Bulk locality and cooperative flows

TL;DR

This paper uses the bit thread approach to distinguish between strong subadditivity and monogamy of mutual information in holographic entanglement, providing a new proof of MMI through explicit geometric constructions.

Contribution

It introduces a novel, explicit geometric construction of cooperative flows to prove monogamy of mutual information in holographic states.

Findings

MMI is more deeply rooted in bulk locality than strong subadditivity.

The explicit construction of cooperative flows applies to complex configurations.

Provides a new proof of MMI using bit threads directly.

Abstract

We use the 'bit thread' formulation of holographic entanglement entropy to highlight the distinction between the universally-valid strong subadditivity and the more restrictive relation called monogamy of mutual information (MMI), known to hold for geometrical states (i.e. states of holographic theories with gravitational duals describing a classical bulk geometry). In particular, we provide a novel proof of MMI, using bit threads directly. To this end, we present an explicit geometrical construction of cooperative flows which we build out of disjoint thread bundles. We conjecture that our method applies in a wide class of configurations, including ones with non-trivial topology, causal structure, and time dependence. The explicit nature of the construction reveals that MMI is more deeply rooted in bulk locality than is the case for strong subadditivity.