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arXiv 1408.6633hep-th
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Fisher信息空间中的测地距离与全息熵公式

Geodesic Distance in Fisher Information Space and Holographic Entropy Formula

Hiroaki Matsueda

摘要:

本文研究了Fisher信息空间中的测地距离,其中度量是由CFT_(1+1)中的纠缠熵定义的。很明显,在这种情况下,在恒定时间的测地线距离是嵌入信息空间的熵数据的函数。在一种特殊情况下,测地线方程可以解析求解,我们发现距离符合Ryu-Takayanagi公式。然后,我们可以理解距离如何看待嵌入的量子信息。结果表明,Fisher度规是构造全息时空的有效工具。

英文摘要:

In this short note, we examine geodesic distance in Fisher information space in which the metric is defined by the entanglement entropy in CFT_(1+1). It is obvious in this case that the geodesic distance at a constant time is a function of the entropy data embedded into the information space. In a special case, the geodesic equation can be solved analytically, and we find that the distance agrees well with the Ryu-Takayanagi formula. Then, we can understand how the distance looks at the embeded quantum information. The result suggests that the Fisher metric is an efficient tool for constructing the holographic spacetime.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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