Three-site tomography conjecture for open-boundary matrix product states

Let $\Psi$ be a translation-invariant $N$-qubit matrix product state with open boundary conditions and bond and physical dimensions $D=d=2$. A reduced density operator on a chain of adjacent sites is obtained by tracing out all other sites. Three-site tomography conjecture. A generic such state is determined up to phase by the reduced density operator on a chain of three adjacent states, but not by a chain of fewer states. This conjecture would be directly relevant to quantum state tomography under tensor-network assumptions; the source explains the associated generic-fibre question in terms of the action of the unit-modulus complex numbers.