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We generalize $1+1$-dimensional formalism derived by Ahmadi et. al. [Phys.Rev. D \textbf{93}, 124031] to investigate an effect of relativisticacceleration on localized two-mode Gaussian quantum states in $3+1$-dimensionalspacetime. The following framework is then used to analyze entanglement of theMinkowski vacuum as witnessed by two accelerating observers that move eithercollinearly or noncollinearly.

Two-mode Gaussian quantum states measured by collinearly and noncollinearly accelerating observers