Recently, it has been shown that the massless quantum vacuum state contains entanglement between timelike separated regions of spacetime, in addition to the entanglement between the spacelike separated regions usually considered. Here, we show that timelike entanglement can be extracted from the Minkowski vacuum and converted into ordinary entanglement between two inertial, two-state detectors at the same spatial location — one coupled to the field in the past and the other coupled to the field in the future. The procedure used here demonstrates a clear time correlation as a requirement for extraction, e.g. if the past detector was active at a quarter to 12:00, then the future detector must wait to become active at precisely a quarter past 12:00 in order to achieve entanglement.
We have attempted to partially answer the question of how timelike entanglement in the Minkowski vacuum can be related to the familiar “entanglement at a given time” between simple, two-state systems by showing that timelike entanglement may be extracted and converted into ordinary entanglement between two two-state detectors. We thus conclude that timelike entanglement may be regarded as a non-classical resource in a manner analogous to the spacelike entanglement that is often studied in the Minkowski vacuum, since any quantum information theoretic protocol may utilize conversion of timelike entanglement to spacelike entanglement as a step in the protocol.
As a thought experiment to illustrate this possibility, we imagine a quantum teleportation protocol in which the entanglement resource is between a detector interacting in P, and a detector interacting in F, and all operations on the P-detector and the qubit-to-be-teleported take place before t = 0. Classical information alone is then sent into F, where the F-detector must interact with the eld there at a particular time to form the other half of the entanglement resource. The classical information from P is then used to transform the F-detector into the teleported qubit. Such a protocol might be called “teleportation in time,” since there exists a period after t = 0 but before the future interaction time where it is not possible to recover the teleported qubit.
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