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arXiv 2004.07960hep-th
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相对态复杂性的全息解释

Holographic Interpretation of Relative State Complexity

Alexander Yosifov, Aditya Iyer, Lachezar Filipov

摘要:

我们研究了一个大的$N$ CFT在一个高能量的纯态耦合到一个小的辅助系统的$M$弱相互作用的自由度,并认为辅助系统的相对状态的复杂性是全息对偶的一个有效的低能量概念的计算成本在散装,\textit{i.e.}的最小深度的量子线路解码其引力对偶。鉴于此,利用Nielsen的方法,提出了一种新的量子混沌电路复杂度演化的度量。研究辅助系统电路复杂度的演化可以揭示大$N$ CFT的混沌特性。这一新的量子混沌诊断对蒸发黑洞的内部动力学有重要意义,因为它意味着辐射霍金云是伪随机的。

英文摘要:

We investigate a large-$N$ CFT in a high-energy pure state coupled to a small auxiliary system of $M$ weakly-interacting degrees of freedom, and argue the relative state complexity of the auxiliary system is holographically dual to an effective low-energy notion of computational cost in the bulk, \textit{i.e.} to the minimal depth of the quantum circuit required to decode its gravitational dual. In light of this, using Nielsen's approach, a new measure of quantum chaos in terms of the evolution of circuit complexity is proposed. It suggests that studying the evolution of circuit complexity of the auxiliary system can teach us about the chaotic properties of the large-$N$ CFT. This new diagnostic for quantum chaos has important implications for the interior dynamics of evaporating black holes as it implies the radiated Hawking cloud is pseudorandom.

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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