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Closed-form expressions for smeared bi-distributions of a massless scalar field: non-perturbative and asymptotic results in relativistic quantum information. (arXiv:2312.13343v1 [quant-ph])

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Using spacetime Gaussian test functions, we find closed-form expressions for
the smeared Wightman function, Feynman propagator, retarded and advanced
Green's functions, causal propagator and symmetric propagator of a massless
scalar field in the vacuum of Minkowski spacetime. We apply our results to
localized quantum systems which interact with a quantum field in Gaussian
spacetime regions and study different relativistic quantum information
protocols. In the protocol of entanglement harvesting, we find a closed-form
expression for the entanglement that can be acquired by probes which interact
in Gaussian spacetime regions and obtain asymptotic results for the protocol.
We also revisit the case of two gapless detectors and show that the detectors
can become entangled if there is two-way signalling between their interaction
regions, providing closed-form expressions for the detectors' final state.

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