结，链接和远程魔法
Knots, links, and long-range magic
摘要：
我们研究在何种程度上结和链接状态（即，在3D陈-西蒙斯理论准备的结和链接的补充路径整合）可以或不能描述的稳定状态。非稳定态的经典混合态被称为“幻态”，在量子资源理论中起着关键作用。通过实现一个特定的魔术单调称为“法力”，我们量化的魔术结和链接状态。特别是，对于$SU(2)_k$陈-西蒙斯理论，我们表明，结和链接状态一般是神奇的。对于链接状态，我们进一步研究了与独立边界之间的相关性相关的法力，这是状态的远程魔法的特征。我们的数值结果表明，大多数链接状态的魔力是完全长程的。我们使这些语句对圆环链接更清晰。
英文摘要：
We study the extent to which knot and link states (that is, states in 3d Chern-Simons theory prepared by path integration on knot and link complements) can or cannot be described by stabilizer states. States which are not classical mixtures of stabilizer states are known as "magic states" and play a key role in quantum resource theory. By implementing a particular magic monotone known as the "mana" we quantify the magic of knot and link states. In particular, for $SU(2)_k$ Chern-Simons theory we show that knot and link states are generically magical. For link states, we further investigate the mana associated to correlations between separate boundaries which characterizes the state's long-range magic. Our numerical results suggest that the magic of a majority of link states is entirely long-range. We make these statements sharper for torus links.
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