Influence of entanglement on precision of parameter estimation in quantum weak measurement

Abstract

An appropriate weak value can be used to amplify weak physical parameters and improve the precision of parameter estimation in the process of quantum weak measurement. The increase of the precision of such a parameter estimation may originate from the entanglement in the system. This paper uses Fisher information to study the influence of the entanglement in the system and the entanglement between the system and the pointer on the estimation precision of the coupling parameters between the system and the pointer in the process of weak measurement. The entanglement of the entangled pure state of the GHZ-like state and the entangled mixed state affected by the depolarization noise and the influence of the entanglement between the system and the pointer on the parameter estimation are analyzed. The results show that the Fisher information quantity increases with the increase of the initial state entanglement degree of the system when the initial state of the system is an entangled pure state or an entangled mixed state affected by depolarization noise, and both the Fisher information quantity and the post-selection probability reach their maximum values when the initial and final state of the system are both the maximum entangled states; but the weaker the entanglement between the system and the pointer, the more the Fisher information obtained in the measurement will be and the higher the accuracy of parameter estimation. These research results show that the entanglement in the system will improve the precision of parameter estimation, while the entanglement between the system and the pointer will reduce the precision of parameter estimation.