基于量子态约化识别局部酉等价
Identifying local unitary equivalence based on reduction of quantum states
AI总结：
研究一类含特定特征值的量子态的局部酉等价识别问题，引入“约化”程序，利用现有标准为约化态建立判别框架，还验证了两族单参数多体混合态的局部酉等价性，展现方法有效性与通用性。
AI中文摘要：
局部酉等价对于纠缠量化和分类至关重要，但识别它仍然是一项艰巨挑战。本文针对一类具有一个高度简并特征值和其余非简并单特征值的量子态解决此问题，这些量子态对量子资源理论中的结构化资源至关重要。我们引入一种“约化”程序，通过消除最高重特征值将每个态映射到“约化态”，并证明原始态的局部酉等价性与其约化对应态的等价。对于得到的纯或非简并约化态，我们采用现有不变量或不动点子群标准建立完整判别框架。此外，我们还验证了通过扰动不同组合起源的绝对最大纠缠态构造的两族单参数多体混合态的局部酉等价性，证明了方法的有效性和通用性。
英文摘要：
Local unitary equivalence is central to entanglement quantification and classification. Identifying the local unitary equivalence remains a formidable challenge. We address this problem for a class of quantum states with one highly degenerate eigenvalue and the rest non-degenerate simple eigenvalues that are pivotal to structured resources in quantum resource theory. We introduce a ``reduction" procedure that maps each state to a ``reduced state" by nullifying the highest-multiplicity eigenvalue and prove that the local unitary equivalence of the original states is equivalent to that of their reduced counterparts. For the resulting pure or non-degenerate reduced states, we employ the existing invariants or fixed-point subgroup criteria to establish a complete discrimination framework, although the existing criteria can not directly identify the local unitary equivalence of the original states. We also verify the local unitary equivalence of two families of single-parameterized multipartite mixed states constructed by perturbing absolutely maximally entangled states from distinct combinatorial origins, demonstrating the efficacy and generality of our approach.
