  We consider estimating the parameter associated with the qubit depolarizing
channel when the available initial states that might be employed are mixed. We
use quantum Fisher information as a measure of the accuracy of estimation to
compare protocols which use collections of qubits in product states to one in
which the qubits are in a correlated state. We show that, for certain parameter
values and initial states, the correlated state protocol can yield a greater
accuracy per channel invocation than the product state protocols. We show that,
for some parameters and initial states, using more than two qubits and channel
invocations is advantageous. These results stand in contrast to the known
optimal case that uses pure initial states and a single channel invocation on a
pair of entangled qubits.
