In the algebraic quantum theory and quantum information perspective, ``observer consensus'' is usually taken as a prior assumption: predictions of different observers eventually agree in overlapping accessible regions. This paper proposes a purely structural characterization: we model observers and their accessible information as local algebra objects with states, with morphisms given by modular inclusions compatible with Tomita--Takesaki modular flow, and construct a ``synchronization operator'
We consider the algebras generated by observables in quantum field theory localized in regions in the null plane. For a scalar free field theory, we show that the one-particle structure can be decomposed into a continuous direct integral of lightlike fibres and the modular operator decomposes accordingly. This implies that a certain form of QNEC is valid in free fields involving the causal completions of half-spaces on the null plane (null cuts). We also compute the relative entropy of null cut algebras with respect to the vacuum and some coherent states.
We develop Interval Algebraic Quantum Field Theory (IAQFT), a finite-precision operational formulation of algebraic quantum field theory (AQFT). Physical experiments provide only finitely many observations at finite resolution and therefore determine regions of compatible states rather than uniquely specified point states. IAQFT represents this information by quantum parcels---non-empty convex weak
∗ open regions of state space---with observational parcels determined by finitely many finite-precision expectation constraints. Exact AQFT states remain indispensable mathematical objects and are recovered under appropriate parcel refinement. We establish reduction to exact states, measurement update and no-signalling, and formulate locality through compatible parcel nets. In finite dimensions an exact Jacobian formula for invertible Lüders updates gives a volume-contraction criterion. Spacelike vacuum correlations and strict CHSH violations persist throughout sufficiently small observational parcels. Reeh--Schlieder cyclicity becomes finite-precision local reachability, while parcel equivalence of vacuum refinements implies vacuum GNS equivalence and hence does not evade Haag-type obstructions. Tomita--Takesaki modular automorphisms act on parcels, measurement update is modularly covariant, and modular conjugation induces a duality between normal parcels of an algebra and its commutant. State-dependent modular correlations are continuous under predual-norm variation of faithful normal states; shrinking parcels with vanishing KMS defect recover a KMS state. Bisognano--Wichmann yields a parcel formulation of the Unruh effect, recovering the exact KMS relation and Unruh temperature under refinement. Finally, limiting projection faces and their conjugation actions recover the Murray--von Neumann factor classification.