Detecting spacelike vacuum entanglement at all distances and promoting negativity to a necessary and sufficient entanglement measure in many-body regimes

Though known to be present, the accessibility of spacelike vacuum entanglement capable of being a fundamental resource for quantum information processing has remained in question at distances beyond the scale of vacuum fluctuations in massive fields. For a broad subclass of physical many-body mixed Gaussian states, including the free scalar field vacuum, the logarithmic negativity is here shown to be a necessary and sufficient measure of entanglement and to be entirely accessible by pairs of single-mode detectors in the continuum. By deriving exact and optimal detection profiles, entanglement resources in the massive field are demonstrated to be available at all distances.