Pure state entanglement harvesting in quantum field theory

Quantum fields in vacuum states carry an infinite amount of quantum entanglement, and its entanglement entropy has ultraviolet divergence. Harvesting protocols of the vacuum entanglement have been investigated, but its efficiency is very low to date. The main reason for the low efficiency originates from the fact that the extracted entanglement is embedded in a mixed state of two external devices. We propose a general protocol with high efficiency by extracting pure state entanglement from the field. We only use bi-linear interactions between the fields and external devices. Even though the ultraviolet cutoff remains finite, the protocol is capable of extracting a huge amount of entanglement. Hence an infinite amount of entanglement extraction is attained without the ultraviolet divergence of the field entanglement entropy in a continuum limit. There exists a trade-off relation between the extracted entanglement and its energy cost.