Bit Threads and Holographic Monogamy

TL;DR

This paper uses the bit thread framework to prove the monogamy of mutual information in holographic entanglement, employing multicommodity flow and convex optimization, and proposes a conjecture for holographic states based on bipartite entanglement.

Contribution

It introduces a novel proof of MMI using bit threads and multicommodity flow, and proposes a new holographic state ansatz based on bipartite and perfect-tensor entanglement.

Findings

Proved monogamy of mutual information using bit threads.

Developed a multicommodity flow approach for holographic entanglement.

Conjectured a holographic state structure involving bipartite entanglement.

Abstract

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.