Teleportation of quantum Fisher information with Gaussian states

Abstract

Quantum Fisher Information (QFI), which sets the fundamental bound on parameter estimation precision via the quantum Cramér-Rao inequality, is investigated for a general single-mode Gaussian state before and after teleportation. Using a two-mode squeezed vacuum state as a shared entanglement resource between Alice and Bob, we analyze the teleportation protocol under environmental noise, focusing on diffusion and dissipation induced by a thermal bath. By comparing QFI for several parameters of the input state before and after teleportation, we evaluate the effectiveness of QFI transfer. We find that increasing the squeezing of the shared state enhances QFI preservation. Notably, under certain conditions, environmental interactions can help maintain QFI, particularly for shared states with high frequency, suggesting a subtle interplay between system dynamics and decoherence.