Protecting quantum Fisher information in curved space-time

Yu-Kun Ren, Xiaolan Wang, Hao‐Sheng Zeng

Yu-Kun Ren, La-Mei Tang, Hao‐Sheng Zeng

Xiao-zhi Liu, Dan Long, Hong-Mei Zou +2 more

Yao Jin

Abstract The dynamics of the quantum Fisher information of the parameters of the initial atomic state and atomic transition frequency is studied, in the framework of open quantum systems, for a static polarizable two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields in cosmic string space-time. Our results show that with the presence of cosmic string, the quantum Fisher information becomes position and atomic polarization dependent. It may be enhanced or depressed as compared to that in flat space-time case. Remarkably, when the atom is extremely close to the cosmic string and the polarization direction of the atom is perpendicular to the direction of the cosmic string, the quantum Fisher information has been totally protected from the fluctuating vacuum electromagnetic fields. So on the one hand, near a cosmic string, precision of estimation can be enhanced by ranging the radial distance between the probe atom and the cosmic string; on the other hand, the cosmic string can be sensed by studying the distribution of parameter induced state-separation.

Marco O. Lanzagorta

Jia‐Xin Peng, Baiqiang Zhu, Weiping Zhang +1 more

The dissipative quantum Fisher information (DQFI) for a dynamic map with a general parameter in an open quantum system is investigated, which can be regarded as an analog of the quantum Fisher information (QFI) in the Liouville space. We first derive a general dissipative generator in the Liouville space, and based on its decomposition form, find the DQFI stems from two parts. One is the dependence of eigenvalues of the Liouvillian supermatrix on the estimated parameter, which shows a linear dependence on time. The other is the variation of the eigenvectors with the estimated parameter. The relationship between this part and time presents rich characteristics, including harmonic oscillation, pure exponential gain and attenuation, as well as exponential gain and attenuation of oscillatory type, which depend specifically on the properties of the Liouville spectrum. This is in contrast to that of the conventional generator, where only oscillatory dependencies are seen. Further, we illustrate the theory through a toy model: a two-level system with spin-flip noise. Especially, by using the DQFI, we demonstrated that the exceptional estimation precision cannot be obtained at the Liouvillian exceptional point.