Entanglement of purification and holography

• Mohammad Asadi (IPM)

The entanglement entropy is an important quantity which nicely characterizes quantum entanglement between two subsystems A and B for a given pure state. According to AdS/CFT, entanglement entropy has a holographic counterpart given by the minimal surface. This gives a close relationship between spacetime geometry and quantum entanglement. On the other hand, for mixed states there are many quantities which measures quantum or classical correlations between two subsystems A and B in quantum information theory, knowing nothing about their holographic dual. There is a nice measure of entanglement called entanglement of purification with known holographic interpretation. Based on AdS/CFT, the candidate in the bulk side is entanglement wedge cross section. In this talk, I review the concept of the underlying quantities.