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This letter further explores the recent scheme of switched quantum channelswith indefinite causal order applied to the reference metrological task ofquantum phase estimation in the presence of noise. We especially extend theexplorations, previously reported with depolarizing noise and thermal noise, tothe class of Pauli noises, important to the qubit and not previously addressed.Nonstandard capabilities, not accessible with standard quantum phaseestimation, are exhibited and analyzed, with significant properties that arespecific to the Pauli noises, while other properties are found in common withthe depolarizing noise or the thermal noise. The results show that the presenceand the type of quantum noise are both crucial to the determination of thenonstandard capabilities from the switched channel with indefinite causalorder, with a constructive action of noise reminiscent of stochastic resonancephenomena. The study contributes to a more comprehensive and systematiccharacterization of the roles and specificities of quantum noise in theoperation of the novel devices of switched quantum channels with indefinitecausal order.

Indefinite causal order for quantum phase estimation with Pauli noise