  We show that a highly-mixed state in terms of a large min-entropy is useless
as a resource state for measurement-based quantum computation in the sense that
if a classically efficiently verifiable problem is efficiently solved with such
a highly-mixed measurement-based quantum computation then such a problem can
also be classically efficiently solved. We derive a similar result also for the
DQC1$_k$ model, which is a generalized version of the DQC1 model where $k$
output qubits are measured. We also show that the measurement-based quantum
computing on a highly-mixed resource state in terms of the von Neumann entropy,
and DQC1$_k$ model are useless in another sense that the mutual information
between the computation results and inputs is very small.
