 Entanglement is endemic in AQFT. Summers and Werner (1985) proved that the vacuum state of a quantum field is not only entangled across algebras associated with certain spacelike separated regions of Minkowski spacetime, but that it also maximally violates Bell inequalities for algebras associated with these regions. They also proved (1988) that every state on a pair of space-like separated open regions whose closures share a single point is maximally entangled across their algebras. For each state, the degree of entanglement decreases rapidly with spatial separation. But if and only if \(R_{A}, R_{B}\) possess what is called the split property is any state decomposable across these algebras.