Entanglement hierarchies in multipartite scenarios

Chirag Srivastava, Mahasweta Pandit, Ujjwal Sen

Experimental detection of entanglement certainly disturbs the underlying shared state. It is possible that the entanglement content of the system is lost in the process of its detection. This observation has led to the study of sequential detection properties of various quantum correlations. Here, we investigate the sequential detection of genuinely multipartite entanglement of quantum systems composed of an arbitrary number of qubits. In order to detect genuine multipartite entanglement sequentially, observers can recycle any fixed subset of all the qubits, thus leading to a hierarchy of scenarios, categorized according to the number of qubits which are recycled by the observers. We show that the sequential detection of genuine multipartite entanglement, for every scenario in the hierarchy, leads to an unboundedly long sequence. This is shown to be possible if the initial state shared among the observers is the multipartite generalized Greenberger-Horne-Zeilinger state and is a class of mixed states. A comparison among different hierarchical scenarios is drawn based on the number of sequential detections of genuine multipartite entanglement for a specific measurement strategy employed by observers.

Awais Khan, Ahmad Farooq, Youngmin Jeong +1 more

Frank E. S. Steinhoff

The states generated by a multiport beam splitter usually display genuine multipartite entanglement between the many spatial modes. Here we investigate the different classes of multipartite entangled states that arise in this practical situation, working within the paradigm of stochastic local operations with classical communication. We highlight three scenarios, one where the multipartite entanglement classes follow a total number hierarchy, another where the various classes follow a nonclassicality degree hierarchy, and a third one that is a combination of the previous two. Moreover, the multipartite entanglement of higher-dimensional versions of Dicke states relates naturally to our results.

Ingemar Bengtsson, Karol Życzkowski

Peter Bierhorst, Jitendra Prakash

According to recent new definitions, a multiparty behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. The new definitions differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources. Here, we categorize the full hierarchy of these new candidate definitions of GMNL in three-party quantum networks, highlighting the intimate link to device-independent witnesses of network effects. A key finding is the existence of a behavior in the simplest nontrivial multipartite measurement scenario (three parties, two measurement settings, and two outcomes) that cannot be simulated in a bipartite network prohibiting entangled measurements and superquantum resources-thus witnessing the most general form of GMNL-but can be simulated with bipartite-only quantum states with an entangled measurement, indicating an approach to device-independent certification of entangled measurements with fewer settings than in previous protocols. Surprisingly, we also find that this (3,2,2) behavior, as well as the others previously studied as device-independent witnesses of entangled measurements, can all be simulated at a higher echelon of the GMNL hierarchy that allows superquantum bipartite resources while still prohibiting entangled measurements. This poses a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.

Zhengfeng Ji, Runyao Duan, Mingsheng Ying