量化对称性破缺
Quantifying Symmetry Breaking with Metric Adjusted Quantum Geometric Tensors
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中文总结 AI 辅助
本文在独立同分布渐近条件下，利用单参数量子Fisher信息矩阵族，完全解决了紧致李群对称性下有限维混合态的对称性破缺量化问题，建立了最优转换率公式，并揭示了不可逆性与激活机制。
中文摘要 AI 辅助
通过量子态操控的极限来量化量子态的性质是量子资源理论的核心目标。对于对称性破缺，量子几何张量支配着渐近纯态转换，但一般混合态的完整表征仍然难以捉摸。在此，我们完全解决了在独立同分布渐近条件下，紧致李群对称性下有限维系统的这一问题。具体而言，我们在不对称性资源理论中，建立了任意态之间最优转换率的单字母公式，且迹距离误差趋于零。该转换率由一族单参数量子Fisher信息（QFI）矩阵决定，该矩阵族在对称和右对数导数QFI之间插值。即使对于$U(1)$对称性，该族中也没有与态无关的有限子集普遍适用，这揭示了与纯态转换的定性区别。我们的公式进一步导出了基于广义量子几何张量的纯态蒸馏率的精确公式，刻画了渐近可逆互转换，并识别了量子钟的束缚不对称性。QFI族不同成员之间的互补性也揭示了量子钟的激活机制。我们的证明依赖于两个独立有趣的发展。首先，我们将量子局部渐近正态性扩展到具有任意秩和谱简并的酉模型。其次，我们根据同一单参数QFI族来表征量子高斯平移模型之间的可转换性。总之，这些结果为独立同分布渐近条件下一般量子态的对称性破缺提供了操作性表征，并揭示了不同的QFI约束如何导致不可逆性和激活。
英文摘要
Quantifying properties of quantum states through the limits of their manipulation is a central goal of quantum resource theories. For symmetry breaking, the quantum geometric tensor (QGT) governs asymptotic pure-state conversion, but a complete characterization for general mixed states has remained elusive. Here we fully resolve this problem for finite-dimensional systems under compact Lie group symmetries in the i.i.d. asymptotic regime. Specifically, we establish a single-letter formula for the optimal conversion rate between arbitrary states, with vanishing trace-distance error, in the resource theory of asymmetry. The rate is determined by a one-parameter family of metric adjusted QGTs, obtained by rescaling quantum Fisher information (QFI) matrices that interpolate between the symmetric logarithmic derivative and right logarithmic derivative (RLD) QFIs. For pure states, the RLD endpoint recovers the standard QGT. No state-independent finite subset of this family suffices in general, even for $U(1)$ symmetry, revealing a qualitative distinction from pure-state conversion. Our formula further yields an exact pure-state distillation-rate formula in terms of a single asymmetry measure, characterizes asymptotically reversible interconversion, and identifies bound asymmetry for quantum clocks. Complementarity among members of the metric adjusted QGT family also reveals an activation mechanism: a state with zero conversion rate to a mixed clock state can still enhance another input's yield under joint processing. Our proof relies on two developments of independent interest. First, we extend quantum local asymptotic normality to unitary models with arbitrary rank and spectral degeneracy. Second, we characterize convertibility between quantum Gaussian shift models in terms of the same one-parameter family of QFIs.
发表机构
- University of Waterloo（滑铁卢大学）
- Perimeter Institute for Theoretical Physics（圆周理论物理研究所）
- Kyushu University（九州大学）
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