Thread/State correspondence: from bit threads to qubit threads

TL;DR

This paper introduces a novel thread/state correspondence linking bit threads and the surface/state correspondence, enabling explicit construction of entangled states and proposing a holographic qubit threads model related to tensor networks and spacetime connectivity.

Contribution

It proposes a new thread/state correspondence, constructs explicit SS states from extremal surfaces, and develops a holographic qubit threads model connected to tensor networks and spacetime structure.

Findings

Explicit expressions for SS states from extremal surfaces

Holographic qubit threads model closely related to tensor networks

Connection between bit threads, kinematic space, and spacetime connectivity

Abstract

Starting from an interesting coincidence between the bit threads and SS (surface/state) correspondence, both of which are closely related to the holographic RT formula, we introduce a property of bit threads that has not been explicitly proposed before, which can be referred to as thread/state correspondence (see~\cite{Lin:2022agc} for a brief pre-release version). Using this thread/state correspondence, we can construct the explicit expressions for the SS states corresponding to a set of bulk extremal surfaces in the SS correspondence, and nicely characterize their entanglement structure. Based on this understanding, we use the locking bit thread configurations to construct a holographic qubit threads model as a new toy model of the holographic principle, and show that it is closely related to the holographic tensor networks, the kinematic space, and the connectivity of spacetime.