Bit Threads and Holographic Monogamy

• DOI: 10.1007/s00220-019-03510-8
• Publication Date: 2019-07-06T16:02:44Z
• Authors: Shawn X. Cui; Patrick Hayden; Temple He; Matthew Headrick; Bogdan Stoica; Michael Walter
• Keywords: High Energy Physics - Theory; Mathematics - Differential Geometry; Quantum Physics; 500; FOS: Physical sciences; 01 natural sciences; High Energy Physics - Theory (hep-th); Differential Geometry (math.DG); 0103 physical sciences; FOS: Mathematics; Mathematics - Combinatorics; Combinatorics (math.CO); Quantum Physics (quant-ph)

58 pages, 5 figures; v2: improvements to presentation; references added; essentially matches published version<br/>Bit threads provide an alternative description of holographic entanglement, replacing the Ryu-Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We use bit threads to prove the monogamy of mutual information (MMI) property of holographic entanglement entropies. This is accomplished using the concept of a so-called multicommodity flow, adapted from the network setting, and tools from the theory of convex optimization. Based on the bit thread picture, we conjecture a general ansatz for a holographic state, involving only bipartite and perfect-tensor type entanglement, for any decomposition of the boundary into four regions. We also give new proofs of analogous theorems on networks.<br/>