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  • Open Access

Entanglement in the symmetric subspace: Mapping multipartite to bipartite states

Carlo Marconi1 and Satoya Imai2,3,4,*

  • 1Istituto Nazionale di Ottica—Consiglio Nazionale delle Ricerche (INO-CNR), Largo Enrico Fermi, 6, 50125 Firenze, Italy
  • 2Institute of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan
  • 3Center for Artificial Intelligence Research (C-AIR), University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan
  • 4INO-CNR and LENS, Largo Enrico Fermi, 2, 50125 Firenze, Italy

  • *Contact author: satoyaimai@yahoo.co.jp
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APS Open Sci. 1, 000036 – Published 3 June, 2026

DOI: https://doi.org/10.1103/6g5t-hlsr

Abstract

We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an N-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves separability and allows to characterize the entanglement of the original multipartite state. In particular, we establish a connection between the border rank and the Schmidt rank, and derive lower bounds on entanglement measures. Finally, we reveal the existence of entangled symmetric subspaces, where all bipartite states are entangled.

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APS Open Sci. 1, 000036– Published 3 June, 2026
Vol. 1
  • Received 8 October 2025
  • Revised 5 May 2026
  • Accepted 18 May 2026
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