Precise space–time positioning for entanglement harvesting

Abstract

We explore the crucial role of relative space-time positioning between the two detectors in an operational two-party entanglement-harvesting protocol. Specifically we show that the protocol is robust if imprecision in spatial positioning and clock synchronization are much smaller than the spatial separation between the detectors and its light-crossing time thereof. This in principle guarantees robustness if the imprecision is comparable to a few times the size of the detectors, which suggests entanglement harvesting could be explored for tabletop experiments. On the other hand, keeping the effects of this imprecision under control would be demanding on astronomical scales.

Entanglement harvesting from the electromagnetic vacuum with hydrogenlike atoms

“…Note that, since this is a fundamental study, in this manuscript we have focused on large time delays and large energy gaps for the scenarios analyzed in the figures, and thus we obtained low values of harvested entanglement. It has been studied elsewhere [29][30][31][32]54] that the value of harvested entanglement (even with the less powerful scalar cases) can be made large enough to be detectable under realistic parameters for shorter delays and lower gaps.…”

“…(44) and (45) starting from Eqs. (31) and (32). For generality, we will not fix the ground state or the excited state and we will perform the calculations as general as possible, beginning only with the assumption that both atoms have the same atomic structure (same ground and excited states), and particularizing to the 1s → 2p z transition only at the very end of each section of this appendix.…”

Degenerate detectors are unable to harvest spacelike entanglement

“…Finally, notice that this proof carries over to the case of 1+1 dimensions if we add an infrared cutoff. Even with an infrared cutoff, the identity (14) still holds in the same way as in (15), so the inability of gapless detectors to harvest entanglement applies also to this case.…”

Harvesting correlations from the quantum vacuum

“…Since Unruh-DeWitt detectors can, in some regimes, be a good approximation to the light-matter interaction [14,15], these pioneering results may imply that it is possible to extract entanglement from the electromagnetic vacuum to atomic qubits, where it could be used as a resource, although, for this purpose, one has to be careful with the impact of time synchronization on entanglement harvesting [16]. Indeed, it has been proved that it is possible to devise quantum optical setups where entanglement can be sustainably and reliably extracted from a quantum field and distilled into Bell pairs, that can be later used as a resource for quantum information tasks.…”