Detecting and preparing spacelike vacuum entanglement in scalar quantum fields

Quantum simulations aim to efficiently simulate complex quantum systems, with quantum fields representing one of the challenging cases. We investigate the entanglement structure of the free scalar field vacuum, advancing the understanding of its quantum informational properties. Being UV-finite and capable of characterizing entanglement between disjoint regions of the many-body vacuum, we begin by identifying the logarithmic negativity as a necessary and sufficient measure of entanglement [2]. We then leverage it to define an entanglement class [1] that enables the derivation of exact and optimal detector profiles, demonstrating that the exponentially decaying accessible entanglement persists across all separations in the scalar field vacuum [2]. When measurements and classical communication with the remaining volume are allowed, entanglement between disjoint vacuum regions can be purified. We identify a lower bound to the maximum of this entanglement resource that decays exponentially slower with separation than the two-point correlation functions [3]. By developing further techniques capable minimizing this entanglement [1] through a semi-definite conic geometry [3], we find an upper bound to the entanglement of formation between detection regions that decays exponentially faster than the two-point correlation functions. The results provide new understanding of the entanglement required for the quantum simulation of quantum fields as observed by arrays of local detectors.