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We introduce and study a quantum channel that arises from the structure of the vacuum state of Dirac fields propagating in a Garfinkle–Horowitz–Strominger (   $$\mathrm {GHS}$$   GHS    ) dilation black hole spacetime. We put forward the concept of quantum information divergence, which is a new measure for relativistic parameter estimation. We employ quantum metrology to estimate the amplitude and relative phase of a Dirac field state using the quantum Fisher information and information divergence. The decoherence of quantum parameter estimation is studied through the evolution of the Bloch vector for arbitrary initial states subjected to the quantum channel and external noises. We find that the quantum information divergence decreases more than the quantum Fisher information as a function of the radiation temperature. Due to the Pauli exclusion principle and Dirac statistics, the estimation precision will gradually decrease to a non-zero value. In order to study the decoherence in the dilation black hole, we obtain the monotonic decrease of quantum coherence when an initial field evolves from the highly correlated state to the current cosmic background. The external noises can further suppress the decoherence effect from the black hole.

Decoherence of quantum parameter estimation for open Dirac particle in Garfinkle–Horowitz–Strominger dilation black hole