Quantum Relative Entropy and Information Flux Resolve Wavefunction Collapse in Spacelike-Separated QED Waveguides

Abstract

Resolving how first-order quantum coherence and definite measurement outcomes emerge from entangled vacuum fluctuations across spacelike-separated regions is unified here by the principle that quantum relative entropy governs the energy-information flux across causal boundaries [P.~Dorau and A.~Much, Phys.~Rev.~Lett.~\textbf{136}, 091602 (2026)]. We establish the exact quantum-optical realization of this principle using dual, spacelike-separated entangled nonlinear biphoton sources implemented in quantum electrodynamics waveguides pumped by an optical frequency comb and seeded by a continuous-wave laser in a coherent state $|α\rangle$. We demonstrate that single-photon-added coherent states (SPACS) generated via coherent seeding possess a quantum relative entropy that precisely quantifies the entanglement deficit between signal and idler fields. Tracing over the unmeasured idler continuum yields an exact spatial Lindblad master equation along the propagation axis, proving that spatial dephasing is driven by an information divergence flux determined by the SPACS overlap fidelity $F = |α|^2/(1+|α|^2)$. Uniting this relative-entropy flow with quotient measurement theory (detailed in Section~S3 of the Supplemental Material), we rigorously resolve nonlocal wavefunction collapse into local coset projections---explaining macroscopic state reduction without superluminal signaling. This exact open-system framework simultaneously saturates the wave-particle-entanglement triality [T.~H.~Yoon and M.~Cho, Sci.~Adv.~\textbf{7}, eabi9268 (2021)] and anchors hardware-native time--frequency Gottesman--Kitaev--Preskill stabilizers to the comb symplectic structure.