论文标题
来自双面黑洞的大叠加的空状态
Null states from large superpositions of two-sided black holes
论文作者
论文摘要
AD/CFT对应关系的标准见解是，散装状态的几何形状的某些方面在其双重边界状态的纠缠结构中编码。由于纠缠不是可观察到的线性量子，因此这意味着重力量子理论中的几何形状同样不应该是可观察的。这允许具有不同几何形状的状态之间的线性依赖性。我们探索具有简单几何双重二元组的某些状态之间的线性依赖性：由Thermofield Double状态的$ N $副本组成的状态以及通过将$ n $右侧侧面置于该状态的状态。有$ n！$这样的状态，都是双重到不同的几何形状。我们得出了一个这样的状态与其他人的线性组合之间最大保真度的表达式，并看到这种保真度接近1，因为黑洞的数字$ n $增加。我们还将获得单个热场双状态获得的可能性是状态叠加的部分痕迹，其拓扑不会连接两个未跟踪的侧面。我们为热场双状态与这种部分痕迹之间的忠诚度得出了下限，并评论了这种状态存在的概念含义。
A standard insight of the AdS/CFT correspondence is that some aspects of the geometry of a bulk state are encoded in the entanglement structure of its dual boundary state. As entanglement is not a linear quantum observable, this means that geometry in a quantum theory of gravity should likewise not be a linear observable. This allows for linear dependencies between states with distinct geometries. We explore linear dependencies between certain states with simple geometric duals: states made up of $n$ copies of a thermofield double state and the states obtained from this one by permuting the $n$ right hand sides. There are $n!$ such states, all dual to distinct geometries. We derive expressions for the maximum fidelity between one such state and a linear combination of the others, and see that this fidelity approaches 1 as the number $n$ of black holes increases. We also consider the possibility of obtaining a single thermofield double state as the partial trace of a superposition of states whose topology does not connect the two untraced sides. We derive lower bounds for the fidelity between the thermofield double state and such partial traces and comment on the conceptual implications of the existence of such states.
