Geometry of two-body correlations in three-qubit states

Year: 2024

Authors: Shravan S., Morelli S., Guhne O., Imai S.

Autors Affiliation: Univ New Mexico, Ctr Quantum Informat & Control, Dept Phys & Astron, Albuquerque, NM 87131 USA; BCAM Basque Ctr Appl Math, Mazarredo 14, Bilbao E-48009, Basque Country, Spain; Tech Univ Wien, Atominst, Stadionallee 2, A-1020 Vienna, Austria; Univ Siegen, Nat wissensch Tech Fak, Walter Flex Str 3, D-57068 Siegen, Germany; QSTAR, INO CNR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy.

Abstract: We study restrictions of two-body correlations in three-qubit states, using three local-unitarily invariant coordinates based on the Bloch vector lengths of the marginal states. First, we find tight nonlinear bounds satisfied by all pure states and extend this result by including the three-body correlations. Second, we consider mixed states and conjecture a tight nonlinear bound for all three-qubit states. Finally, within the created framework, we give criteria to detect different types of multipartite entanglement as well as characterize the rank of the quantum state.

Journal/Review: PHYSICAL REVIEW A

Volume: 110 (6)      Pages from: 62419-1  to: 62419-12

More Information: We would like to thank Akimasa Miyake, Ties Ohst, Jens Siewert, and Nikolai Wyderka for discussions. We would like to particularly thank Konrad Szymanski for his inputs leading to the analytical proof for Eq. (E8) in Appendix E. S.S. also thanks Anil Shaji for all the support given during the initial part of the project. This work was supported by the DAAD, the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Projects No. 447948357 and No. 440958198) , the Sino-German Center for Research Promotion (Project No. M-0294) , the ERC (Consolidator Grant No. 683107/TempoQ) , and the German Ministry of Education and Research (Project QuKuK, BMBF Grant No. 16KIS1618K) , Horizon Europe programme HORIZON-CL4-2022-QUANTUM-02-SGA via Project No. 101113690 (PASQuanS2.1) , and by the European Commission through the H2020 QuantERA ERA-NET Cofund in Quantum Technologies projects SQUEIS, BCAM-IKUR, funded by the Basque Government by the IKUR Strategy and by the European Union NextGeneration EU/PRTR, the Basque Government through the BERC2022-2025 program, and by the Ministry of Science and Innovation: BCAM Severo Ochoa accreditation CE X2021-001142-S/MICIN/AEI/10.13039/501100011033.
KeyWords: Entanglement; Separability
DOI: 10.1103/PhysRevA.110.062419