  For the quantum depolarizing channel with any finite dimension, we compare
three schemes for channel identification: unentangled probes, probes maximally
entangled with an external ancilla, and maximally entangled probe pairs. This
comparison includes cases where the ancilla is itself depolarizing and where
the probe is circulated back through the channel before measurement. Compared
on the basis of (quantum Fisher) information gained per channel use, we find
broadly that entanglement with an ancilla dominates the other two schemes, but
only if entanglement is cheap relative to the cost per channel use and only if
the external ancilla is well shielded from depolarization. We arrive at these
results by a relatively simple analytical means. A separate, more complicated
analysis for partially entangled probes shows for the qudit depolarizing
channel that any amount of probe entanglement is advantageous and that the
greatest advantage comes with maximal entanglement.
