The Limited Communication Theorem: Entanglement-Induced Environmental Expansion Beyond the Correlation Boundary

This paper introduces a formal framework for analyzing the environmental consequences of quantum coordination from the perspective of an excluded observer — one with no access to the quantum state, measurement outcomes, or local inputs. We prove that when spatially separated agents respond to independent local conditions under entangled resources, the reachable environmental state space strictly exceeds the reachable state space under any local hidden-variable model, while non-signalling constraints are fully preserved. The principal result is a leakage-performance separation theorem: quantum coordination simultaneously exceeds the classical performance ceiling while leaking zero information about local conditions to the excluded observer, breaking the classical Pareto frontier between coordination performance and operational security.