发表机构
Jadavpur University; Presidency University（贾达普大学; 总统大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在相互作用玻色子模型中发现部分动力学对称性（PDS）的量子信息指纹为标签方差，可区分可解与混合本征态，还在量子比特寄存器上编码模型以制备相关本征态。
AI 中文摘要
部分动力学对称性（PDS）是一种代数结构，其中规定的对称性既非精确也未完全破缺：一部分本征态保持好量子数且可解，而其余能谱发生混合。目前，PDS通过光谱数据、带首能量、能级系统学和B(E2)比值来识别。我们探究其是否在本征态中也存在纯结构特征，结果表明存在，但并非体现在纠缠度上。自然的诊断量是对称性卡西米（Casimir）的方差，即标签方差$\text{Var}\{\cal C}[G]$，我们证明它与块相干熵和块杂质等价：当态仅携带一个不可约表示标签时，三者均精确为零。逐态解析可知，在稳定对称点以及Leviatan的一阶、二阶临界点，该量在可解子集上为零，在混合态上为$N^2$量级，且在临界点处呈现由相变阶次决定的两种不同形式。相比之下，二分纠缠度无法区分可解态与混合态，即便标签精确也会发生漂移。我们以$^{168}$Er为锚点展开分析，将块纯度与准动力学对称性文献中的“纯度/相干性”表述相联系，证明标签方差与多体纠缠及量子魔力（magic）均无关联。最后，我们在量子比特寄存器上编码该模型，并变分制备其可解与混合本征态，为在量子设备上评估该诊断量奠定基础。
英文摘要
Partial dynamical symmetry (PDS) is an algebraic structure in which a prescribed symmetry is neither exact nor completely broken: a subset of eigenstates keeps good quantum numbers and remains solvable while the rest of the spectrum mixes. PDS is currently identified from spectroscopic data, band-head energies, level systematics, and $B(E2)$ ratios. We ask whether it also has a purely structural signature in the eigenstates, and find that it does, though not in the magnitude of entanglement. The natural diagnostic is the variance of a symmetry Casimir, the label variance $\Var\,\C[G]$, which we show coincides with a block-coherence entropy and a block impurity: all three vanish exactly when a state carries a single irreducible-representation label. Resolved state by state, this quantity is zero on the solvable subset and of order $N^2$ on the mixed states, at stable symmetry points and at Leviatan's first- and second-order critical points, where it takes two distinct forms set by the order of the transition. The magnitude of bipartite entanglement, by contrast, does not separate solvable from mixed states and drifts even where the labels are exact. We anchor the analysis in $^{168}$Er, connect the block purity to the ``purity/coherence'' language of the quasi-dynamical-symmetry literature, and show the label variance is uncorrelated with multipartite entanglement and with magic. Finally we encode the model on a qubit register and prepare its solvable and mixed eigenstates variationally, as a step toward evaluating the diagnostic on a quantum device.
