https://doi.org/10.1140/epjp/s13360-026-07426-w
Regular Article
Distributed nonclassical magnon–photon–phonon entanglement without direct cavity coupling
1
Basic Teaching and Research Department, Shenyang Urban Construction University, 110167, Shenyang, China
2
Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, 710049, Xi’an, China
3
Department of Mathematics, College of Sciences, University of Bisha, 61922, Bisha, Saudi Arabia
4
Institute of Theoretical Physics and Astronomy, Vilnius University, Sauletekio 3, 10257, Vilnius, Lithuania
a
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Received:
27
November
2025
Accepted:
9
February
2026
Published online:
27
February
2026
Abstract
We investigate a hybrid quantum platform composed of three spatially separated cavity–magnon–phonon units, each realized by placing a yttrium iron garnet (YIG) sphere inside an individual microwave cavity. The cavities are mutually uncoupled, and no direct cavity–cavity interaction is introduced. Instead, nonlocal quantum correlations are supplied by externally prepared nonclassical three-mode entangled probe fields that are injected independently into the three cavities and act as a shared quantum resource. Our focus is not on modeling or monitoring the source that generates the entangled probes, but rather on how such injected nonclassical inputs are redistributed and converted into steady-state hybrid entanglement via local magnon–photon and magnon–phonon interactions within each cavity. Treating each subsystem as coupled to an independent Markovian reservoir, we analyze the driven–dissipative dynamics in a linearized quantum Langevin framework and solve the Lyapunov equation for the steady-state covariance matrix. We systematically characterize the distributed entanglement structure among remote magnons 
, cavity photons 
, and representative hybrid triplets including 
, 
, and 
. Our results show that robust steady-state tripartite entanglement can be established and maintained under realistic parameters , and that engineered nonclassical probe fields substantially enhance and distribute genuine tripartite entanglement between distant subsystems beyond what is achievable via purely classical phase synchronization. The proposed modular and reconfigurable architecture offers a scalable route toward continuous-variable quantum networks, distributed quantum memories, and hybrid interfaces tailored for quantum transduction applications.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
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.
