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

TL;DR

This paper demonstrates that for certain many-body Gaussian states, including the free scalar field vacuum, entanglement can be detected at all distances using optimized local detectors, establishing negativity as a complete entanglement measure.

Contribution

It proves that logarithmic negativity is necessary and sufficient for entanglement detection in these states and provides optimal detection profiles for accessible entanglement at any distance.

Findings

Entanglement is detectable at all distances in many-body Gaussian states.

Logarithmic negativity is a complete measure of entanglement for the studied states.

Optimal detection profiles enable practical access to vacuum entanglement.

Abstract

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.