Bargmann invariants and local unitary equivalence

• URL: http://arxiv.org/abs/2607.16878v1
• Date: Sat, 18 Jul 2026 16:34:31 GMT
• Title: Bargmann invariants and local unitary equivalence
• Abstract summary: We study the local unitary equivalence of quantum states on $mathbbCnotimesmathbbCn$.<n>For the case $n=2$, the local unitary orbits of two-qubit states are completely determined by their local unitary Bargmann invariants.
• Score: 10.534809869409832
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study the local unitary equivalence of quantum states on $\mathbb{C}^n\otimes\mathbb{C}^n$, which is an important notion in quantum information theory. For the case $n=2$, the local unitary orbits of two-qubit states are completely determined by their local unitary Bargmann invariants. We show that the local unitary Bargmann invariants do not form a complete set of invariants of local unitary orbits for $n\geqslant 3$, which negatively answers a problem proposed by L. Zhang and B. Xie.

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