Beyond the Holographic Entropy Cone via Cycle Flows

Abstract

Motivated by bit threads, we introduce a new prescription for computing entropy vectors outside the holographic entropy cone. By utilizing cycle flows on directed graphs, we show that the maximum cycle flow associated to any subset of vertices, which corresponds to a subsystem, manifestly obeys purification symmetry. Furthermore, by restricting ourselves to a subclass of directed graphs, we prove that the maximum cycle flow obeys both subadditivity and strong subadditivity, thereby establishing it as a viable candidate for the entropy associated to the subsystem. Finally, we demonstrate how our model generalizes the entropy vectors obtainable via conventional flows in undirected graphs, as well as conjecture that our model similarly generalizes the entropy vectors arising from hypergraphs.

31 pages, 9 figures; v2: Significant change to Theorem 1, specified to networks satisfying a nesting property which we characterize by necessary and sufficient conditions, demoted Proposition 4 to Conjecture 1, minor typos and clarifications added, references added; v3: Fixed minor typo, clarified discussion in Appendix A.2, version to appear in CIMP

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• Testing holographic entropy inequalities in 2+1 dimensions
• Towards a complete classification of holographic entropy inequalities
• Purely GHZ-like entanglement is forbidden in holography
• On the completeness of contraction map proof method for holographic entropy inequalities
• Exploring the holographic entropy cone via reinforcement learning