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Genuine Multipartite Entanglement in Time
by Simon Milz, Cornelia Spee, Zhen-Peng Xu, Felix A. Pollock, Kavan Modi, Otfried Gühne
|As Contributors:||Otfried Gühne · Simon Milz|
|Arxiv Link:||https://arxiv.org/abs/2011.09340v2 (pdf)|
|Date submitted:||2021-02-19 18:34|
|Submitted by:||Milz, Simon|
|Submitted to:||SciPost Physics|
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.
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Anonymous Report 1 on 2021-5-9 Invited Report
The submitted manuscript entitled "Genuine Multipartite Entanglement in Time" by S. Milz et al. addresses the question of obtaining genuine multipartite entanglement in temporal processes. In this work using the so-called quantum comb procedure temporal processes are transformed to the spatial domain with the restriction that temporal correlations have to admit causal ordering (unlike spatial correlations). This mapping allows the Authors to apply established tools in the theory of multipartite entanglement to reveal the structure of temporal quantum correlations.
In my view this is a very nice piece of work which unifies several key concepts about multiple-time temporal processes. In particular, the paper gives conditions for the presence of "bipartite entanglement" in different splittings associated with two-time processes. The studied scenarios are linked to the well-developed concepts of quantum memory, entanglement breaking channels and EPR steering. Furthermore, explicit examples are provided in the two-time scenario for the enigmatic GHZ and W-states.
In my view, the paper is very well written and the results obtained are correct. Also, all the presented examples are elegant. I highly recommend the paper for publication.
Minor technical comment/question:
- Page 32: second line above the bottom of the page: "non-commuting" -> "non-communicating"
- Section 6: The Authors show the existence of processes that are entangled in any bipartition, yet these processes are not genuinely tripartite entangled. In other words, it is shown that entanglement in every splitting E(A:BC)>0, E(C:AB)>0, E(B:AC)>0 does not imply in general genuinely tripartite entanglement. I would like to ask whether the stronger conditions for entanglement in the three marginals E(A:B)>0, E(B:C)>0, E(A:C)>0 would still imply genuinely tripartite entanglement for temporal processes.