Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality
Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality
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计算伪随机性、虫洞生长悖论以及 AdS/CFT 对偶性的约束
DOI：
10.4230/lipics.itcs.2020.63
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
U. Vazirani
中科院分区：
文献类型：
--
作者：
Adam Bouland;Bill Fefferman;U. Vazirani
在AdS/CFT对应的一个基本问题是虫洞增长悖论。Susskind对这个悖论的解决方案是将虫洞的体积与其在CFT中的对偶量子态的电路复杂性等同起来。我们从复杂性理论的角度研究这个猜想的后果。具体来说，我们给出了证据的存在计算伪随机状态的CFT，并认为虫洞体积是可测量的非物理的，但计算的意义上，通过合并的经验，多个观察员在虫洞。换句话说，这个猜想把一个难以计算的量等同于一个容易计算的量。伪随机性论证进一步暗示这是虫洞增长悖论的任何解决方案的必要特征，而不仅仅是Susskind的复杂性=体积猜想。作为推论，我们得出结论，要么AdS/CFT字典映射必须是指数复杂的，或者量子扩展丘奇-图灵命题在量子引力中必须是错误的。
A fundamental issue in the AdS/CFT correspondence is the wormhole growth paradox. Susskind's conjectured resolution of the paradox was to equate the volume of the wormhole with the circuit complexity of its dual quantum state in the CFT. We study the ramifications of this conjecture from a complexity-theoretic perspective. Specifically we give evidence for the existence of computationally pseudorandom states in the CFT, and argue that wormhole volume is measureable in a non-physical but computational sense, by amalgamating the experiences of multiple observers in the wormhole. In other words the conjecture equates a quantity which is difficult to compute with one which is easy to compute. The pseudorandomness argument further implies that this is a necessary feature of any resolution of the wormhole growth paradox, not just of Susskind's Complexity=Volume conjecture. As a corollary we conclude that either the AdS/CFT dictionary map must be exponentially complex, or the quantum Extended Church-Turing thesis must be false in quantum gravity.