\u2013686 (2015)","journal-title":"Nature"},{"key":"3540_CR13","doi-asserted-by":"publisher","first-page":"33802","DOI":"10.1038\/srep33802","volume":"6","author":"II Arkhipov","year":"2016","unstructured":"Arkhipov, I.I., Perina, J., Jr., Haderka, O., Allevi, A., Bondani, M.: Entanglement and nonclassicality in four-mode Gaussian states generated via parametric down-conversion and frequency up-conversion. Sci. Rep. 6, 33802 (2016)","journal-title":"Sci. Rep."},{"key":"3540_CR14","doi-asserted-by":"publisher","first-page":"053601","DOI":"10.1103\/PhysRevLett.94.053601","volume":"94","author":"X Li","year":"2005","unstructured":"Li, X., Voss, P.. L., Sharping, J.. E., Kumar, P.: Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band. Phys. Rev. Lett. 94, 053601 (2005)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR15","doi-asserted-by":"publisher","first-page":"2513","DOI":"10.1103\/PhysRevLett.84.2513","volume":"84","author":"O Benson","year":"2000","unstructured":"Benson, O., Santori, C., Pelton, M., Yamamoto, Y.: Regulated and entangled photons from a single quantum dot. Phys. Rev. Lett. 84, 2513 (2000)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR16","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1038\/nature07751","volume":"457","author":"AM Marino","year":"2009","unstructured":"Marino, A.M., Pooser, R.C., Boyer, V., Lett, P.D.: Tunable delay of Einstein\u2013Podolsky\u2013Rosen enatnglement. Nature (London) 457, 859 (2009)","journal-title":"Nature (London)"},{"key":"3540_CR17","doi-asserted-by":"publisher","first-page":"123902","DOI":"10.1103\/PhysRevLett.108.123902","volume":"108","author":"N Bergeal","year":"2012","unstructured":"Bergeal, N., Schackert, F., Frunzio, L., Devoret, M.H.: Two-mode correlation of microwave quantum noise generated by parametric down-conversion. Phys. Rev. Lett. 108, 123902 (2012)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR18","doi-asserted-by":"publisher","first-page":"31862","DOI":"10.1364\/OE.404522","volume":"28","author":"Zhi-Bo Yang","year":"2020","unstructured":"Yang, Zhi-Bo., et al.: Entanglement enhanced by Kerr nonlinearity in a cavity-optomagnonics system. Opt. Express 28, 31862 (2020)","journal-title":"Opt. Express"},{"key":"3540_CR19","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1103\/PhysRev.73.155","volume":"73","author":"C Kittel","year":"1948","unstructured":"Kittel, C.: On the theory of ferromagnetic resonance absorption. Phys. Rev. 73, 155 (1948)","journal-title":"Phys. Rev."},{"key":"3540_CR20","doi-asserted-by":"publisher","first-page":"127003","DOI":"10.1103\/PhysRevLett.111.127003","volume":"111","author":"H Huebl","year":"2013","unstructured":"Huebl, H., et al.: High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids. Phys. Rev. Lett. 111, 127003 (2013)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR21","doi-asserted-by":"publisher","first-page":"227201","DOI":"10.1103\/PhysRevLett.114.227201","volume":"114","author":"L Bai","year":"2015","unstructured":"Bai, L., Harder, M., Chen, Y.P., Fan, X., Xiao, J.Q., Hu, C.M.: Spin pumping in electrodynamically coupled magnon\u2013photon systems. Phys. Rev. Lett. 114, 227201 (2015)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR22","doi-asserted-by":"publisher","first-page":"105101","DOI":"10.1088\/1402-4896\/ac0c97","volume":"96","author":"C Castro","year":"2021","unstructured":"Castro, C., Ara\u00fajo, M.R., Cruz, C.: Entanglement dynamics of a dc SQUID interacting with a single mode radiation field. Phys. Scr. 96, 105101 (2021)","journal-title":"Phys. Scr."},{"key":"3540_CR23","doi-asserted-by":"publisher","first-page":"203601","DOI":"10.1103\/PhysRevLett.121.203601","volume":"121","author":"J Li","year":"2018","unstructured":"Li, J., Zhu, S.Y., Agarwal, G.S.: Magnon\u2013photon\u2013phonon entanglement in cavity magnomechanics. Phys. Rev. Lett. 121, 203601 (2018)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR24","doi-asserted-by":"publisher","first-page":"213604","DOI":"10.1103\/PhysRevLett.124.213604","volume":"124","author":"M Yu","year":"2020","unstructured":"Yu, M., Shen, H., Li, J.: Magnetostrictively induced stationary entanglement between two microwave fields. Phys. Rev. Lett. 124, 213604 (2020)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR25","doi-asserted-by":"publisher","first-page":"021801(R)","DOI":"10.1103\/PhysRevA.99.021801","volume":"99","author":"J Li","year":"2019","unstructured":"Li, J., Zhu, S.Y., Agarwal, G.S.: Squeezed states of magnons and phonons in cavity magnomechanics. Phys. Rev. A 99, 021801(R) (2019)","journal-title":"Phys. Rev. A"},{"key":"3540_CR26","doi-asserted-by":"publisher","first-page":"024005","DOI":"10.1088\/2058-9565\/abd982","volume":"6","author":"J Li","year":"2021","unstructured":"Li, J., Gr\u00f6blacher, S.: Entangling the vibrational modes of two massive ferromagnetic spheres using cavity magnomechanics. Quantum Sci. Technol. 6, 024005 (2021)","journal-title":"Quantum Sci. Technol."},{"key":"3540_CR27","doi-asserted-by":"publisher","first-page":"31862","DOI":"10.1364\/OE.404522","volume":"28","author":"ZB Yang","year":"2020","unstructured":"Yang, Z.B., et al.: Entanglement enhanced by Kerr nonlinearity in a cavity-optomagnonics system. Opt. Exp. 28, 31862 (2020)","journal-title":"Opt. Exp."},{"key":"3540_CR28","doi-asserted-by":"publisher","first-page":"e1501286","DOI":"10.1126\/sciadv.1501286","volume":"2","author":"X Zhang","year":"2016","unstructured":"Zhang, X., Zou, C.L., Jiang, L., Tang, H.X.: Cavity magnomechanics. Sci. Adv. 2, e1501286 (2016)","journal-title":"Sci. Adv."},{"key":"3540_CR29","doi-asserted-by":"publisher","first-page":"836","DOI":"10.1103\/PhysRev.110.836","volume":"110","author":"C Kittel","year":"1958","unstructured":"Kittel, C.: Interaction of spin waves and ultrasonic waves in ferromagnetic crystals. Phys. Rev. 110, 836 (1958)","journal-title":"Phys. Rev."},{"key":"3540_CR30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.101.125404","volume":"101","author":"C Gonzalez-Ballestero","year":"2020","unstructured":"Gonzalez-Ballestero, C., H\u00fcmmer, D., Gieseler, J., Romero-Isart, O.: Theory of quantum acoustomagnonics and acoustomechanics with a micromagnet. Phys. Rev. B 101, 125404 (2020)","journal-title":"Phys. Rev. B"},{"key":"3540_CR31","doi-asserted-by":"publisher","first-page":"083603","DOI":"10.1103\/PhysRevLett.113.083603","volume":"113","author":"Y Tabuchi","year":"2014","unstructured":"Tabuchi, Y., Ishino, S., Ishikawa, T., Yamazaki, R., Usami, K., Nakamura, Y.: Hybridizing ferromagnetic magnons and microwave photons in the quantum limit. Phys. Rev. Lett. 113, 083603 (2014)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR32","doi-asserted-by":"publisher","first-page":"054002","DOI":"10.1103\/PhysRevApplied.2.054002","volume":"2","author":"M Goryachev","year":"2014","unstructured":"Goryachev, M., Farr, W.G., Creedon, D.L., Fan, Y., Kostylev, M., Tobar, M.E.: High-cooperativity cavity QED with magnons at microwave frequencies. Phys. Rev. Appl. 2, 054002 (2014)","journal-title":"Phys. Rev. Appl."},{"key":"3540_CR33","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/PhysRevLett.121.203601 for additional proofs, which includes Refs. [34,35]"},{"key":"3540_CR34","doi-asserted-by":"publisher","first-page":"2726","DOI":"10.1103\/PhysRevLett.84.2726","volume":"84","author":"R Simon","year":"2000","unstructured":"Simon, R.: Peres\u2013Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2726 (2000)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR35","doi-asserted-by":"publisher","first-page":"1098","DOI":"10.1103\/PhysRev.58.1098","volume":"58","author":"T Holstein","year":"1940","unstructured":"Holstein, T., Primakoff, H.: Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys. Rev. 58, 1098 (1940)","journal-title":"Phys. Rev."},{"key":"3540_CR36","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04103-1","volume-title":"Quantum Noise","author":"C. W Gardiner","year":"2000","unstructured":"Gardiner, C.. W., Zoller, P.: Quantum Noise. Springer, Berlin (2000)"},{"key":"3540_CR37","first-page":"2814","volume":"57","author":"A Sohail","year":"2018","unstructured":"Sohail, A., Ahmed, R., Yu, C.S.: Tunable optomechanically induced transparency and fano resonance in optomechanical system with levitated nanosphere. IJTP 57, 2814 (2018)","journal-title":"IJTP"},{"key":"3540_CR38","first-page":"739","volume":"60","author":"A Sohail","year":"2021","unstructured":"Sohail, A., Ahmed, R., Yu, C.S.: Switchable and enhanced absorption via qubit-mechanical nonlinear interaction in a hybrid optomechanical system. IJTP 60, 739 (2021)","journal-title":"IJTP"},{"key":"3540_CR39","volume-title":"Stability Theory","author":"PC Parks","year":"1993","unstructured":"Parks, P.C., Hahn, V.: Stability Theory. Prentice Hall, New York (1993)"},{"key":"3540_CR40","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1007\/s11128-020-02888-y","volume":"19","author":"A Sohail","year":"2020","unstructured":"Sohail, A., Rana, M., Ikram, S., Munir, T., Hussain, T., Ahmed, R., Yu, C.S.: Enhancement of mechanical entanglement in hybrid optomechanical system. Quantum Inf. Process. 19, 372 (2020)","journal-title":"Quantum Inf. Process."},{"key":"3540_CR41","unstructured":"Eisert, J.: Entanglement in Quantum Information Theory. Ph.D. thesis, University of Potsdam, Potsdam, Germany (2001)"},{"key":"3540_CR42","doi-asserted-by":"publisher","first-page":"032314","DOI":"10.1103\/PhysRevA.65.032314","volume":"65","author":"G Vidal","year":"2002","unstructured":"Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)","journal-title":"Phys. Rev. A"},{"key":"3540_CR43","doi-asserted-by":"publisher","first-page":"090503","DOI":"10.1103\/PhysRevLett.95.090503","volume":"95","author":"MB Plenio","year":"2008","unstructured":"Plenio, M.B.: Logarithmic negativity: a full entanglement monotone that is not convex. Phys. Rev. Lett. 95, 090503 (2008)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR44","doi-asserted-by":"publisher","first-page":"7821","DOI":"10.1088\/1751-8113\/40\/28\/S01","volume":"40","author":"G Adesso","year":"2007","unstructured":"Adesso, G., Illuminati, F.: Entanglement in continuous-variable systems: recent advances and current perspectives. J. Phys. A 40, 7821 (2007)","journal-title":"J. Phys. A"},{"key":"3540_CR45","doi-asserted-by":"publisher","first-page":"023021","DOI":"10.1103\/PhysRevResearch.1.023021","volume":"1","author":"Z Zhang","year":"2019","unstructured":"Zhang, Z., Scully, M.O., Agarwal, G.S.: Quantum entanglement between two magnon modes via Kerr nonlinearity driven far from equilibrium. Phys. Rev. Res. 1, 023021 (2019)","journal-title":"Phys. Rev. Res."},{"key":"3540_CR46","doi-asserted-by":"publisher","first-page":"057202","DOI":"10.1103\/PhysRevLett.120.057202","volume":"120","author":"YP Wang","year":"2018","unstructured":"Wang, Y.P., Zhang, G.Q., Zhang, D., Li, T.F., Hu, C.M., You, J.Q.: Bistability of cavity magnon polaritons. Phys. Rev. Lett. 120, 057202 (2018)","journal-title":"Phys. Rev. Lett."},{"key":"3540_CR47","doi-asserted-by":"publisher","first-page":"224410","DOI":"10.1103\/PhysRevB.94.224410","volume":"94","author":"YP Wang","year":"2016","unstructured":"Wang, Y.P., Zhang, G.Q., Zhang, D., Luo, X.Q., Xiong, W., Wang, S.P., Li, T.F., Hu, C.M., You, J.Q.: Enhanced sideband responses in a PT-symmetric-like cavity magnomechanical system. Phys. Rev. B 94, 224410 (2016)","journal-title":"Phys. Rev. B"},{"key":"3540_CR48","doi-asserted-by":"publisher","first-page":"2934","DOI":"10.1038\/s41467-019-11021-2","volume":"10","author":"JW Rao","year":"2019","unstructured":"Rao, J.W., Kaur, S., Yao, B.M., Edwards, E.R.J., Zhao, Y.T., Fan, X., Xue, D., Silva, T.J., Gui, Y.S., Hu, C.M.: Analogue of dynamic Hall effect in cavity magnon polariton system and coherently controlled logic device. Nat. Commun. 10, 2934 (2019)","journal-title":"Nat. Commun."},{"key":"3540_CR49","doi-asserted-by":"publisher","first-page":"2972","DOI":"10.1109\/TAP.2009.2028602","volume":"57","author":"GQ Luo","year":"2009","unstructured":"Luo, G.Q., Hu, Z.F., Liang, Y., Yu, L.Y., Sun, L.L.: Development of low profile cavity backed crossed slot antennas for planar integration. IEEE Trans. Antennas Propag. 57, 2972 (2009)","journal-title":"IEEE Trans. Antennas Propag."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03540-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-022-03540-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03540-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,23]],"date-time":"2022-10-23T18:22:38Z","timestamp":1666549358000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-022-03540-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,14]]},"references-count":49,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["3540"],"URL":"https:\/\/doi.org\/10.1007\/s11128-022-03540-7","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,14]]},"assertion":[{"value":"12 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 May 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"207"}}