Packaged Quantum States in Field Theory: No Partial Factorization, Multi-Particle Packaging, and Hybrid Gauge-Invariant Entanglement

Abstract: We demonstrate that quantum field excitations can generate packaged entangled states, in which all internal quantum numbers (IQNs) (e.g., electric charge, flavor, and color) are inseparably entangled and constrained to irreducible representation (irrep) blocks. This is a consequence of local gauge invariance and superselection rules. The confinement restricts the net gauge charge to a single superselection sector, thereby excluding cross-sector superpositions but allowing entanglement within one sector. We establish theorems that: \textbf{(1)} Explain how these packaged entangled states naturally arise from quantum field excitations, \textbf{(2)} Show how they remain gauge invariant or transform covariantly within a fixed net-charge sector, and \textbf{(3)} Illustrate how external degrees of freedom (DOFs) (e.g., spin or momentum) can combine with packaged internal charges to yield gauge-invariant entanglement. Finally, we show that spin or momentum measurements on these hybrid states induce a collapse of the internal entanglement.