  We investigate relations between computational power and correlation in
resource states for quantum computational tensor network, which is a general
framework for measurement-based quantum computation. We find that if the size
of resource states is finite, not all resource states allow correct projective
measurements in the correlation space, which is related to non-vanishing
two-point correlations in the resource states. On the other hand, for
infinite-size resource states, we can always implement correct projective
measurements if the resource state can simulate arbitrary single-qubit
rotations, since such a resource state exhibits exponentially-decaying
two-point correlations. This implies that a many-body state whose two-point
correlation cannot be upperbounded by an exponentially-decaying function cannot
simulate arbitrary single-qubit rotations.
