量子通道的旋网络
Spin networks of quantum channels
AI总结：
本文提出将量子通道引入旋网络框架，以描述环境效应，并通过Kraus算子定义新的旋网络状态和希尔伯特空间。
摘要：
在环量子引力中，旋网络传统上由单位ary holonomies描述，对应于无噪声转换。在本工作中，我们扩展了这一框架，以纳入一般的量子通道，这些通道可以建模环境效应，并在普朗克尺度上变得显著。具体而言，我们证明了Kraus算子的变换性质，这些算子定义了完全正迹保持（CPTP）映射，与旋网络的规范不变性一致。这使得能够引入通用的旋网络状态，这些状态可以以Kraus算子表示。此外，提出了一种相关的内积概念，允许引入希尔伯特空间。我们通过涉及Wilson环和偶极子网络的例子来说明这些构造。
英文摘要：
Spin networks in Loop Quantum Gravity are traditionally described by unitary holonomies corresponding to noiseless transformations. In this work, we extend this framework to incorporate general quantum channels that model effects of environment, which can become significant at the Planck scale. Specifically, we demonstrate that the transformation properties of Kraus operators, which define completely positive trace-preserving (CPTP) maps, are consistent with the gauge invariance of spin networks. This enables the introduction of generalized spin network states that can be expressed in terms of the Kraus operators. Furthermore, the associated notion of an inner product is proposed, allowing for introduction of the Hilbert space. We illustrate these constructions with examples involving a Wilson loop and a dipole network.
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