量子态纹理度量与纹理变换
Quantum-state texture measure and texture transformation
- Inner Mongolia University（内蒙古大学）
- Xiamen University（厦门大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文扩展量子态纹理理论，研究无纹理操作下的态转换，提出两类新纹理度量并证明纹理单调量的逆构造，形成较全面的资源理论框架。
AI中文摘要：
量子态纹理量化了所选基下态的结构不规则性，并已成为通用电路中门表征的宝贵资源。因此，人们提出了基于收缩距离的纹理度量类以及构建凸包扩展纹理度量的框架。在此，我们从多个方向扩展这一理论。我们研究了在无纹理操作下纯态到任意态的转换性，并完全解决了量子比特情形下任意两态之间的确定性变换问题。随后，我们提出了两类纹理度量：基于凸函数的度量和通过纯态中所含纹理的最小代价定义的纹理代价。此外，我们证明每个纹理单调量都会产生一个非负函数，该函数具有与凸包扩展中所用函数相同的性质——从而为该构造提供了逆命题。我们的工作因此为量子态纹理提供了一个相对全面的资源理论表述。
英文摘要：
Quantum-state texture quantifies structural irregularities of a state in a selected basis and has emerged as a valuable resource for gate characterization in universal circuits. Consequently, a class of contractive distance based texture measures and a framework for constructing convex-roof extended texture measure have been proposed. Here, we extend this theory in several directions. We examine the convertibility of a pure state to any state under texture-free operations, and fully solve the deterministic transformation problem between any two states in the qubit case. We then propose two classes of texture measures: convex-function-based measures and texture cost defined via minimal cost of texture contained in pure states. Moreover, we show that every texture monotone gives rise to a non-negative function which admits the same properties as the function used in the convex-roof extension---thus providing a converse to that construction. Our work thereby offers a relatively comprehensive resource-theoretic formulation of quantum-state texture.
