Entanglement, Photons, and Photonic Logic Gates

This work develops a spectral interpretation of quantum entanglement, photons, and photonic quantum gates within the framework of Internal Spectral Theory (IST). IST starts from a pre-geometric relational spectral structure in which neither physical space, time, nor quantum mechanics is assumed at the fundamental level. Hilbert-space representations arise only at a subsequent readability stage, where spectral projectors, observables, and effective quantum states can be defined. Within this hierarchy, quantum entanglement is investigated as an effective manifestation of a deeper non-factorizable spectral organization. The paper examines how non-separability in the represented regime can inherit structural constraints from the underlying spectral system, while maintaining a clear distinction between fundamental non-factorization and ordinary quantum entanglement. The photonic sector is described through a distinguished low-energy spectral subspace in the effective theory. Photonic quantum operations are then characterized by the preservation of this logical subspace. For a projector Pph onto the admissible photonic sector, an ideal operation satisfies [U,Pph]=0 while departures from this condition generate leakage outside the logical space. This provides a quantitative framework for analysing the robustness of photonic gates and architectures. The construction is connected to the broader IST emergence chain: relational spectral structure → readable represented regime → nucleation → crystallization → effective quantum description → emergent three-dimensional space → separate temporal evolution → local 3D+t physics. The results concerning gate invariance and leakage bounds are operator-theoretic within the stated effective assumptions. The identification of the photon sector with a specific fundamental spectral structure, and the complete derivation of quantum entanglement from the pre-geometric IST kernel, remain open problems. The framework therefore provides both a concrete mathematical criterion for photonic operations and a set of falsifiable directions for further investigation.