Indefinite causal order for parameter estimation of channel with depolarization noise

Abstract

When incorporating the indefinite causal order method into quantum channel parameter estimation, the target parameter information of the channel can be encoded into the control qubit, and the ultimate precision upper limit can be assessed using quantum Fisher information. In this study, we examine the characteristics of a switched channel in which a single path contains multiple copies of a qubit unitary channel affected by depolarization noise. Our focus lies on the superposition coupling term generated by the switched channel, as it plays a crucial role in determining the quantum Fisher information for parameter estimation. In addition, we classify and discuss the case where a single path contains three copies. Given that the quantum Fisher information is determined by the coupling terms, we rigorously compute the values of these coupling terms in all scenarios. Subsequently, we analyze the characteristics of the quantum Fisher information and compare them with those arising from two copies of a single path.