量子态块纹理及其量化
Quantum-state block texture and its quantification
AI总结：
研究将量子态纹理推广到量子态块纹理，开创框架并提出三种块纹理度量，比较其区别与关系，证明几何度量是迹距离度量上限，对特定量子态族评估度量值并采样数据，揭示不同方法构建的度量有不同特征及潜在作用。
AI中文摘要：
量子态纹理（QST）是一种新兴的量子资源，随着量子理论的发展受到越来越多的关注。在这项工作中，我们将QST推广到量子态块纹理（QSBT）。这种推广为量化量子态在量子信息处理中的优势提供了深刻的操作解释。我们开创了一个用于表征和量化量子态块纹理的替代框架，并提出了三种类型的块纹理度量。通过比较这些QSBT度量，我们研究了它们的区别和相互关系。我们证明几何度量是基于迹距离度量的上限。对于特定的量子态族，我们评估了两种基于迹距离度量的值。然后我们从这个态族中采样四组数据，每组分别包含\(5\times10^4\)、\(10^5\)、\(5\times10^5\)和\(10^6\)个样本，并给出了相应的分布。我们的结果表明，通过不同方法构建的QSBT度量具有不同的特征，表明它们在量化量子态块纹理方面的潜在作用。
英文摘要：
Quantum-state texture (QST) is an emerging quantum resource that has garnered increasing attention amid advances in quantum theory. In this work, we generalize the QST to quantum-state block texture (QSBT). This generalization provides profound operational interpretations for quantifying the advantages of quantum states in quantum information processing. We pioneer an alternative framework for characterizing and quantifying quantum-state block texture, and propose three types of block texture measures. By comparing these QSBT measures, we investigate their distinctions and interrelationships. We demonstrate that the geometric measure serves as an upper bound for the trace distance-based measure. For a specific family of quantum states, we evaluate the values of two trace distance-based measures. Then we sample four sets of data from this family of states, with each set comprising $5\times 10^4, 10^5, 5\times 10^5$ and $10^6 $ samples, respectively, and present the corresponding distributions. Our results reveal that the QSBT measures constructed via different approaches show distinct characteristics, indicating their potential roles in quantifying the block texture of quantum states.
