The holographic dual of the GHZ state

Abstract

Current holographic research mostly focuses on a subset of quantum systems with a classical gravity dual. Although the precise boundary of this subset remains unknown, certain constraints are recognized; for instance, holographic entropies obey inequalities that are violated by general quantum states such as the GHZ states. This paper, however, proposes a gravity dual for the GHZ states -- a non-manifold geometry termed the booklet wormhole. We demonstrate an exact match for all entropy properties with the GHZ state, as well as the identity of the Euclidean partition functions for both systems. The booklet wormhole circumvents the conventional holographic entropy inequalities because different topologies are inevitably included in the gravitational path integral, even in the large-$N$ limit. This provides the first explicit holographic duality with a non-perturbative quantum effect. Remarkably, the construction is simple, and the dual state is maximally entangled, making it ideal for gedanken experiments.