Bit threads and holographic entanglement of purification

Understand

The entanglement of purification (EoP), which measures the classical correlations and entanglement of a given mixed state, has been conjectured to be dual to the area of the minimal cross section of the entanglement wedge in holography.

• Using the surface-state correspondence, we propose a `bit thread' formulation of the EoP.
• With this formulation, proofs of some known properties of the EoP are performed.
• Moreover, we show that the quantum advantage of dense code (QAoDC), which reflects the increase in the rate of classical information transmission through quantum channel due to entanglement, also admits a flow interpretation.