Genuine Multipartite Entanglement in Time

TL;DR

This paper explores the structure of genuine multipartite entanglement in temporal quantum processes using the quantum comb formalism, revealing conditions for entanglement, connections to quantum memory, and examples of complex entangled processes over multiple times.

Contribution

It provides a comprehensive framework for understanding multipartite entanglement in temporal processes, including necessary and sufficient conditions and explicit examples.

Findings

Necessary and sufficient conditions for bipartite entanglement in temporal processes.

Construction of explicit W-type and GHZ-type genuinely multipartite entangled processes.

Existence of genuinely entangled processes across multiple times for any number of probes.

Abstract

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.