Study On The Quantum Fisher Information In A Qubit-qutrit System

Quantum metrology is a new discipline related to quantum measurement and parameter estimation,and its theory has been widely used in quantum frequency standards,quantum imaging,gravitational wave detection and quantum gyroscope,etc.As an important part of quantum metrology,the quantum Fisher information(QFI)gives the upper bound for the estimation precision of unknown parameters due to the quantum Cramer-Rao's theorem.Therefore,the achievable accuracy limit of estimation can be obtained by calculating the QFI when investigating the precision of the parameter estimation.Additionally,the combination of quantum information science,general relativity and quantum field theory has attracted widespread attention.This combination can not only broaden the application of quantum information theory,but also deepen people's understanding of quantum effects.In this thesis,we use the QFI as the main indicator to study the problem of unknown parameter estimation in GHS dilation space-time.Our main research contents are as follows:1.Firstly,we study the QFI of a qubit-qutrit system with respect to the state parameter ? and dilation parameter D in GHS dilation space-time by considering a quantum memory,one of which locates near the event horizon of the black hole as a qubit and another one stays at the asymptotically flat region as a qutrit.For the given initial state,our results show that the QFI for the parameter ? is a fixed value,which means that the dilation of black hole and the state parameter ? will not cause any disturbance on the estimation precision of ?.The QFI for the estimation of D varies with parameters D and ?.Additionally,we propose an effective strategy to steer the QFI by means of quantum weak measurement reversal.We find that the QFI can be enhanced significantly by adjusting measurement strengths appropriately.2.Secondly,we investigate the dynamic evolution of QFI for the qubit-qutrit system suffering from amplitude damping noise and phase damping noise,and propose a strategy to protect the QFI under amplitude damping noise channel by employing weak measurement and reversal measurement.The results show that,the QFI decays as the amplitude damping decoherence strength increases.What surprise us is the QFI is nearly a constant with the increase of phase damping decoherence strength.In addition,by applying prior weak measurements and post optimal weak measurement reversals on the particle which passing through the noise channel,the protection of physically accessible QFI is achieved.Meanwhile,the higher QFI can be attained with respect to an appropriate value of measurement strengths and reversal strengths.