Mixed State Entanglement For The Holographic Axion Model

In holographic theory,Ad S / CFT pointed out that the(d + 1)-dimensional Anti-de Sitter space-time quantum gravity theory and the d-dimensional space-time conformal field theory are dual,where the d-dimensional space-time is(d + 1)-dimensional Ad S space-time boundary.In a nutshell,there are two different but equivalent ways of describing a physical system.It can be described either by quantum gravity theory or by quantum field theory.These two methods seem very different,but in fact The information is completely equivalent.And a very valuable feature of Ad S / CFT is that it is a strong-weak duality: the fields in quantum field theory have very strong / weak interactions,while the interaction of gravitational fields is very weak / strong In this way,we can turn the weak / strong correlation physics problem into a classic gravity problem that is also easier to deal with in mathematics.Therefore,the holographic theory opens a window for understanding the strong correlation system(See Figure 1.4).On the other hand,as a novel method,holographic theory is of great value because it can be applied to the research field of quantum information(QI),such as holographic entanglement entropy(HEE),R?enyi entropy,complexity,mutual information MI developed by HEE and purified entanglement EoP,These problems all have simple geometric correspondence through the method of holographic gravitation,which greatly simplifies the research of quantum information properties(See Figure 1.5).Quantum system can be divided into pure state and mixed state.For the pure state system,the entanglement entropy(EE)can measure the entanglement degree of two subsystems.However,for the mixed state system,the traditional EE is not suitable to measure the entanglement.The reason is that under EE metric,the non entangled direct product states may have non-zero entanglement entropy.In this way,a new physical quantity such as MI and EoP is defined to measure the entanglement between the two subsystems in a new way.The purpose and motivation of our study is to calculate MI and EoP,two kinds of mixed attitude variables with geometric correspondence,based on a mixed thermodynamic system in the framework of holographic gravitation theory.Of course,such a system should be simple enough and important enough,and the momentum dissipation holographic model just satisfies these two points.Based on the momentum dissipative holographic model,the relationship between the entanglement and the momentum dissipative properties of mixed states is explored by numerical calculation and discussion of MI and EoP under different parameters.We find that the HEE,MI and EoP exhibit very distinct behaviors with system parameters.The HEE exhibits universal monotonic behavior with system parameters,while the behaviors of MI and EoP relate to the specific system parameters and configurations.We find that MI and EoP can characterize mixed state entanglement better than HEE since they are less affected by thermal effects.Specifically,the MI partly cancels out the thermal entropy contribution,while the holographic EoP is not dictated by the thermal entropy in any situation.Moreover,we argue that EoP is more suitable for describing mixed state entanglement than MI.Because the MI of large configurations are still dictated by the thermal entropy,while the EoP will never be controlled only by the thermal effects.