We consider estimating the parameters governing the strengths of the phase-flip and qubit depolarizing channels. Quantifying the accuracy of any protocol via the quantum Fisher information per channel invocation, it is known that the optimal protocols use pure input states. For the phase-flip channel the optimal uses unentangled single qubits and, for the depolarizing channel, pairs of entangled qubits.
We consider situations where the available initial states are mixed and compare protocols that use qubits in product states to a protocol that uses multiple qubits in a correlated state. We show that, for certain parameter values and initial state purities, the correlated state protocol provides a greater accuracy than the product state protocol. We show that, when comparing protocols using mixed initial states, not only do any estimation accuracy enhancements typical of the pure initial-state cases survive but that additional advantages emerge. Specifically, we show that the estimation accuracy can increase with more than two qubits in a correlated state and the enhancement in the accuracy for the mixed-state case can exceed the enhancement in the accuracy for the pure initial-state case.