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.
Highlights
We provide explicit circuits for each of the discussed cases, and relate them to existing phenomena discussed in the literature, like entanglement breaking superchannels [34], channel steering [35], as well as the aforementioned concepts of genuine quantum memory and the superposition of direct and common causes
Given that an action of any of the parties destroys it, we conclude that the genuine multipartite entangled (GME) such processes possess is somewhat inaccessible; if Bob feeds forward any state, Alice and Charlie do not share an entangled state, while any measurement on Alice’s (Charlie’s) system will only allow for an entanglement breaking channel between Bob and Charlie (Alice)
In this work – using the quantum comb framework – we studied the entanglement properties of temporal processes
Summary
Correlations form the basis for scientific inferences about the world. They are used, amongst others, to detect (and discern different types of) causal relations [1,2,3], to distinguish theories that abide by local realism from those that do not [4,5,6], and to test if quantum mechanics satisfies the assumptions of non-invasive measurements and realism per se [7,8,9]. We provide explicit circuits for each of the discussed cases, and relate them to existing phenomena discussed in the literature, like entanglement breaking superchannels [34], channel steering [35], as well as the aforementioned concepts of genuine quantum memory and the superposition of direct and common causes. In this way we provide a comprehensive picture of the entanglement properties of temporal processes
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