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Using spacetime Gaussian test functions, we find closed-form expressions forthe smeared Wightman function, Feynman propagator, retarded and advancedGreen's functions, causal propagator and symmetric propagator of a masslessscalar field in the vacuum of Minkowski spacetime. We apply our results tolocalized quantum systems which interact with a quantum field in Gaussianspacetime regions and study different relativistic quantum informationprotocols. In the protocol of entanglement harvesting, we find a closed-formexpression for the entanglement that can be acquired by probes which interactin Gaussian spacetime regions and obtain asymptotic results for the protocol.We also revisit the case of two gapless detectors and show that the detectorscan become entangled if there is two-way signalling between their interactionregions, providing closed-form expressions for the detectors' final state.

Closed-form expressions for smeared bi-distributions of a massless  scalar field: non-perturbative and asymptotic results in relativistic quantum  information