Multipartite entanglement in the diagonal symmetric subspace

Year: 2025

Authors: Romero-Palleja J., Ahiable J., Romancino A., Marconi C., Sanpera A.

Autors Affiliation: Univ Autonoma Barcelona, Dept Fis, Fis Teor Informacio & Fenomens Quant, Bellaterra 08193, Spain; Univ Palermo, Dipartimento Fis & Chim E Segre, Via Archirafi 36, I-90123 Palermo, Italy; Ist Nazl Ott CNR INO, Largo Enrico Fermi 6, I-50125 Florence, Italy; ICREA, Pg Lluis Co 23, Barcelona 08010, Spain.

Abstract: We investigate the entanglement properties in the symmetric subspace of N-partite d-dimensional systems (qudits). As it happens already for bipartite diagonal symmetric states, also in the multipartite case the local dimension d plays a crucial role. Here, we demonstrate that there is no bound entanglement for d = 3, 4 and N = 3. Using different techniques, we present strong analytical evidence that no bound entanglement exist for any N if d <= 4. Interestingly, bound entanglement of diagonal symmetric states exist for any number of parties, N >= 2, and local dimensions d >= 5.

Journal/Review: JOURNAL OF MATHEMATICAL PHYSICS

Volume: 66 (2)      Pages from: 22203-1  to: 22203-14

More Information: J.R.-P. acknowledges financial support from Ministerio de Ciencia e Innovacion of the Spanish Goverment FPU22/01511. J.A. and A.S. acknowledge financial support from Ministerio de Ciencia e Innovacion of the Spanish Goverment with funding from European Union NextGenerationEU (PRTR-C17.I1) and by Generalitat de Catalunya. C.M. acknowledges support from the European Union – NextGeneration EU, Integrated infrastructure initiative in Photonic and Quantum Sciences – I-PHOQS (IR0000016, ID D2B8D520, CUP B53C22001750006). A.S. acknowledges financial support from the European Commission QuantERA grant ExTRaQT (Spanish MICIN Project No. PCI2022-132965). We acknowledge financial support from the Spanish MICIN (Project No. PID2022-141283NB-I00) with the support of FEDER funds, and by the Ministry for Digital Transformation and of Civil Service of the Spanish Government through the QUANTUM ENIA project call – Quantum Spain project, and by the European Union through the Recovery, Transformation and Resilience Plan – NextGeneration EU within the framework of the Digital Spain 2026 Agenda.
KeyWords: Separability
DOI: 10.1063/5.0240964