Quantum Wave-Particle Duality in Free-Electron--Free-Electron Entanglement

Abstract:Point-particle descriptions of electron-electron interaction omit the coherent longitudinal extent of a free-electron quantum wave packet (QEW). A relativistic two-electron wave-packet theory identifies the longitudinal QEW size as a direct control parameter for entanglement generated by mutual electromagnetic coupling. For two electrons in spatially separated paths, the quadratic interaction phase gives a dimensionless entangling parameter $\Gee$ and the logarithmic negativity $\EN=\operatorname{arsinh}(\Gee)/\ln2$. Full time-dependent Schrödinger equation calculations confirm the scaling for narrow QEWs and reveal higher-order Coulomb effects at larger spatial extent. Free drift increases the interaction-point QEW width while preserving the momentum probability distribution, thereby enhancing the subsequently generated entanglement. The results establish a direct connection between free-electron wave-particle duality and bipartite entanglement.

arXiv:2608.16292 [quant-ph]

(or arXiv:2608.16292v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.16292 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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