发表机构
School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究确定了量子比特各向同性态和两量子比特贝尔对角态的精确纠缠代价，并利用半群方法和张量积定理推导出qudit态及退极化信道的一般下界，显著改进了现有结果。
AI 中文摘要
纠缠代价是制备量子态所需的贝尔对的渐近速率。其正则化定义使得精确计算变得困难，即使对各向同性态（即退极化的最大纠缠态）也是如此。在这项工作中，我们确定了每个量子比特各向同性态以及更一般地每个两量子比特贝尔对角态的纠缠代价。我们的证明使用一族适当调谐的量子比特半群，将一般的对数Sobolev熵界转化为Wootters函数的支撑线。Dong等人最近的一个精确张量积定理[arXiv:2606.17729]将这些界扩展到任意多个副本，从而得到纠缠代价的一般下界。将该下界与形成纠缠相匹配，也确定了更广泛的两量子比特态类别的精确代价。对于qudit各向同性态，我们从完全退极化$2\to 3$范数推导出另一个一般下界。该下界显著优于PPT相对熵纠缠，并且几乎与形成纠缠相匹配，留下的差距至多为$\log d$的$2\\%$，且随着$d$的增长而消失。最后，精确的量子比特结果和qudit界扩展到在并行和顺序策略下制备量子退极化信道的纠缠代价。
英文摘要
Entanglement cost is the asymptotic rate of Bell pairs required to prepare a quantum state. Its regularized definition has made exact evaluation difficult, even for isotropic states (i.e., depolarized maximally entangled states). In this work, we determine the entanglement cost of every qubit isotropic state and, more generally, every two-qubit Bell-diagonal state. Our proof uses a family of suitably tuned qubit semigroups to transform a general log-Sobolev entropy bound into supporting lines of Wootters' function. A recent exact tensorization theorem of Dong et al. [arXiv:2606.17729] extends these bounds to arbitrarily many copies, yielding a general lower bound on entanglement cost. Matching this bound with the entanglement of formation also determines the exact cost for a broader class of two-qubit states. For qudit isotropic states, we derive another general lower bound from the full depolarizing $2\to 3$ norm. This bound substantially improves on the PPT-relative entropy of entanglement and nearly matches the entanglement of formation, leaving a gap of at most $2\%$ of $\log d$ that vanishes as $d$ grows. Finally, the exact qubit results and qudit bounds extend to the entanglement cost of preparing quantum depolarizing channels under both parallel and sequential strategies.
Commentscomments are welcome
