Ancilla-assisted Frequency Estimation Under Markovian Noises With Greenberger-Horne-Zeilinger States

Precision measurement is a comprehensive discipline combining metrology,physics,information technology and other fields.The development of quantum mechanics theory has brought new development opportunities,and has produced many advanced new measurement experiments,such as gravitational wave detection,atomic clock frequency calibration,quantum magnetometer,and quantum gyroscope.But these quantum features may be easily destroyed by shot noises.By using the non-classical state probe method,the limit of shot noises can be broken in the ideal case.The Heisenberg limit can be reached when the maximum entangled state is used.However,entangled quantum state is very fragile,and any small amount of realistic noise restricts the advantage of quantum strategies to an improvement by a constant factor.Therefore,to explore and find an appropriate scheme to eliminate the negative effects of environmental noise and to maximize the measurement sensitivities is a topic of current research,which is of great significance to both basic theoretical research and specific experimental operation.It has been shown in some literature that the optimal sensitivity obtained with the GHZ state is the same as the frequency estimation obtained with the uncorrelated state in the presence of uncorrelated Markovian dephasing noises.Recently,ancilla-assisted strategy has been proposed for robust phase estimation.Here,we extend the above problem by examining the optimal frequency sensitivity that can be achieved by the ancilla-assisted strategy which has been identified as an effective way of preserving sensitivities in phase estimation under some noisy channels and also experimentally demonstrated.we address this issue by examining the sensitivities achievable with generalized GHZ states in frequency estimation suffering from a general class of Markovian noises,of which the processes commute with the unitary evolution governed by the system Hamiltonian,which is referred as phase covariant noises.We also demonstrate the effectiveness of the ancilla-assisted strategy in maintaining frequency sensitivity to specific physical ground noise,including Phase-damping Channel,Amplitude-damping Channel and Depolarizing Channel.In addition,we also study the effectiveness of the ancilla-assisted strategy under parallel noise and transversal noise,and prove the superiority of the ancilla-assistedt strategy under transversal noise.