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arXiv:2608.09670

Microscopic QED origin of spin entanglement

Moslem Zarei

quant-phSubmitted Aug 10, 2026• Announced Aug 11, 2026• 0 citations
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Abstract

We study effective spin interactions arising from quantum electrodynamics (QED) scattering between localized fermionic spins. By integrating out photon and mediator fields, the dynamics reduce to an effective spin Hamiltonian. For two qubits in the nonrelativistic regime, the resulting interaction takes a tensor dipolar form with an asymptotic decay proportional to \(R^{-3}\). We obtain analytical expressions for the entanglement negativity, highlighting its dependence on coupling strength and spatial configuration. We then examine a setup in which two bath spins interact via a sequential exchange with an intermediate fermionic mediator. At the perturbative order considered, the mediator remains unentangled and induces an effective bath--bath interaction with stronger spatial suppression than in the photon-mediated case. Extending the construction to an \(N\)-spin setting yields an effective interaction network mediated by virtual exchange processes, which can support the generation of multipartite entanglement across the system.

Comments
23 pages, 3 figures

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We study effective spin interactions arising from quantum electrodynamics (QED) scattering between localized fermionic spins. By integrating out photon and mediator fields, the dynamics reduce to an effective spin Hamiltonian.
For two qubits in the nonrelativistic regime, the resulting interaction takes a tensor dipolar form with an asymptotic decay proportional to (R^{-3}). We obtain analytical expressions for the entanglement negativity, highlighting its dependence on coupling strength and spatial configuration.
We then examine a setup in which two bath spins interact via a sequential exchange with an intermediate fermionic mediator. At the perturbative order considered, the mediator remains unentangled and induces an effective bath--bath interaction with stronger spatial suppression than in the photon-mediated case.
Extending the construction to an (N)-spin setting yields an effective interaction network mediated by virtual exchange processes, which can support the generation of multipartite entanglement across the system.
We study real-time meson-meson scattering processes in (1+1)(1+1)(1+1)-dimensional QED by means of Tensor Networks. We prepare initial meson wave packets with given momentum and position, starting from the free fermions model and extending it to the interaction theory. Then, we compute the dynamics of two initially separated colliding mesons, observing a rich phenomenology as the interaction strength and the initial states are varied in the weak and intermediate coupling regimes. Finally, we measure the scattering amplitudes for the process in terms of the initial and final momenta and the entanglement produced by the collision. We remarkably find two different regimes for the asymptotic entanglement between the two mesons: it is perturbatively small for weak couplings, while, in the intermediate regime, it turns out to reach a non-zero value at long times after the scattering.
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Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.
Dispersively coupled distant qubits in a shared cavity can become entangled through virtual photon exchange with energy-conserving phase evolution of their quantum states. This interaction can potentially be accelerated by operating on resonance, allowing for the exchange of real photons. In this theoretical study, we examine photon-mediated entanglement between two distant spins of electrons confined in double quantum dots formed in a Si/SiGe heterostructure. We calculate the dynamics of the combined system comprised of both spin qubits and the cavity, assuming that both spin qubits can be tuned into and out of resonance with the host cavity. We demonstrate that the exchange of real photons between the two spin qubits can result in rapid entanglement that is robust against decoherence. These results pave the way for the development of quantum gates on resonantly coupled distant semiconductor spin qubits.
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We develop a susceptibility-based open-system theory for two localized qubits coupled through a candidate two-dimensional U(1)\mathrm{U}(1)U(1) Dirac-spin-liquid-like bath. The central input is the gauge-invariant retarded physical spin susceptibility XR(q,ω)\Chi^R(q,ω)XR(q,ω) of the bath. We show that this single response kernel controls both coherent and dissipative qubit dynamics: its real part generates the nonlocal mediated exchange, while its absorptive part determines relaxation and dephasing through the equilibrium noise spectrum. This gives a unified reduced two-qubit description in which the usefulness of the bath as an entanglement bus is governed by the competition between susceptibility-mediated exchange and bath-induced decoherence. As an analytically transparent benchmark, we evaluate the spinon mean-field Dirac susceptibility and recover the static algebraic exchange Jeff(R)∝Jlocal2/(vFR3)J_{\mathrm{eff}}(R)\propto J_{\rm local}^2/(v_F R^3)Jeff​(R)∝Jlocal2​/(vF​R3), together with pseudogap-suppressed relaxation Γ1∝Jlocal2ω03/vF4Γ_1\propto J_{\rm local}^2ω_0^3/v_F^4Γ1​∝Jlocal2​ω03​/vF4​. We then formulate a beyond-mean-field extension in which gauge-field dressing and other interaction effects are absorbed into a dressed physical susceptibility, without changing the reduced qubit-sector mapping. The resulting framework provides a direct route from the many-body spin response of a correlated two-dimensional bath to reduced-dynamics simulations of entanglement generation, coherence loss, and the operational phase space of a candidate Dirac spin-liquid quantum interconnect.