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Title: 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.

Authors:
 [1];  [2];  [3];  [2]
  1. Brookhaven National Laboratory, University of California, Berkeley
  2. University of California, Berkeley
  3. University of California, Santa Barbara
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1708952
Grant/Contract Number:  
SC0019380
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 9 Journal Issue: 5; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Bao, Ning, Cheng, Newton, Hernández-Cuenca, Sergio, and Su, Vincent P. The quantum entropy cone of hypergraphs. Netherlands: N. p., 2020. Web. https://doi.org/10.21468/SciPostPhys.9.5.067.
Bao, Ning, Cheng, Newton, Hernández-Cuenca, Sergio, & Su, Vincent P. The quantum entropy cone of hypergraphs. Netherlands. https://doi.org/10.21468/SciPostPhys.9.5.067
Bao, Ning, Cheng, Newton, Hernández-Cuenca, Sergio, and Su, Vincent P. Tue . "The quantum entropy cone of hypergraphs". Netherlands. https://doi.org/10.21468/SciPostPhys.9.5.067.
@article{osti_1708952,
title = {The quantum entropy cone of hypergraphs},
author = {Bao, Ning and Cheng, Newton and Hernández-Cuenca, Sergio and Su, Vincent P.},
abstractNote = {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.},
doi = {10.21468/SciPostPhys.9.5.067},
journal = {SciPost Physics Proceedings},
number = 5,
volume = 9,
place = {Netherlands},
year = {2020},
month = {11}
}

Journal Article:
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https://doi.org/10.21468/SciPostPhys.9.5.067

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