Geometry of distributive multiparty entanglement in 4 − qubit hypergraph states. Issue 1 (19th November 2021)

• Record Type: Journal Article
• Authors: Sarkar, Ramita; Banerjee, Shreya; Bag, Subhasish; Panigrahi, Prasanta K.
• Other Names: Sengupta Diganta guestEditor.; Abd El‐Latif Ahmed guestEditor.; De Debashis guestEditor.; Navi Keivan guestEditor.; Bagherzadeh Nader guestEditor.
• Is Part Of: IET quantum communication. Volume 3:Issue 1(2022)
• Page Start: 72
• Page End: 84
• Publication Date: 2021-11-19
• Subjects: concurrence -- distributive entanglement -- geometry of quantum entanglement -- hypergraph states -- multiparty entanglement -- tangle; Quantum communication -- Periodicals; Quantum communication; Periodicals; 004.6
• DOI: 10.1049/qtc2.12027
• Languages: English
• ISSNs: 2632-8925

Abstract

Abstract: A detailed investigation of the multiparty entanglement present in the 4 − qubit quantum hypergraph states is presented, following a measurement‐based geometrical approach. Considering a classification of the 4 − party quantum system represented by a mathematical hypergraph based on the connections between its vertices, the genuine 4 − party entanglement present in each bi‐partition of the states have been measured. A strong correlation between the connectivity of the vertices of the hypergraphs and the genuine 4 − party entanglement has been found. The equivalence of the genuine 4 − party entanglement present in each bi‐partition is shown considering similar connectivity of the vertices. This explicates the cyclic permutation symmetry of the multiparty entanglement present in the 4 − qubit hypergraph states. Physically, one may expect the quantum systems with superposition of many states to behave in this symmetric manner while mapped into a network‐type picture, which the authors have quantified, as well as classified in this work.