Improved proof-by-contraction method and relative homologous entropy inequalities
arXiv:2204.03192 · doi:10.1007/JHEP06(2022)153
Abstract
The celebrated holographic entanglement entropy triggered investigations on the connections between quantum information theory and quantum gravity. An important achievement is that we have gained more insights into the quantum states. It allows us to diagnose whether a given quantum state is a holographic state, a state whose bulk dual admits semiclassical geometrical description. The effective tool of this kind of diagnosis is holographic entropy cone (HEC), an entropy space bounded by holographic entropy inequalities allowed by the theory. To fix the HEC and to prove a given holographic entropy inequality, a proof-by-contraction technique has been developed. This method heavily depends on a contraction map , which is very difficult to construct especially for more-region () cases. In this work, we develop a general and effective rule to rule out most of the cases such that can be obtained in a relatively simple way. In addition, we extend the whole framework to relative homologous entropy, a generalization of holographic entanglement entropy that is suitable for characterizing the entanglement of mixed states.
arXiv comment1+27 pages; Version matches published one in JHEP
References in corpus (56)
- Gauge Theory Correlators from Non-Critical String Theory
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- A Covariant Holographic Entanglement Entropy Proposal
- Holography from Conformal Field Theory
- 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
- 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
- Bit threads and holographic entanglement
- Entanglement Wedge Cross Section from the Dual Density Matrix
- Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
- Entanglement Wedge Reconstruction and Entanglement of Purification
- Geometric Aspects of Holographic Bit Threads
- Entanglement of Purification for Multipartite States and its Holographic Dual
- Holographic entanglement contour, bit threads, and the entanglement tsunami
- Holographic Subregion Complexity from Kinematic Space
- 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
- Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
- Entanglement of Purification in Free Scalar Field Theories
- Pulling the Boundary into the Bulk
- Entanglement of Purification in Many Body Systems and Symmetry Breaking
- Towards Entanglement of Purification for Conformal Field Theories
- The connection between holographic entanglement and complexity of purification
- Lorentzian threads as 'gatelines' and holographic complexity
- Bulk locality and cooperative flows
- Holographic entanglement of purification for thermofield double states and thermal quench
- Entanglement of Purification and Multiboundary Wormhole Geometries
- Bit threads and holographic entanglement of purification
- Bit Threads in Higher Curvature Gravity
- Modular Flow as a Disentangler
- Quantum Extremal Surfaces and the Holographic Entropy Cone
- Holographic Entropy Cone with Time Dependence in Two Dimensions
- On the foundations and extremal structure of the holographic entropy cone
- The Quantum Entropy Cone of Hypergraphs
- Entanglement of Purification in Holographic Systems
- Maximin is Not Enough
- The holographic entropy zoo
- Hypergraph min-cuts from quantum entropies
- Complexity-action of subregions with corners
- Inequalities of Holographic Entanglement of Purification from Bit Threads
- Entanglement of Purification and Projective Measurement in CFT
- A Gap Between the Hypergraph and Stabilizer Entropy Cones
- Gravity from entanglement for boundary subregions
- Holographic relations for OPE blocks in excited states
- Minimal Purifications, Wormhole Geometries, and the Complexity=Action Proposal