发表机构
Duke University（杜克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究以负性秩为工具，探究qudit-qudit纠缠对量子噪声的敏感性，明确了负性秩与噪声鲁棒性的关联，推导了APPT子空间噪声边界等紧界，拓展了对纠缠与量子设备实际环境关系的认知。
AI 中文摘要
量子多体系统的复杂性体现在其展现纠缠的能力，纠缠是量子计算核心的独特量子关联。为定量探究量子噪声对纠缠资源的削弱效应，我们聚焦于负性见证（一种基于局域时间反演变换的纠缠度量，在简单物理场景中可作为完美见证）。除计算负性外，我们分析qudit-qudit二分系统的部分转置密度矩阵的相关本征值谱，发现更高的负性秩对目标噪声具有更强鲁棒性，对去极化噪声则鲁棒性更弱。特别地，我们将可任意混入纠缠纯系综且仍保留负性的可分态最大数量扩展至恰好等于原始负性秩。此外，我们阐明负性秩在完全去极化信道中的作用，可直接计算：（1）绝对正部分转置（APPT）子空间的某些噪声边界，超出该边界后无幺正算子可产生负性；（2）最大qutrit-qutrit APPT纯度。这些结果除证明紧界并助力持续开展的APPT纠缠研究外，还深化了我们对基于纠缠的计算与量子设备实际运行环境之间微妙关系的理解。
英文摘要
One aspect of complexity for quantum many-body systems resides in their ability to exhibit entanglement, uniquely quantum correlations central to quantum computation. To quantitatively explore the diminishing effect that quantum noise has on entanglement resources, we focus on the negativity witness, an entanglement measure based on local time reversal transformations that provides a perfect witness in simple physical contexts. Beyond calculation of the negativity, we analyze the associated eigenvalue spectra of partially transposed density matrices for qudit-qudit bipartitions, finding that higher negativity rank provides greater(reduced) robustness to targeted(depolarizing) noise. In particular, we extend the maximum number of separable states that can be arbitrarily mixed into an entangled pure ensemble while retaining negativity to be exactly equal to the original negativity rank. Furthermore, we report how understanding the role of the negativity rank with respect to the completely depolarizing channel allows direct calculation of (1) certain noise boundaries for the Absolutely Positive Partial Transpose (APPT) subspace beyond which no unitary operator is capable of generating negativity and (2) the maximum qutrit-qutrit APPT purity. Beyond proving tight bounds and contributing to the ongoing search for APPT entanglement, these results expand our understanding of the nuanced relationship between computation with entanglement and practical environments for operating quantum devices.
Comments20 pages, 2 figures
