The connection between holographic entanglement and complexity of purification

Understand

In this work we study how entanglement of purification (EoP) and the new quantity of "complexity of purification" are related to each other using the $E_P=E_W$ conjecture.

• First, we consider two strips in the same side of a boundary and study the relationships between the entanglement of purification of this mixed state and the parameters of the system such as dimension, temperature, length of the strips and the distance between them.
• Next, using the same setup, we introduce two definitions for the complexity of mixed states, complexity of purification (CoP) and the interval volume (VI).
• We study their connections to other parameters similar to the EoP case.