Quantum Limit Research Of Phase Estimation In Noisy Systems

Quantum-enhanced precision measurement is a new research direction that is emerging.Parameter estimation in the dynamics process is a core issue in science and technology.In practical applications,the system will inevitably be coupled to the environment.When this coupling is also taken into account,the quantum enhancement effect is diminished.For measurement systems,in addition to the optical field loss environment,there is also the phase diffusion environment.In order to solve the problem of how to solve the system quantum Fischer information in the presence of multiple noise environments,we propose a new method,that is,an initial pure state system is subjected to two uncorrelated noise field environments ?phase diffusion environment and optical field loss environment?during the phase parameterization process.The impact of the analysis yields the upper bound of the quantum Fischer information of the system.For the phase diffusion environment,a purification process combines the system and the phase diffusion environment to form a new pure state,and the pure state includes a generalized phase transformation of phase shift and phase diffusion coefficients.Then this new pure state evolves along with the environment of the light field loss,which is equivalent to a set of Kraus operators that describe this new pure state and evolve.By changing the environmental parameters of the optical field loss,the minimum of the total quantum Fischer information of the noise field environment plus two noise systems can be obtained as the upper limit of the new pure state quantum Fischer information.In the same way,by changing the phase diffusion environment parameters,the minimum of the quantum Fischer information of the system plus the phase diffusion environment can be finally obtained as the upper limit of the quantum Fischer information of the system.Finally,we take the SU(1,1)interferometer as an example to numerically analyze the phase sensitivity in the phase diffusion environment and the optical field loss environment.