Holographic inequalities and entanglement of purification
Holographic inequalities and entanglement of purification
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DOI：
10.1007/jhep03(2018)006
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发表时间：
2017-10
影响因子：
5.4
通讯作者：
N. Bao;Illan F. Halpern
中科院分区：
文献类型：
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作者：
N. Bao;Illan F. Halpern
我们研究了纯化纠缠和纠缠楔形截面之间推测的全息对偶性。我们概括了这两个量并证明了涉及它们的几个信息论不等式。这些包括条件互信息和三方信息的上限，以及三方信息的下限。这些不等式在全息态和一般量子态中都得到了证明。此外，我们利用循环熵不等式推导了纠缠楔形截面的新全息不等式，并提供了数值证据证明相应的纯化纠缠不等式一般来说可能是正确的。最后，我们利用位线程的直觉将猜想扩展到次优纯化的全息对偶。
We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.