Tensor Networks, AdS/CFT Correspondence, and Quantum Secret Sharing Schemes

Abstract

We investigate the bulk-boundary correspondence in AdS/CFT from the perspective of Quantum Secret Sharing Schemes and Perfect Tensors. Recently, it has been shown that Ads/CFT correspondence can accommodate error correcting properties due to the nature of correlations in hyperbolic AdS geometry from bulk to boundary. If one has sufficient collection of operators living in the boundary region, a bulk operator can be non-locally reconstructed within the space of a special set of states called low-energy subspace. From a discrete standpoint, we also aim to understand how perfect tensors, which have the special property of having maximal entanglement for any bipartition of their indices can be used to represent the AdS Geometry, pure and mixed state quantum secret sharing schemes and the relationship between geometry and entanglement.