Quantum-Switch-Assisted Teleportation of Quantum Fisher Information under Composite Pauli Channels

The teleportation of Quantum Fisher Information (QFI) is central to the precision limits of distributed quantum metrology, yet it is inevitably degraded by environmental decoherence. Here we investigate QFI teleportation under composite Pauli channels and show that a quantum switch can improve the outcome-resolved and success-probability-weighted QFI relative to the corresponding fixed-order protocol. The enhancement arises from a coherent reorganization of Pauli error trajectories rather than from a reduction of the physical error probabilities. For the three binary pairs of anti-commuting Pauli channels studied here, we identify a heralded branch whose normalized state has the ideal QFI whenever that branch has nonzero probability. These findings highlight the potential of utilizing quantum switches to mitigate Pauli-noise-induced QFI degradation in quantum communication and sensing networks.