Pure dephasing destroys two-photon amplitude, not nonlinear phase

A two-level emitter chirally coupled to a waveguide imprints a $π$ conditional phase on a two-photon pulse, a key component assumed in quantum photonic neural network architectures, but whether it survives the pure dephasing of a solid-state emitter is unknown, since no two-photon scattering treatment includes it. We derive the dephased two-photon amplitude in closed form and validate it against an independent Fock-state master equation. The conditional phase is pinned at exactly $π$ at every dephasing rate examined: dephasing destroys the amplitude carrying the nonlinear phase rather than rotating it. The one- and two-photon channels are not attenuated equally, so dephasing does not simply scale the node down but reweights it between photon-number sectors---an error no phase setting can train away. The standard factorization of two-photon correlators, exact for arbitrary loss, fails at first order in $γ_φ$, discarding $16$--$81\%$ of pairs over $γ_φ/γ=0.1$--$1$.

Source: arXiv:2610.30098v1 - http://arxiv.org/abs/2610.30098v1 PDF: https://arxiv.org/pdf/2610.30098v1 Original Link: http://arxiv.org/abs/2610.30098v1