Definition: Declared data on the boundary region

Boundary data mean a quantum state on $\mathcal{A}(B)$, with its extension to $\mathcal{A}(B)\otimes \mathcal{B}({\mathcal{H}}_R)$ when a reference system $R$ is retained. They do not mean only the first moment of $\beta$, an occupation count, or one finite sample of a classical measurement record.