发表机构
National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究最大化Rényi稳定子熵的量子态，提出Pauli平坦态概念，探讨其存在性、构造、纠缠与非局域性，为量子魔力与Pauli相关结构关系提供新视角。
AI 中文摘要
量子魔力是容错量子计算所必需的一种资源，它刻画了量子态偏离经典可模拟的稳定子集合的程度。受其在量子信息处理中作用的启发，我们研究了最大化Rényi稳定子熵的量子态的相关结构，重点关注T型态和Hoggar态。受这些态独特性质的启发，我们探索了Pauli平坦态的概念，即所有Pauli弦上的期望值绝对值相等的N量子比特态。这些态重现了高魔力态的相关结构，这也可以被解释为Pauli协变N量子比特对称信息完备（SIC）Weyl-Heisenberg基准态的一种混合变体，尽管它们不一定具有非平凡的量子魔力。我们研究了它们的存在性和可能的构造，包括稳定子多胞体内部和外部的例子。为了识别后者，我们考察了一个针对所引入态族定制的魔力见证者。最后，我们讨论了它们的纠缠和Bell非局域性，对其量子性质提供了更广泛的刻画。为了完整性，我们找到了在Pauli期望值上具有放宽条件（迫使不等元素为零）的纯态，并讨论了它们的非稳定子性。我们的结果为量子魔力与Pauli相关结构之间的关系提供了新视角。它们与量子力学的几何方法、纠缠和魔力检测以及估计任务相关。
英文摘要
Quantum magic is a necessary resource for fault-tolerant quantum computing, capturing the departure of quantum states from the classically simulable stabiliser set. Motivated by its role in quantum information processing, we investigate the correlation structure of states that maximize the Rényi stabiliser entropies, focusing on the T-type and Hoggar states. Inspired by their distinctive properties, we explore the notion of Pauli flat states, defined as N-qubit states whose expectation values on all Pauli strings are equal in absolute value. These states reproduce the correlation structure of highly magical states, which could also be interpreted as a mixed variant of Pauli covariant N-qubit symmetric informationally complete (SIC) Weyl-Heisenberg fiducial states, while not necessarily possessing nontrivial quantum magic. We investigate their existence and possible constructions, including examples both inside and outside of the stabiliser polytope. To identify the latter, we examine a magic witness tailored to the introduced family of states. Finally, we discuss their entanglement and Bell nonlocality, providing a broader characterization of their quantum properties. For completeness, we find pure states with a relaxed condition on the Pauli expectations, which forces unequal elements to zero, and discuss their non-stabiliserness. Our results offer a new perspective on the relation between quantum magic and Pauli correlation structures. They hold relevance to geometrical approaches to quantum mechanics, entanglement and magic detection, as well as estimation tasks.
CommentsAll comments are highly welcomed. 6 pages + appendix
