The Quantum Entropy Cone of Hypergraphs

Abstract

In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone. This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs. In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks. We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy. We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction. To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match.

40+6 pages, 7 figures

References in corpus (4)

• Multi-party entanglement in graph states
• Maximally multipartite entangled states
• All Maximally Entangled Four Qubits States
• The holographic entropy arrangement

Cited by in corpus (21)

• Quantum Extremal Surfaces and the Holographic Entropy Cone
• On the foundations and extremal structure of the holographic entropy cone
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• Approximate Bacon-Shor Code and Holography
• The Symmetrized Holographic Entropy Cone
• The holographic entropy cone from marginal independence
• Hypergraph min-cuts from quantum entropies
• Topological Link Models of Multipartite Entanglement
• On the relation between the subadditivity cone and the quantum entropy cone
• Testing holographic entropy inequalities in 2+1 dimensions
• Towards a complete classification of holographic entropy inequalities
• Properties of the contraction map for holographic entanglement entropy inequalities
• An Entropic Lens on Stabilizer States
• Improved proof-by-contraction method and relative homologous entropy inequalities
• Inner bounding the quantum entropy cone with subadditivity and subsystem coarse grainings
• Beyond the Holographic Entropy Cone via Cycle Flows
• Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the $\mathsf{N}=6$ solution
• The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States
• Spectral theory of weighted hypergraphs via tensors
• Hyperthreads in holographic spacetimes
• Exploring the holographic entropy cone via reinforcement learning