## Quantum Channel Parameter Estimation with Noisy Initial States

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.