title: Quantum-enhanced metrology for multiple phase estimation with noise.
abstract: 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 SE scheme in the variance of the estimation may disappear asymptotically when photon loss becomes significant and then only a constant advantage over that of IE scheme demonstrates. Potential application of those results is presented.
authors.affiliation: Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Jie-Dong
authors.initials: JD
authors.lastname: Yue
authors.affiliation: Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Yu-Ran
authors.initials: YR
authors.lastname: Zhang
authors.affiliation: 1] Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China [2] Collaborative Innovation Center of Quantum Matter, Beijing 100190, China.
authors.forename: Heng
authors.initials: H
authors.lastname: Fan
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