 Algebraic quantum field theory (AQFT) represents the state in a region of spacetime by means of a function from an algebra of associated “field” or “observable” operators: the value of this function for a self-adjoint operator represents the expected result of a measurement of the corresponding observable on that region. A state is said to be decomposable (some say separable) across algebras \(R_{A}, R_{B}\) associated with regions \(A, B\) if its restriction \(\omega\) to the algebra \(R_{AB}\) generated by \(R_{A}, R_{B}\) is a product state—i.e. satisfies \(\omega(XY)=\omega(X)\omega(Y)\), for all \(X\in R_{A}, Y\in R_{B}\); or if \(\omega\) is a limit of convex combinations of product states: otherwise, it is said to be entangled across \(R_{AB}\) (see e.g. Valente 2010, pp. 1031–2). This is a natural reformulation of a generalization to mixed states of the first condition for entanglement given in  section 8.