Enhancing quantum Fisher information by utilizing uncollapsing measurements

As an indicator of estimation precision, quantum Fisher information (QFI) lies at the heart of quantum metrology theory. In this work, an effective scheme for enhancing QFI is proposed by utilizing quantum uncollapsing measurements. Two kinds of strategies for the arbitrary two-qubit pure state with weight parameter and phase parameter are implemented under different situations, respectively. We derive the explicit conditions for the optimal measurement strengths, and verify that the QFI can be improved quite well. Meanwhile, due to the relation of quantum correlation and QFI, the maximal value of QFI associated with phase parameter for pure state is always equal to 1. It is worth noting that the optimal measurement strength is only related to the weight parameter, as uncollapsing measurements operation does not induce any disturbance on the value of phase parameter. The scheme also can be extended to improve the parameter estimation precision for an N-qubit pure state. In addition, as an example, the situation of an arbitrary single-qubit state under amplitude damping channel is investigated. It is shown that our scheme also works well for enhancing QFI under decoherence.