New Methods For Quantum-enhanced Multiple Phase Estimation And Quantum Clock Synchronization

We present a general quantum metrology framework to study the simultaneous estimation of multiple phases in the presence of noise as a discretized model for phase imaging.This approach can lead to nontrivial bounds of the precision for multiphase estimation.Our results show that simultaneous estimation(SE)of multiple phases is always better than individual estimation(IE)of each phase even in noisy environment.The utility of the bounds of multiple phase estimation for photon loss channels is exemplified explicitly.When noise is low,those bounds possess the Heisenberg scale showing quantum-enhanced precision with the O(d)advantage for SE,where d is the number of phases.However,this O(d)advantage of the SE scheme in the variance of the estimation may disappear asymptotically when photon loss becomes significant.Potential application of those results is presented.We also present a novel quantum clock synchronization(QCS)scheme of multiple parties which uses operation as the trigger to start the evolution of the initial state.In comparison,the existing QCS protocols use measurement to start the evolution.We show that our protocol links the QCS problem to a multiple phase estimation problem,such that we have provided a general framework for the study of QCS.We can use the Fisher information to give the precision of the synchronization,and we explicitly show that the Heisenberg scale of synchronization is achieved in the two party case.We prove that the measurement triggered QCS(MTQCS)is included in the operation triggered QCS(OTQCS),so OTQCS is in general more powerful than MTQCS.We show that our protocol is very efficient in synchronizing a clock to the average time of other clocks.