Improving The Accuracy Of Quantum Parameter Estimation For Teleportation Under Noise

Quantum teleportation is the process of precisely transferring an unknown quantum state to the receiver using shared entanglement.It is not only a key conceptual protocol in the development of quantum information theory,but also a fundamental element in the development of many quantum technologies.In recent years,it has been studied extensively and intensively,both theoretically and in terms of experimental implementation.For traditional information communication,one would tend to focus more on the integrity of the information attached to the signal rather than the integrity of the signal.For quantum information communication,this means that researchers will be more concerned with the specific quantum parameters encoded on the quantum state rather than the quantum state itself.In quantum metrology,the lower bound on the variance of the parameter estimate is linked to the quantum Fisher information and the quantum Fisher information matrix through the quantum CramérRao bound.In this paper,quantum weak measurement and environment-assisted measurement techniques are employed to suppress the effect of noise and improve the accuracy of quantum parameter estimation of the teleported states.The main aspects of the work are as follows:(1)In the quantum teleportation of two-dimensional systems,we focus on the more general non-Markovian noise.It is found that the quantum Fisher information of the teleported state decays to 0 after several oscillations due to the non-Markovian effect.The reduction of the quantum Fisher information implies the reduction of the parameter estimation accuracy.To address this problem,two schemes are proposed to improve the parameter estimation accuracy of the quantum teleportation in the non-Markovian noise environment.One is to control the quantum system by weak measurement and quantum measurement reversal.The other is to correct the evolution of the quantum system according to the environmental monitoring results and recover the quantum Fisher information by quantum measurement reversal.In the nonMarkovian environment,both schemes can improve the accuracy of quantum parameter estimation for teleportation.And by choosing the appropriate strength of weak measurement and measurement reversal,the influence of environmental noise can be completely eliminated and the teleportation of initial quantum Fisher information can be realized.A comprehensive comparison shows that the second scheme not only has a higher probability of success than the first scheme,but also has a more obvious improvement in the estimation accuracy of quantum parameters for teleportation.(2)In the teleportation of three-dimensional quantum systems,quantum weak measurement and environment-assisted measurement are used to improve the accuracy of multi-parameter estimation under amplitude damping noise.The multi-parameter quantum Fisher information matrix of teleportation under noise is calculated,and the influence of noise on the estimation accuracy of multi-parameters is discussed.Two schemes are proposed for using weak measurement and environment-assisted measurement to combat the amplitude damping noise and improve the multi-parameter estimation accuracy of the quantum teleportation.The results show that both schemes can effectively improve the parameters estimation accuracy no matter in the case of independent estimation or simultaneous estimation,and the environment-assisted measurement scheme is better than the weak measurement scheme in both cases.It is worth noting that the environment-assisted measurement scheme can probabilistically guarantee that the quantum parameter estimation accuracy is not contaminated by amplitude damping noise.