01106nas a2200133 4500008004100000245005100041210005100092260001400143520072500157100001400882700001700896700002200913856003700935 2021 eng d00aMagic State Distillation from Entangled States0 aMagic State Distillation from Entangled States c6/23/20213 a

Magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can improve the distillation outcome. We analyze a few explicit examples and show that spin squeezing can be used to convert non-distillable states into distillable ones.
Our analysis also suggests that the conventional product input states assumed by magic distillation protocols are extremely atypical among general states with distillable magic. It further justifies the need for studying a diverse range of entangled inputs that yield magic states with high probability.

1 aBao, Ning1 aCao, ChunJun1 aSu, Vincent, Paul uhttps://arxiv.org/abs/2106.1259101494nas a2200181 4500008004100000245005100041210005100092260001500143300001100158490000700169520100800176100001401184700001701198700002501215700001901240700001601259856003701275 2020 eng d00aMore of the Bulk from Extremal Area Variations0 aMore of the Bulk from Extremal Area Variations c12/24/2020 a0470010 v383 a

It was shown recently, building on work of Alexakis, Balehowksy, and Nachman that the geometry of (some portion of) a manifold with boundary is uniquely fixed by the areas of a foliation of two-dimensional disk-shaped surfaces anchored to the boundary. In the context of AdS/CFT, this implies that (a portion of) a four-dimensional bulk geometry can be fixed uniquely from the entanglement entropies of disk-shaped boundary regions, subject to several constraints. In this Note, we loosen some of these constraints, in particular allowing for the bulk foliation of extremal surfaces to be local and removing the constraint of disk topology; these generalizations ensure uniqueness of more of the deep bulk geometry by allowing for e.g. surfaces anchored on disconnected asymptotic boundaries, or HRT surfaces past a phase transition. We also explore in more depth the generality of the local foliation requirement, showing that even in a highly dynamical geometry like AdS-Vaidya it is satisfied.

1 aBao, Ning1 aCao, ChunJun1 aFischetti, Sebastian1 aPollack, Jason1 aZhong, Yibo uhttps://arxiv.org/abs/2009.07850