Optimal quantum strategy for locating Unruh channels

From the perspective of quantum information theory, the effect of Unruh radiation on a two-level accelerated detector can be modeled as a quantum channel. In this work, we employ the tools of channel-position finding to locate Unruh channels. The signal-idler and idler-free protocols are explored to determine the position of the target Unruh channel within a sequence of background channels. We derive the fidelity-based bounds for the ultimate error probability of each strategy and obtain the conditions where the signal-idler protocol is superior to the protocol involving idler-free states. It is found that the lower bound of the error probability for the signal-idler scheme exhibits clear advantages in all cases, while the idler-free scheme can only be implemented when the temperature of the two channels is very close and the number of initial states is insufficient. Interestingly, it is shown that the optimal detection protocol relies on the residual correlations shared between the emitted probe state and the retained idler modes.