Topological Link Models of Multipartite Entanglement

Abstract

We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be represented by graphs or hypergraphs. Furthermore, we show that the contraction map proof method generalizes to the topological setting, though now requiring oracular solutions to well-known but difficult problems in knot theory.

15 pages, 2 figures; v2 formatted for publication in Quantum

References in corpus (3)

• Multi-party entanglement in graph states
• Quantum Extremal Surfaces and the Holographic Entropy Cone
• Entanglement entropy from SU(2) Chern-Simons theory and symmetric webs

Cited by in corpus (12)

• Holographic Entropy Inequalities and Multipartite Entanglement
• The Symmetrized Holographic Entropy Cone
• The holographic entropy cone from marginal independence
• Testing holographic entropy inequalities in 2+1 dimensions
• Properties of the contraction map for holographic entanglement entropy inequalities
• Towards a complete classification of holographic entropy inequalities
• Entanglement Classification from a Topological Perspective
• Beyond the Holographic Entropy Cone via Cycle Flows
• Multipartite Entanglement Structure of Fibered Link States
• On the completeness of contraction map proof method for holographic entropy inequalities
• Entanglement in Typical States of Chern-Simons Theory
• Exploring the holographic entropy cone via reinforcement learning