Simon Milz, Cornelia Spee, Zhen-Peng Xu, Felix A. Pollock, Kavan Modi, Otfried Gühne
SciPost Phys. 10, 141 (2021) ·
published 11 June 2021
While spatial quantum correlations have been studied in great detail, much
less is known about the genuine quantum correlations that can be exhibited by
temporal processes. Employing the quantum comb formalism, processes in time can
be mapped onto quantum states, with the crucial difference that temporal
correlations have to satisfy causal ordering, while their spatial counterpart
is not constrained in the same way. Here, we exploit this equivalence and use
the tools of multipartite entanglement theory to provide a comprehensive
picture of the structure of correlations that (causally ordered) temporal
quantum processes can display. First, focusing on the case of a process that is
probed at two points in time -- which can equivalently be described by a
tripartite quantum state -- we provide necessary as well as sufficient
conditions for the presence of bipartite entanglement in different splittings.
Next, we connect these scenarios to the previously studied concepts of quantum
memory, entanglement breaking superchannels, and quantum steering, thus
providing both a physical interpretation for entanglement in temporal quantum
processes, and a determination of the resources required for its creation.
Additionally, we construct explicit examples of W-type and GHZ-type genuinely
multipartite entangled two-time processes and prove that genuine multipartite
entanglement in temporal processes can be an emergent phenomenon. Finally, we
show that genuinely entangled processes across multiple times exist for any
number of probing times.