Reconstructing quantum geometry from quantum information: Area renormalisation, coarse-graining and entanglement on spin networks
Reconstructing quantum geometry from quantum information: Area renormalisation, coarse-graining and entanglement on spin networks
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从量子信息重建量子几何：自旋网络上的面积重正化、粗粒度和纠缠
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Daniel R. Terno
中科院分区：
文献类型：
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作者：
E. Livine;Daniel R. Terno
在简要回顾了自旋网络及其作为（空间）几何波函数的解释之后，我们讨论了环量子引力中区域算子的重整化。在这样一个背景无关的框架中，我们建议通过分析其区域的粗粒化和重整化流来探测表面的结构。我们进一步引入了一种处理粗粒自旋网络态的方法，并定量地研究了在此过程中自由度的减少。最后，我们使用这些粗粒度工具来定义自旋网络各部分之间的关联和纠缠，并讨论它们作为这种量子几何状态下距离的自然度量的潜在解释。
After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose to probe the structure of a surface through the analysis of the coarse-graining and renormalisation flow(s) of its area. We further introduce a procedure to coarse-grain spin network states and we quantitatively study the decrease in the number of degrees of freedom during this process. Finally, we use these coarse-graining tools to define the correlation and entanglement between parts of a spin network and discuss their potential interpretation as a natural measure of distance in such a state of quantum geometry.