巴尔加门不变量与局部酉等价
Bargmann invariants and local unitary equivalence
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中文总结 AI 辅助
研究\(\mathbb{C}^n\otimes\mathbb{C}^n\)上量子态的局部酉等价性，\(n = 2\)时两量子比特态局部酉轨道由局部酉巴尔加门不变量确定，而\(n\geqslant 3\)时该不变量不构成完备不变量，否定了L. Zhang和B. Xie的问题。
中文摘要 AI 辅助
本文研究了\(\mathbb{C}^n\otimes\mathbb{C}^n\)上量子态的局部酉等价性，这是量子信息论中的一个重要概念。对于\(n = 2\)的情况，两量子比特态的局部酉轨道完全由其局部酉巴尔加门不变量确定。我们证明，对于\(n\geqslant 3\)，局部酉巴尔加门不变量并不构成局部酉轨道的一组完备不变量，这对L. Zhang和B. Xie提出的一个问题给出了否定答案。
英文摘要
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.
