The connection between holographic entanglement and complexity of purification
arXiv:1902.02475 · doi:10.1007/JHEP09(2019)009
Abstract
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 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.
arXiv comment47 pages, 39 figures, Accepted version in JHEP
References in corpus (61)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Aspects of Holographic Entanglement Entropy
- Black holes as mirrors: quantum information in random subsystems
- Fast Scramblers
- Complexity Equals Action
- Entanglement Renormalization and Holography
- Complexity, action, and black holes
- The (2+1)-Dimensional Black Hole
- Causality & holographic entanglement entropy
- Holographic Entanglement of Purification
- Holographic Mutual Information is Monogamous
- Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
- Exploring Localization in Nuclear Spin Chains
- The entanglement of purification
- Holographic Complexity
- Universal Resistivity from Holographic Massive Gravity
- Surface/State Correspondence as a Generalized Holography
- Bit threads and holographic entanglement
- Optimal teleportation with a mixed state of two qubits
- On Volumes of Subregions in Holography and Complexity
- Subsystem Complexity and Holography
- Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
- Massive charged BTZ black holes in asymptotically (a)dS spacetimes
- Holographic complexity is nonlocal
- Geometric Aspects of Holographic Bit Threads
- Entanglement of Purification for Multipartite States and its Holographic Dual
- Topological Complexity in AdS3/CFT2
- The Case of the Missing Gates: Complexity of Jackiw-Teitelboim Gravity
- Holographic Subregion Complexity from Kinematic Space
- Uncertainty, Monogamy, and Locking of Quantum Correlations
- Holographic Entanglement of Purification from Conformal Field Theories
- Conditional and Multipartite Entanglements of Purification and Holography
- Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions
- Riemannian and Lorentzian flow-cut theorems
- Holographic subregion complexity under a thermal quench
- Locking entanglement measures with a single qubit
- Subregion Action and Complexity
- Schwinger Effect and Entanglement Entropy in Confining Geometries
- Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
- Quantum Correlations in Large-Dimensional States of High Symmetry
- Spreading of correlations in exactly-solvable quantum models with long-range interactions in arbitrary dimensions
- Modular Berry Connection
- Entanglement of Purification in Free Scalar Field Theories
- The holographic entropy arrangement
- On complexity growth in massive gravity theories, the effects of chirality and more
- Holographic entanglement of purification for thermofield double states and thermal quench
- Bulk locality and cooperative flows
- Optimal resource states for local state discrimination
- Bit Threads in Higher Curvature Gravity
- Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity
- Binding Complexity and Multiparty Entanglement
- Revisiting Conserved Charges in Higher Curvature Gravitational Theories
- Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
- Holographic Subregion Complexity in Einstein-Born-Infeld theory
- Superradiant instability of -dimensional Reissner-Nordström-anti-de Sitter black hole mirror system
- Pure state estimation and the characterization of entanglement
- Entanglement fidelity of quantum memories
- Phase transitions in Bergshoeff-Hohm-Townsend Massive Gravity
- Quantum information/entanglement transfer rates between subsystems
- Strict entanglement monotonicity under local operations and classical communication
- Holographic complexity of the disk subregion in (2+1)-dimensional gapped systems
Cited by in corpus (43)
- Quantum Information in Holographic Duality
- Balanced Partial Entanglement and the Entanglement Wedge Cross Section
- Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
- Generalizations of Reflected Entropy and the Holographic Dual
- Bath deformations, islands and holographic complexity
- Quantum and Classical Correlations Inside the Entanglement Wedge
- Aspects of Hyperscaling Violating Geometries at Finite Cutoff
- Islands for Entanglement Negativity
- Bit thread, entanglement distillation, and entanglement of purification
- The Early Universe as an Open Quantum System: Complexity and Decoherence
- Pseudo complexity of purification for free scalar field theories
- Complexity and Emergence of Warped Space-time from Chiral Liouville Action
- Holographic study of entanglement and complexity for mixed states
- Holographic subregion complexity under thermal quench in Einstein-Maxwell-Axions theory with momentum relaxation
- Informational properties for Einstein-Maxwell-Dilaton Gravity
- Subsystem complexity in warped AdS
- Informational properties of holographic Lifshitz field theory
- Holographic Subregion Complexity in General Vaidya Geometry
- Entanglement Wedge Minimum Cross-section in Holographic Massive Gravity Theory
- Entanglement wedge reconstruction and correlation measures in mixed states: modular flows versus quantum recovery channels
- Inequalities of Holographic Entanglement of Purification from Bit Threads
- Entanglement wedge cross section for noncommutative Yang-Mills theory
- Quantum bit threads and holographic entanglement
- Correlations of mixed systems in confining backgrounds
- Large- phase transitions in holographic mutual information
- The Interior Volume of Kerr-AdS Black Holes
- Three-dimensional AdS black holes in massive-power-Maxwell theor
- Entanglement Wedge Cross Section with Gauss-Bonnet Corrections and Thermal Quench
- Mixed state information theoretic measures in boosted black brane
- The entanglement properties of holographic QCD model with a critical end point
- Multipartite Optimized Correlation Measures and Holography
- Optimized Correlation Measures in Holography
- Improved proof-by-contraction method and relative homologous entropy inequalities
- On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures
- Probing Phase Structure of Strongly Coupled Matter with Holographic Entanglement Measures
- Non-Conformal Behavior of Holographic Entanglement Measures
- Encoded information of mixed correlations: the views from one dimension higher
- Critical distance and Crofton form in confining geometries
- Information theoretic measures for Lifshitz system
- String amplitudes and mutual information in confining backgrounds: the partonic behavior
- Phase Transitions of Correlations in Black Hole Geometries
- Krylov complexity of purification
- Probing the self-coherence of primordial quantum fluctuations with complexity