Enhancing the teleportation of quantum Fisher information by weak measurement and environment-assisted measurement

The quantum teleportation is reexamined in a Fisher information perspective. Two proposals of enhancing the teleportation of quantum Fisher information (QFI) under amplitude damping channel are proposed by utilizing the weak measurement and environment-assisted measurement (EAM), respectively. Although both schemes enable us to improve the teleportation of QFI with a certain probability, the latter proposal can completely recover the initial QFI, while the former only approaches to it. A detailed comparison confirms that the scheme of EAM outperforms the WM one in the improvements of QFI. The underlying reason is that the EAM is a post-measurement; thus, it extracts more information from the system and environment than the pre-posed WM. Our research offers an active way to enhance the teleportation of QFI under the amplitude damping decoherence, which is very important for quantum metrology and other quantum information tasks.