Thread/State correspondence: from bit threads to qubit threads

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 [50] 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.

Automated summary

In this paper, we introduce a property of bit threads called thread/state correspondence, which has not been explicitly proposed before. By using this correspondence, we can construct explicit expressions for the SS states corresponding to a set of bulk extremal surfaces in the holographic SS correspondence. Furthermore, we demonstrate the close relationship between the holographic qubit threads model and holographic tensor networks, kinematic space, and spacetime connectivity.