The purpose of this letter is to explore the relation between gauge fields, which are at the base of our understanding of fundamental interactions, and the quantum entanglement. To this end, we investigate the case of ${\rm SU}(2)$ gauge fields. It is first shown that holonomies of the ${\rm SU}(2)$ gauge fields are naturally associated with maximally entangled two-particle states. Then, we argue that the notion of such gauge fields can be deduced from the transformation properties of maximally entangled two-particle states. This new insight unveils a possible relation between gauge fields and spin systems, as well as contributes to understanding of the relation between tensor networks (such as MERA) and spin network states considered in loop quantum gravity. In consequence, our results turn out to be relevant in the context of the emerging Entanglement/Gravity duality.

中文翻译：

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规范场和量子纠缠

这封信的目的是探索规范场与量子纠缠之间的关系，规范场是我们理解基本相互作用的基础。为此，我们研究了 ${\rm SU}(2)$ 规范场的情况。它首先表明，${\rm SU}(2)$ 规范场的完整度自然地与最大纠缠的两粒子态相关联。然后，我们认为这种规范场的概念可以从最大纠缠的两粒子态的变换性质推导出来。这一新见解揭示了规范场和自旋系统之间可能存在的关系，并有助于理解张量网络（如 MERA）与圈量子引力中考虑的自旋网络状态之间的关系。结果，