Inequalities of Holographic Entanglement of Purification from Bit Threads
arXiv:1912.00557 · doi:10.1140/epjc/s10052-020-8283-1
Abstract
There are increasing evidences that quantum information theory has come to play a fundamental role in quantum gravity especially the holography. In this paper, we show some new potential connections between holography and quantum information theory. Particularly, by utilizing the multiflow description of the holographic entanglement of purification (HEoP) defined in relative homology, we obtain several new inequalities of HEoP under a max multiflow configuration. Each inequality derived for HEoP has a corresponding inequality of the holographic entanglement entropy (HEE). This is further confirmed by geometric analysis. In addition, we conjecture that, based on flow considerations, each property of HEE that can be derived from bit threads may have a corresponding property for HEoP that can be derived from bit threads defined in relative homology.
arXiv comment20 pages, 4 figures; improvements to presentation, references added, and new section added to roughly comment about the entropy cone of HEoP. Accepted for publication in EPJC
References in corpus (60)
- Gauge Theory Correlators from Non-Critical String Theory
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- The World as a Hologram
- A Covariant Holographic Entanglement Entropy Proposal
- Entanglement Renyi entropies in holographic theories
- Entanglement as a Probe of Confinement
- Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
- The Gravity Dual of a Density Matrix
- Causality & holographic entanglement entropy
- Holographic Entanglement of Purification
- Holographic Mutual Information is Monogamous
- A holographic proof of the strong subadditivity of entanglement entropy
- The entanglement of purification
- The Holographic Entropy Cone
- Entanglement of purification: from spin chains to holography
- Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
- AdS Bubbles, Entropy and Closed String Tachyons
- AdS/CFT and Strong Subadditivity of Entanglement Entropy
- Bit threads and holographic entanglement
- Entanglement Wedge Cross Section from the Dual Density Matrix
- Holographic evolution of the mutual information
- Derivation of holographic negativity in AdS/CFT
- Thermalization of mutual and tripartite information in strongly coupled two dimensional conformal field theories
- Geometric Aspects of Holographic Bit Threads
- Entanglement Wedge Reconstruction and Entanglement of Purification
- Entanglement of Purification for Multipartite States and its Holographic Dual
- Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
- Holographic entanglement contour, bit threads, and the entanglement tsunami
- Holographic Entanglement of Purification from Conformal Field Theories
- Conditional and Multipartite Entanglements of Purification and Holography
- Riemannian and Lorentzian flow-cut theorems
- The Holographic Entropy Cone for Five Regions
- Some Aspects of Entanglement Wedge Cross-Section
- Bit Threads and Holographic Monogamy
- Bit threads and holographic entanglement of purification
- Holographic Inequalities and Entanglement of Purification
- Entanglement of Purification in Free Scalar Field Theories
- Towards Entanglement of Purification for Conformal Field Theories
- Entanglement of Purification in Many Body Systems and Symmetry Breaking
- Dynamics of Entanglement Wedge Cross Section from Conformal Field Theories
- Quantum and Classical Correlations Inside the Entanglement Wedge
- The connection between holographic entanglement and complexity of purification
- Multipartite Reflected Entropy
- Notes on entanglement wedge cross sections
- Holographic entanglement of purification for thermofield double states and thermal quench
- Bulk locality and cooperative flows
- Entanglement of Purification and Multiboundary Wormhole Geometries
- Bit threads and holographic entanglement of purification
- Bit Threads in Higher Curvature Gravity
- Holographic Entropy Cone with Time Dependence in Two Dimensions
- Calibrated Entanglement Entropy
- Correlation measures and distillable entanglement in AdS/CFT
- Entanglement of Purification in Holographic Systems
- CFT sewing as the dual of AdS cut-and-paste
- Entanglement of purification and disentanglement in CFTs
- Entanglement of Purification and Projective Measurement in CFT
- A Gap Between the Hypergraph and Stabilizer Entropy Cones
- Bit Threads and the Membrane Theory of Entanglement Dynamics
- On the Entropy Cone for Large Regions at Late Times
- Minimal Purifications, Wormhole Geometries, and the Complexity=Action Proposal
Cited by in corpus (10)
- Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
- Bit threads, Einstein's equations and bulk locality
- The PEE aspects of entanglement islands from bit threads
- A Field Theory Study of Entanglement Wedge Cross Section: Odd Entropy
- Quantum bit threads and holographic entanglement
- Bounding entanglement wedge cross sections
- Thread/State correspondence: from bit threads to qubit threads
- Improved proof-by-contraction method and relative homologous entropy inequalities
- Towards bit threads in general gravitational spacetimes
- Holographic complexity for nonlinearly charged Lifshitz black holes