Gaussian interferometric power in the localized two-mode Gaussian states

With localized two-mode Gaussian quantum states in a relativistic setting, we study how to use the Gaussian interferometric power, which is given by the minimum quantum Fisher information, to guarantee the precision of the estimation of the Unruh temperature. We note that the interferometric power will be reduced with increase in the Unruh temperature because the Unruh radiation acts as a thermal bath on the probe state and it will destroy available quantum resources. By comparing the interferometric power with the entanglement, we also find that the larger squeezing parameter, the more similar the variation of entanglement and interferometric power. The maximum value of entanglement and interferometric power appears in the same condition. That is, for the states with larger entanglement, we can get higher precision of estimation. Moreover, we find that the interferometric power remains nonzero even for high Unruh temperature. This reflects the robust behavior of the Gaussian interferometric power against thermal noises.