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.
Highlights
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
We shall show that even under general evolution, simultaneous estimation (SE) is still better than individual estimation (IE), but the O(d) advantage may disappear gradually, with photon loss taken as an example
We have presented a lower bound for the error in multi-parameter estimation under noise, within the framework of quantum metrology, and photon loss is exemplified
Summary
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. Those bounds possess the Heisenberg scale showing quantum-enhanced precision with the O(d) advantage for SE, where d is the number of phases This O(d) advantage of SE scheme in the variance of the estimation may disappear asymptotically when photon loss becomes significant and only a constant advantage over that of IE scheme demonstrates. A general framework is proposed recently to obtain attainable and useful lower bound of the quantum Fisher information (QFI.) ipnffinffiffiffioisy systems[27] This lower bound captures the main features of the transition from the 1/N to 1 N precisions for the cases of noisy channels such as photon loss and dephasing. Similar as for single phase, our result of multiphase can capture the main features of the transition from Heisenberg limit to standard quantum limit
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
