Using Non-Gaussian State To Improve Measurement Accuracy Of Linear Interferometer

Quantum metrology is one of the most important branches in the field of quantum science,which is of great significance to the development of science and technology application today.Mach-Zehnder interferometer(MZI)as an important linear measuring instrument,can be used to improve the measurement accuracy,so it is widely used in the field of quantum measurement.Because non-Gaussian operations can improve the nonclassical property of quantum states,the research on improving the measurement accuracy by using non-Gaussian operations has received more and more attention in recent years.Based on the advantages of the MZI and non-Gaussian operation,this paper proposes to use the quantum states prepared by non-Gaussian operation(Laguerre polynomial excitation operation and photon catalytic operation)as the inputs of the MZI,studies the phase sensitivity of parity detection and the quantum Fisher information,and comprehensively analyzes the conditions to improve the phase measurement accuracy.Firstly,we introduce a kind of non-Gaussian state,the Laguerre excited squeezed state as the inputs of the MZI to study the phase estimation in realistic case.The influence of photon losses on phase estimation is investigated by using the phase sensitivity of the parity detection and the quantum Fisher information.The results show that when the dissipation occurs in one path of the MZI,the internal dissipation has less influence on the phase sensitivity than the external dissipation,while the internal dissipation on the two paths and external dissipation(relatively small dissipation)have basically the same influence on the phase sensitivity.The phase sensitivity and the quantum Fisher information can be improved by increasing the excited photon number or the squeezing parameter.Although photon losses exist,the ideal phase sensitivity with two-mode squeezed vacuum can be surpassed in a certain region of phase shift by increasing the excited photon number.In addition,the phase sensitivity and the quantum Cramér-Rao bound can break the standard quantum limit and even beat the Heisenberg limit.Secondly,we introduce the photon-catalyzed squeezed vacuum state(PCSVS)that prepared by photon catalysis in squeezed vacuum state(SVS),and use the coherent state mixed PCSVS as the inputs of the MZI to improve the phase measurement accuracy.It is found that photon catalysis,especially multi-photon catalysis,can effectively improve the phase sensitivity of parity detection.When the photon losses exist,the phase sensitivity of internal dissipation can be better than that of external dissipation.In addition,the quantum Fisher information in the ideal and realistic case of photon losses is studied.It is found that when the transmissivity of the optical beam splitter used to prepare PCSVS is low,the quantum Fisher information can be significantly increased by multi-photon catalytic operation,increasing the squeezing parameter and the amplitude of the coherent state,and the Cramér-Rao can exceed the HL.