The Symmetrized Holographic Entropy Cone

• URL: http://arxiv.org/abs/2112.03862v2
• Date: Wed, 15 Dec 2021 18:48:30 GMT
• Title: The Symmetrized Holographic Entropy Cone
• Authors: Matteo Fadel, Sergio Hern\'andez-Cuenca
• Abstract summary: The holographic entropy cone (HEC) characterizes the entanglement structure of quantum states which admit geometric bulk duals in holography. We introduce a symmetrization procedure that projects the HEC onto a natural lower dimensional subspace. By applying this symmetrization to the quantum entropy cone, we are able to quantify the typicality of holographic entropies.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The holographic entropy cone (HEC) characterizes the entanglement structure of quantum states which admit geometric bulk duals in holography. Due to its intrinsic complexity, to date it has only been possible to completely characterize the HEC for at most $n=5$ numbers of parties. For larger $n$, our knowledge of the HEC falls short of incomplete: almost nothing is known about its extremal elements. Here, we introduce a symmetrization procedure that projects the HEC onto a natural lower dimensional subspace. Upon symmetrization, we are able to deduce properties that its extremal structure exhibits for general $n$. Further, by applying this symmetrization to the quantum entropy cone, we are able to quantify the typicality of holographic entropies, which we find to be exponentially rare quantum entropies in the number of parties.

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