Abstract
Quantum Fisher information of phase estimation is studied for a single qubit which is influenced by the two generalized amplitude damping channels (GADCs) with indefinite causal order (ICO). The phase shift occurs between two consecutive applications of the GADCs. It is shown that the quantum Fisher information can be enhanced by the ICO of the quantum channels. Furthermore, even a completely incoherent state of the qubit is found to be useful for estimating the phase shift due to the ICO.
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