The Symmetrized Holographic Entropy Cone

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.

Quantum information in holographic duality

“…The holographic cone of average entropies. The last point-that holographic entropy inequalities decompose entropy vectors into atomic constituents-recently found a generalization to arbitrarily many regions [223] (see also [224]). To explain the assertion, we define S p as the average of all p-region entropies, with and without the purifier O included.…”

Properties of the contraction map for holographic entanglement entropy inequalities

“…2 Also, by appealing to a related object, the holographic cone of averaged entropies [26,27], a seven-party inequality was found in [28].…”