Quantum multiparameter estimation with multi-mode photon catalysis entangled squeezed state

Abstract

We propose a method to generate the multi-mode entangled catalysis squeezed vacuum states (MECSVS) by embedding the cross-Kerr nonlinear medium into the Mach−Zehnder interferometer. This method realizes the exchange of quantum states between different modes based on Fredkin gate. In addition, we study the MECSVS as the probe state of multi-arm optical interferometer to realize multi-phase simultaneous estimation. The results show that the quantum Cramer−Rao bound (QCRB) of phase estimation can be improved by increasing the number of catalytic photons or decreasing the transmissivity of the optical beam splitter using for photon catalysis. In addition, we also show that even if there is photon loss, the QCRB of our photon catalysis scheme is lower than that of the ideal entangled squeezed vacuum states (ESVS), which shows that by performing the photon catalytic operation is more robust against photon loss than that without the catalytic operation. The results here can find applications in quantum metrology for multiparatmeter estimation.

Graphical abstract

Keywords

quantum metrology / squeezing vacuum / quantum catalysis / multi-parameter estimation

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Acknowledgements

This work was supported by the National Key R&D Program of China (Grant No. 2021YFA1400800), the Key-Area Research and Development Program of Guangdong Province (Grant No. 2018B030329001), the Natural Science Foundation of Guangdong (Grant No. 2021A1515010039), the National Natural Science Foundation of China (No. 11964013), and the Major Discipline Academic and Technical Leaders Training Program of Jiangxi Province (No. 20204BCJL22053).

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