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.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Monash University
- 2 Institut für Quantenoptik und Quanteninformation Wien / Institute for Quantum Optics and Quantum Information Vienna [IQOQI Vienna]
- 3 Universität Siegen / University of Siegen
- Alexander von Humboldt-Stiftung / Alexander von Humboldt Foundation
- Australian Research Council [ARC]
- Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
- Bundesministerium für Bildung, Wissenschaft und Forschung (through Organization: Bundesministerium für Wissenschaft, Forschung und Wirtschaft / Federal Ministry of Science, Research and Economics [BMWFW])
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- Deutscher Akademischer Austauschdienst / German Academic Exchange Service [DAAD]
- European Research Council [ERC]
- Horizon 2020 (through Organization: European Commission [EC])
- Österreichischen Akademie der Wissenschaften (through Organization: Österreichische Akademie der Wissenschaften / Austrian Academy of Sciences [ÖAW])