AI 中文总结
研究任意维度\(d\)的最大纠缠量子位在非马尔可夫纯退相下的纠缠与量子失协，利用独立玻色子模型精确解，通过托普利兹结构得闭式表达式及最优测量，证明两量随维度增长饱和到与维度无关值，收敛速率\(1/d\)，并经多种方法验证。
AI 中文摘要
我们使用独立玻色子模型的精确解，研究任意维度\(d\)的一对最大纠缠量子位在非马尔可夫纯退相下的纠缠和量子失协的时间演化。由于该解无需玻恩 - 马尔可夫、林德布拉德或旋转波近似，这里报告的每个结果都直接来自精确动力学。利用所得密度矩阵的托普利兹结构，我们得到了作为有限和的负性的闭式表达式，对任意维度和演化时间均有效，以及量子失协的相应闭式表达式。对于这里考虑的退相最大纠缠态族，我们证明在整个测量算子空间中计算基测量是全局最优的，从而消除了评估量子失协所需的数值优化。我们进一步表明，随着维度增长，这两个量都饱和到与维度无关的极限值，收敛速率恰好为\(1/d\)。对于负性，通过一个严格定理建立了这种标度律，包括阶为\(e^{-\alpha d^2}\)的高斯型误差界，并在洛伦兹和欧姆两类不同谱密度的六个独立参数区域得到证实；对于失协，在六个洛伦兹区域通过数值方法发现了相同的主导行为。分析结果通过独立数值方法验证，包括从基本定义重建、任意精度算术和互补伪模交叉检查。
英文摘要
We study the time evolution of entanglement and quantum discord for a pair of maximally entangled qudits of arbitrary dimension $d$ under non-Markovian pure dephasing, using the exact solution of the independent boson model. Because this solution requires no Born--Markov, Lindblad, or rotating-wave approximation, every result reported here follows directly from the exact dynamics. Exploiting the Toeplitz structure of the resulting density matrix, we obtain a closed-form expression for the negativity as a finite sum, valid for arbitrary dimension and evolution time, together with a corresponding closed-form expression for the quantum discord. For the family of dephased maximally entangled states considered here, we prove that a computational-basis measurement is globally optimal over the entire POVM space, thereby eliminating the numerical optimization otherwise required for evaluating the quantum discord. We further show that both quantities saturate, as the dimension grows, to a dimension-independent limiting value, with a convergence rate of exactly $1/d$. For negativity, this scaling law is established through a rigorous theorem, including a Gaussian-type error bound of order $e^{-αd^2}$, and is confirmed across six independent parameter regimes for two distinct classes of spectral density, Lorentzian and Ohmic; for discord, the same leading-order behavior is found numerically across the six Lorentzian regimes. The analytical results are validated by independent numerical approaches, including reconstruction from the underlying definitions, arbitrary-precision arithmetic, and a complementary pseudomode cross-check.
Comments39 pages, 4 figures
