Quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters.Similar to the estimation of a constant phase,there is a standard quantum limit for stochastic phase ...Quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters.Similar to the estimation of a constant phase,there is a standard quantum limit for stochastic phase estimation,which can be obtained with the Mach-Zehnder interferometer and coherent input state.Recently,it has been shown that the stochastic standard quantum limit can be surpassed with nonclassical resources such as squcezed light.However,practical methods to achieve quantum enhancement in the stochastic phase estimation remain largely unexplored.Here we propose a method utilizing the SU(1,1)interferometer and coherent input states to cstimate a stochastic optical phase.As an example,we investigate the Ornstcin-Uhlenback stochastic phase.We analyze the performance of this method for three key estimation problems:prediction,tracking,and smoothing.The results show significant reduction of the mean square error compared with the Mach-Zehnder interferometer under the same photon number flux inside the interferometers.In particular,we show that the method with the SU(1,1)interferometer can achieve fundamental quantum scaling,achieve stochastic Heisenberg scalinga and surpass the precision of the canonical measurement.展开更多
基金National Key Research and Development Program of China(2017YFA0303703,2019YFA0308704)National Natural Science Foundation of China(11664017,11590052,11574155,51490711,61973077,91436211,91836303)+3 种基金Fundamental Research Funds for the Central Universitics(No.020214380068)Natural Science Foundjarion of Shanghai(17ZR1442900)Nanjing Universiry Innovation and Creative Program for PhD candidatc(2016017)Basic Research Project of Shanghai Science and Technology Commission(20JC1416100).
文摘Quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters.Similar to the estimation of a constant phase,there is a standard quantum limit for stochastic phase estimation,which can be obtained with the Mach-Zehnder interferometer and coherent input state.Recently,it has been shown that the stochastic standard quantum limit can be surpassed with nonclassical resources such as squcezed light.However,practical methods to achieve quantum enhancement in the stochastic phase estimation remain largely unexplored.Here we propose a method utilizing the SU(1,1)interferometer and coherent input states to cstimate a stochastic optical phase.As an example,we investigate the Ornstcin-Uhlenback stochastic phase.We analyze the performance of this method for three key estimation problems:prediction,tracking,and smoothing.The results show significant reduction of the mean square error compared with the Mach-Zehnder interferometer under the same photon number flux inside the interferometers.In particular,we show that the method with the SU(1,1)interferometer can achieve fundamental quantum scaling,achieve stochastic Heisenberg scalinga and surpass the precision of the canonical measurement.
