The connection between holographic entanglement and complexity of purification

• Published in: The journal of high energy physics Vol. 2019; no. 9; pp. 1 - 44
• Main Authors: Ghodrati, Mahdis, Kuang, Xiao-Mei, Wang, Bin, Zhang, Cheng-Yong, Zhou, Yu-Ting
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2019; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Classical and Quantum Gravitation; Complexity; Elementary Particles; Entanglement; Gauge-gravity correspondence; High energy physics; Holography and condensed matter physics (AdS/CMT); Parameters; Physics; Physics and Astronomy; Purification; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; AdS-CFT Correspondence; Gauge-gravity correspondence; Holography and condensed matter physics (AdS/CMT)
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2019)009

A bstract 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. Then, we extend our study to more general examples of BTZ black holes solution in massive gravity, charged black holes and multipartite systems. Finally, we give various interpretations of our results using resource theories such as LOCC and also bit thread picture.