Research On Kerr Phase Estimation Beyond Heisenberg Limit

Quantum metrology,also known as quantum parameter estimation,is one of the most promising applications of quantum technologies.The aim of this research field is the estimation of unknown parameters exploiting quantum resources,whose application can realize more precise measurements than can be achieved with classical methods.To date,quantum metrology has been widely applied in the measurement of atomic clocks,gyroscopes,gravimeters,and gravitational wave detection etc.Quantum mechanics places limits on the precision with which the parameter can be determined.For linear phase estimations,the optical interferometer with uncorrelated or classically correlated photons is highly possible to attain a phase sensitivity scaling as standard quantum limit(SQL),as a consequence of the quantum fluctuation of photons.Utilizing quantum probes as the input,such as squeezing and entanglement,the SQL can be exceed so that the uncertainty of the estimator reaches the Heisenberg Limit(HL).However,in contrast to the linear one,nonlinear phase estimation has been receiving increasing attention due to its ability to suppress the threshold to beat HL without entangled resources,to which Kerr phase estimation.In this paper,we analytically investigate the sensitivity of Kerr nonlinear phase estimation with two-mode squeezed vacuum(TMSV)states,twin Fock(TF)states and entangled coherent(EC)states using the quantum Fisher information to quantify.We have shown that the TF states can approach the generalized sensitivity limit proposed by Boixo et al.(BGSL),while the TMSV states can lead to a supersensitivity beyond the BGSL for any power of intensity of incident light.Meanwhile,on the basis of error propagation formula,we identify parity detection as a quasi-optimal measurement for both TF and TMSV states and a genuine-optimal measurement for the EC state in the present Kerr nonlinear phase estimation settings.Moreover,we elaborate that the supersensitive behavior observed with the TMSV states is attributed to the problematic definition of the BGSL for cases associating with fluctuating number of photons.To address this problem,we propose a generalized BGSL which is applicable for these cases with probe states of unfixed number of photons,to which our scheme belongs.