Holographic Entanglement Of Purification And Its Bit-Thread Description

Quantum gravity has always been an important research direction in theoretical physics.Then the holographic principle and the AdS/CFT correspondence bring new light to the exploration of quantum gravity.It states that a theory of gravity in a curved spacetime is equivalent to a quantum field theory that has no gravity at the boundary of that spacetime.This shows that the physical quantities in these two theories corresponds to each other.Since the AdS/CFT correspondence was proposed,the related topics have been widely studied.Researches in this field have an important influence on many other areas.This paper however focuses on the studies and application of quantum information theory in holographic gravity theory.In the AdS/CFT correspondence,a large number of studies have shown that there is a very deep connection between the gravitational spacetime and the boundary quantum entanglement.Introducing the concept of quantum information into AdS/CFT is very important to further understand the holographic gravity.The entanglement of purification(EoP)is a physical quantity that describes the strength of classical correlations and entanglement in mixed bipartite states in quantum information.It has been conjectured that the entanglement of purification is dual to a geometric quantity Ew on gravity side.The concept of holographic entanglement purification is helpful for us to understand the quantum-information meaning in holographic gravity.In this thesis,we mainly study the holographic entanglement of purification(HEoP)and bit threads under the framework of AdS/CFT correspondence.Based on the bit-thread formulation of holographic entanglement entropy and the Surface/State duality,we propose the bit-thread formulation for the holographic entanglement of purification.And we give a bit-thread description for the so-called quantum advantage of dense coded(QAoDC)in quantum information.In this picture,the basic properties of holographic entanglement purification can be proved.We prove the monogamy relation satisfied by quantum advantage of dense coded with entanglement of purification by using bit-thread description.A lower bound is also obtained which is tighter than the Araki-Lieb inequality.Then,we further give a multiflow description of the holographic entanglement of purification,and derive a series of new properties for the holographic entanglement of purification under the so-called max multiflow configuration.This is further confirmed by geometric analysis.We further conjecture that,for any inequality property of holographic entanglement entropy that can be derived from bit threads,we can find a corresponding new property for the holographic entanglement of purification in relative homology meaning.