发表机构
Department of Physics, Faculty of Science, Universiti Malaya（马来亚大学理学院物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建非幺正形变非厄米二体模型，分离非厄米简并与纠缠，通过两量子比特实现揭示纠缠随非厄米性参数单调增长，非局域魔术在中间耦合处最大，为相关研究提供诊断方法。
AI 中文摘要
非厄米简并通常通过谱合并讨论，而纠缠是本征向量的属性，无需仅由本征值决定。我们构建了一个紧凑的二体模型以分离这两个概念：对具有简并本征空间的厄米算符进行可逆非幺正相似变换，得到的哈密顿量为非厄米的，且在非厄米性参数的每个有限值处均保留非缺陷简并。对于可严格求解的两量子比特实现，尽管谱不变，右本征态仍从乘积态连续演化为最大纠缠态。我们区分了正右态约化密度矩阵与通常非正的双正交约化（其熵可能为复数）；该两量子比特解给出了闭合的部分转置负性与施密特规范非局域魔术。纠缠随非厄米性参数单调增长，而非局域魔术在乘积态与最大纠缠态极限下均消失，在中间耦合处达到最大。在更大的二体空间中，佩奇熵与哈尔平均纯度为本征态典型性提供参考值，这些诊断量可分离非缺陷简并、奇异点敏感性、哈尔典型纠缠及非稳定器关联，无需依赖大量依赖基的谱量。
英文摘要
Non-Hermitian degeneracies are usually discussed through spectral coalescence, whereas entanglement is a property of eigenvectors and need not be fixed by the eigenvalues alone. We formulate a compact bipartite model that separates these two notions. A Hermitian operator with a degenerate eigenspace is transformed by an invertible non-unitary similarity map. The resulting Hamiltonian is non-Hermitian and retains a non-defective degeneracy at every finite value of the non-Hermiticity parameter. For an exactly solvable two-qubit realization, the right eigenstates evolve continuously from product states to maximally entangled states although the spectrum is unchanged. We distinguish the positive right-state reduced density matrix from the generally non-positive biorthogonal reduction, for which entropy may become complex. The same two-qubit solution gives a closed partial-transpose negativity and a Schmidt-gauged non-local magic. Entanglement grows monotonically with the non-Hermiticity parameter, whereas the non-local magic vanishes for both the product and maximally entangled limits and is largest at an intermediate coupling. In larger bipartite spaces, the Page entropy and Haar-averaged purity provide reference values for eigenstate typicality. These diagnostics separate non-defective degeneracy, exceptional-point sensitivity, Haar-typical entanglement, and non-stabilizer correlations without relying on a proliferation of basis-dependent spectral quantities.
