Commutators with multiple unitary symmetry

• URL: http://arxiv.org/abs/2504.09232v1
• Date: Sat, 12 Apr 2025 14:16:23 GMT
• Title: Commutators with multiple unitary symmetry
• Authors: Shu Li, Jie Wang, Binfeng Wang, Lin Chen,
• Abstract summary: Commutators are essential in quantum information theory, influencing quantum state symmetries and information storage robustness.<n>This paper systematically investigates the characteristics of bipartite and multipartite quantum states invariant under local unitary group actions.
• Score: 8.572991879638712
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Commutators are essential in quantum information theory, influencing quantum state symmetries and information storage robustness. This paper systematically investigates the characteristics of bipartite and multipartite quantum states invariant under local unitary group actions. The results demonstrate that any quantum states commuting with $U \otimes U^{\dagger}$ and $U \otimes V$ can be expressed as $\frac{1}{n}I_n$, where $U$ and $V$ are arbitary $n\times n$ unitary matrices. Furthermore, in tripartite systems, any quantum states commuting with $U \otimes U \otimes U^{\dagger}$ must necessarily adopt the form: $W = xI_{n^3} + y\left(\sum_{i,j=1}^n (|i\rangle \langle j|) \otimes (|j\rangle \langle i|)\right) \otimes I_n$, where $F_n$ represents the canonical swap operator. These results provide theoretical tools for characterizing multipartite entanglement constraints and designing symmetry-protected quantum protocols.

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