AI 中文总结
研究魔法保护纠缠，开发克利福德轨道框架，利用残余纠缠定义相关特征。确定魔法纠缠相互作用的\(T\) - 魔法和\(W\) - 魔法两种状态及转变，将魔法纠缠作为非稳定性保护量子相关性的轨道级诊断。
AI 中文摘要
我们开发了一个用于研究魔法保护纠缠（我们称之为魔法纠缠）的克利福德轨道框架，魔法纠缠是二分纠缠在最优稳定器简化后剩余的部分。此构建利用克利福德约化下的残余纠缠作为魔态空间的态级组织原则。它定义了表征态的克利福德不可约结构的典范代表、谱和秩。我们确定了魔法纠缠相互作用的两种状态。在\(T\) - 魔法状态下，局部非稳定器资源可与纠缠共存，但受保护部分仍然较弱且依赖于态。在\(W\) - 魔法状态下，相反，纠缠与非稳定性克利福德不可约地联系在一起，产生典型的、强自平均行为。分析示例和随机电路数值支持从广泛的\(T\) - 魔法涨落到集中的、类似哈尔的\(W\) - 魔法行为的转变。这些结果将魔法纠缠确定为非稳定性如何保护量子相关性免受克利福德约化影响的轨道级诊断。
英文摘要
We develop a Clifford-orbit framework for studying magic-protected entanglement, which we refer to as magical entanglement: the part of bipartite entanglement that remains after optimal stabilizer simplification. This construction leverages residual entanglement under Clifford reduction as a state-level organizing principle for magic state space. It defines canonical representatives, spectra, and ranks that characterize the Clifford-irreducible structure of a state. We identify two regimes of the magic-entanglement interplay. In the $T$-magic regime, local nonstabilizer resources can coexist with entanglement, but the protected component remains weak and state-dependent. In the $W$-magic regime, by contrast, entanglement is Clifford-irreducibly tied to nonstabilizerness, producing typical, strongly self-averaging behavior. Analytical examples and random-circuit numerics support a crossover from broad $T$-magic fluctuations to concentrated, Haar-like $W$-magic behavior. These results identify magical entanglement as an orbit-level diagnostic of how nonstabilizerness protects quantum correlations against Clifford reduction.
Comments18 pages, 7 figures, 1 table
