基于希尔伯特-施密特代价的可分量子最优传输的度量性
Metricity of separable quantum optimal transport with the Hilbert-Schmidt cost
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中文总结 AI 辅助
该研究证明了基于希尔伯特-施密特代价的可分量子最优传输相关距离的度量性，确立了特定量子最优传输构造的三角不等式，为量子最优传输的理论性质提供了关键支撑。
中文摘要 AI 辅助
我们证明，与反对称子空间上正交投影相关的可分量子最优传输代价的平方根，定义了密度矩阵之间的真实距离。等价地，这确立了由纯态间希尔伯特-施密特距离诱导的二阶Beatty-França量子最优传输构造的三角不等式。该结果还证明了由可分SWAP保真度导出的对应距离的度量性。证明中用凸包络对偶和厄米算子的与维度无关的插值结果替代了不可用的粘合论证。
英文摘要
We prove that the square root of the separable quantum optimal transport cost associated with the orthogonal projection onto the antisymmetric subspace defines a genuine distance between density matrices. Equivalently, this establishes the triangle inequality for the order-two Beatty-França quantum optimal transport construction induced by the Hilbert-Schmidt distance between pure states. The result also proves metricity of the corresponding distance derived from separable SWAP fidelity. The proof replaces the unavailable gluing argument by convex-roof duality and a dimension-independent interpolation result for Hermitian operators.
发表机构
- Copernicus Center for Interdisciplinary Studies（哥白尼跨学科研究中心）
- Jagiellonian University（雅盖隆大学）
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