非定域魔力：闭式解与纯化魔力的等价性
Non-local Magic: closed-form solution and equivalence with magic of purification
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中文总结 AI 辅助
该研究针对对数稳定子保真度给出非定域魔力的闭式解，引入纯化魔力并证明其与非定域魔力的等价性，为非定域魔力提供解析表征与混合态资源理论解释。
中文摘要 AI 辅助
非定域魔力用于量化双体量子态中无法通过局域幺正变换去除的非稳定子性。尽管其定义自然，但其评估通常需要对所有局域幺正变换进行复杂优化。本文针对对数稳定子保真度，证明该优化存在仅依赖施密特谱的精确闭式解析解。接着，我们引入纯化魔力，定义为混合态所有纯化态中纯态魔力的最小值，并证明其自然诱导出一种资源理论，其中自由态为归一化稳定子码投影算符。对于对数稳定子保真度，纯化魔力可基于Uhlmann保真度表述为距离形式。值得注意的是，我们证明非定域魔力与约化密度算子幺正轨道上的最小纯化魔力完全一致。本文结果为非定域魔力提供了高效的解析表征及混合态资源理论解释。
英文摘要
Non-local magic quantifies the non-stabilizerness of a bipartite quantum state that cannot be removed by local unitary transformations. Despite its natural definition, its evaluation generally requires a difficult optimization over local unitaries. Here, we show that for the log-stabilizer fidelity this optimization admits an exact closed-form analytic solution depending only on the Schmidt spectrum. We then introduce the magic of purification, defined as the minimum pure-state magic over all purifications of a mixed state, and show that it naturally induces a resource theory whose free states are normalized stabilizer-code projectors. For the log-stabilizer fidelity, the magic of purification admits a distance-based formulation in terms of the Uhlmann fidelity. Remarkably, we prove that non-local magic coincides with the minimum magic of purification along the unitary orbit of the reduced density operator. Our results provide both an efficient analytical characterization and a mixed-state resource-theoretic interpretation of non-local magic.
发表机构
- Università degli Studi di Salerno（萨莱诺大学）
- Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）
- Scuola Superiore Meridionale（南方高等学院）
- Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）
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