Indefinite causal ordering (ICO) refers to quantum channels arranged so that the path through them is a super-position of different possible paths. The ICO is called pure when the the path superposition is a pure quantumstate. Channel probing, in which probes in prepared quantum states are passed through copies of the channelto estimate one or more channel parameters, is aided by ICO. Specifically, pure ICO is known to increase thequantum Fisher information (QFI) in the processed probe state about the unknown parameter(s). We considerthe case complementary to pure ICO in which the path state is maximally mixed for a given indefiniteness.Deriving the QFI under this condition by a new approach, we find that mixed ICO-assisted probing, while notas beneficial as pure ICO probing, still yields greater QFI than does the comparable scheme with definite causalorder. The d-dimensional quantum depolarizing channel is used as the channel model for this study. Whilemixed ICO-assisted probing, like pure ICO-assisted probing, is generally advantageous for probing the depolar-izing channel, mixed ICO's relative effectiveness decreases with probe dimension, just as for pure ICO-assistedprobing, each being most effective for qubit probes.
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