Entanglement, Locality, and Measurement from Coherent Sector Dynamics

Algebraic quantum field theory (AQFT) separates locality of observable algebras from factorization of states: spacelike algebras may commute while a state on their joint algebra remains entangled. We formulate the precise MTT-compatible version of this distinction. Given an upper local net indexed over a globally hyperbolic four-dimensional base, a decomposable coherent projector, and the coherent-preserving local subalgebra, the fixed-point locality-descent theorem transports isotony and microcausality to the compressed net. Nonfactorizing states may restrict to that net, but admissibility and locality alone neither force entanglement nor select a Bell-violating state. Bell/CHSH violation is therefore compatible with upper-local dynamics when a suitable nonseparable state and local instruments are independently supplied. Measurement is treated as an ordinary localized completely positive instrument. Such instruments obey operational no-signaling under the standard locality assumptions; they cannot increase an entanglement monotone on average, although an individually postselected branch need not lose entanglement. Common-ancestor protocols and finite-speed correlation spreading remain standard local mechanisms. The result is a conditional AQFT-compatible MTT encoding, not a derivation of all physical states or measurement probabilities from admissibility alone.