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PreprintarXiv licencearXiv

Characterizing local unitary equivalence of multipartite states by local unitary Bargmann invariants

  • Yi Shen
  • Lin Chen
  • Shao-Ming Fei
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Abstract

Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.

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Cite

BibTeXRIS
BibTeX
@misc{shen2026characterizing,
  title = {{Characterizing local unitary equivalence of multipartite states by local unitary Bargmann invariants}},
  author = {Yi Shen and Lin Chen and Shao-Ming Fei},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22902},
  eprint = {2609.22902},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22902},
}
RIS
TY  - UNPB
TI  - Characterizing local unitary equivalence of multipartite states by local unitary Bargmann invariants
AU  - Yi Shen
AU  - Lin Chen
AU  - Shao-Ming Fei
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22902
UR  - https://arxiv.org/abs/2609.22902
AB  - Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.
ER  -