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.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 2 Ning Bao,
- 2 Newton Cheng,
- 3 Sergio Hernández-Cuenca,
- 2 Vincent P. Su
- 1 Brookhaven National Laboratory [BNL]
- 2 University of California, Berkeley [UCBL]
- 3 University of California, Santa Barbara [UCSB]
- Empire State Development Corporation (through Organization: New York State Department of Economic Development / Empire State Development [ESD])
- National Science Foundation [NSF]
- United States Department of Energy [DOE]
- “la Caixa” Foundation