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arXiv · 2607.16878

Bargmann invariants and local unitary equivalence

Minghui Ma·Rui Shi
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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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Minghui Ma, Rui Shi. 2026-07-18. Bargmann invariants and local unitary equivalence. https://arxiv.org/abs/2607.16878

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