Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1307.6659 · International Journal of Theoretical Physics

Local Unitary Invariants for Multipartite States

Ting-Gui Zhang, Ming‐Jing Zhao, Xianqing Li‐Jost, Shao-Ming Fei

Published Apr 19, 2013• 8 citations
arXivHTMLPDF
DOI
10.1007/s10773-013-1593-4

Related papers

Multipartite states under local unitary transformations

Sergio A Albeverio, Laura Cattaneo, Shao-Ming Fei +1 more

arXiv:quant-ph/0512083•Reports on Mathematical Physics•Dec 1, 2005•22 citations

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

Yi Shen, Lin Chen, Shao-Ming Fei

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.

quant-pharXiv:2609.22902•Sep 22, 2026•0 citations

Addendum to “multipartite states under local unitary transformations”

Sergio A Albeverio, Laura Cattaneo, Shao-Ming Fei +1 more

arXiv:quant-ph/0703026•Reports on Mathematical Physics•Oct 1, 2006•3 citations

The Local Unitary Equivalence of Multipartite Pure States

Yan-Ling Wang, Mao-Sheng Li, Shao-Ming Fei +1 more

arXiv:1407.2400•International Journal of Theoretical Physics•Jul 10, 2014•5 citations

Characterization of multipartite entanglement

Nengkun Yu, Youming Qiao, Xiudong Sun

In this paper, we provide a characterization of multipartite entanglement in terms of equivalence classes of states under local unitary transformation (LU) by demonstrating a simple method to construct all homogenous polynomials that are invariant under local unitary group(LUIPs) for any fixed degree. We give an upper bound on the degree of the LUIP such that the ring of LUIPs can be generated by LUIPs with degree lower than the bound. Our characterization can directly generate an algorithm whose output is a generating set of LUIPs. By employing the concept of LUIPs, we prove that multipartite entanglement is additive in the sense that two multipartite states are LU equivalent if and only if $n$-copies of these two states are LU equivalent for some $n$. The method for studying LU equivalence is also used to classify the different types of multipartite mixed entanglement according to equivalence classes of states under stochastic local operations and classical communication (SLOCC), where the pure states case was previously studied by Gour and Wallach using another approach.

•Jan 12, 2014•2 citations

Local Unitary Invariants for Multipartite Quantum Systems

Wang Jing, Li Zhi ming, 费少明 +1 more

We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340(2013) 1205-1208].Detailed examples are given to compute such invariant in detail. It is shown that these invariants can be used to detect the local unitary equivalence of degenerated quantum states.

理论物理通讯：英文版•Jan 1, 2014•0 citations
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.
In this paper, we provide a characterization of multipartite entanglement in terms of equivalence classes of states under local unitary transformation (LU) by demonstrating a simple method to construct all homogenous polynomials that are invariant under local unitary group(LUIPs) for any fixed degree. We give an upper bound on the degree of the LUIP such that the ring of LUIPs can be generated by LUIPs with degree lower than the bound. Our characterization can directly generate an algorithm whose output is a generating set of LUIPs. By employing the concept of LUIPs, we prove that multipartite entanglement is additive in the sense that two multipartite states are LU equivalent if and only if nnn-copies of these two states are LU equivalent for some nnn. The method for studying LU equivalence is also used to classify the different types of multipartite mixed entanglement according to equivalence classes of states under stochastic local operations and classical communication (SLOCC), where the pure states case was previously studied by Gour and Wallach using another approach.