发表机构
School of Mathematics and Statistics, Hainan University; Hainan International Exchange Center for Theoretical Physics（海南大学数学与统计学院; 海南理论物理国际交流中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对伪密度矩阵（PDM），证明存在满足幺正不变性和强可加性的唯一冯·诺依曼熵扩展，还验证其对单量子比特动力学次可加性并分析示例行为。
AI 中文摘要
伪密度矩阵（PDM）形式主义自然地将密度算子的概念扩展到时空域。PDM是厄米矩阵且迹为单位，但其在编码类空分离系统无法达到的时间关联时会出现负本征值。因此，已有多种方法将仅定义于正算子的冯·诺依曼熵扩展至PDM。本文证明，存在唯一的冯·诺依曼熵泛函扩展，适用于迹为单位的厄米矩阵，满足两个简单假设：幺正不变性和关于区间[-1,1]内仿射组合的强可加性，我们证明该区间包含PDM的本征值。我们还证明，该冯·诺依曼熵到PDM的唯一扩展对单量子比特动力学是次可加的，并分析其在多个示例中的行为。
英文摘要
The pseudo-density matrix (PDM) formalism naturally extends the notion of density operator to the spatiotemporal domain. While PDMs are Hermitian and of unit trace, they admit negative eigenvalues when encoding temporal correlations unattainable for spacelike separated systems. Consequently, there have been various approaches to extending the von~Neumann entropy---which is only defined for positive operators---to PDMs. Here, we prove that there exists a unique extension of the von~Neumann entropy functional to Hermitian matrices of unit trace satisfying two simple assumptions: unitary invariance and strong additivity with respect to affine combinations within the interval $[-1,1]$, which we prove contains the eigenvalues of a PDM. We also prove that this unique extension of von~Neumann entropy to PDMs is subadditive for single qubit dynamics, and we analyze its behavior in a number of examples.
Comments21 pages and 3 figures
