Entanglement and quantum correlation measures for quantum multipartite mixed states
Year: 2023
Authors: Vesperini A., Bel-Hadj-Aissa G., Franzosi R.
Autors Affiliation: Univ Siena, DSFTA, Via Roma 56, I-53100 Siena, Italy; INFN Sez Perugia, I-06123 Perugia, Italy; QSTAR & CNR Ist Nazl Ott, Largo Enrico Fermi 2, I-50125 Florence, Italy.
Abstract: Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science, such as quantum communication, quantum computing, and quantum interferometry. Nevertheless, to our best knowledge, a directly or numerically computable measure for the entanglement of multipartite mixed states is still lacking. In this work, (i) we derive a measure of the degree of quantum correlation for mixed multipartite states. The latter possesses a closed-form expression valid in the general case unlike, to our best knowledge, all other known measures of quantum correlation. (ii) We further propose an entanglement measure, derived from this quantum correlation measure using a novel regularization procedure for the density matrix. Therefore, a comparison of the proposed measures, of quantum correlation and entanglement, allows one to distinguish between quantum correlation detached from entanglement and the one induced by entanglement and, hence, to identify separable but non-classical states. We have tested our quantum correlation and entanglement measures, on states well-known in literature: a general Bell diagonal state and the Werner states, which are easily tractable with our regularization procedure, and we have verified the accordance between our measures and the expected results for these states. Finally, we validate the two measures in two cases of multipartite states. The first is a generalization to three qubits of the Werner state, the second is a one-parameter three qubits mixed state interpolating between a bi-separable state and a genuine multipartite state, passing through a fully separable state.
Journal/Review: SCIENTIFIC REPORTS
Volume: 13 (1) Pages from: to:
More Information: We acknowledge support from the RESEARCH SUPPORT PLAN 2022 – Call for applications for funding allocation to research projects curiosity driven (F CUR) – Project Entanglement Protection of Qubits’ Dynamics in a Cavity- EPQDC and the support by the Italian National Group of Mathematical Physics (GNFM-INdAM). We also acknowledge discussions with Lorenzo Capra. We also acknowledge the support by Fondo Open Access 2023 of the University of Siena.KeyWords: SeparabilityDOI: 10.1038/s41598-023-29438-7Citations: 10data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-17References taken from IsiWeb of Knowledge: (subscribers only)