Quantum error correction and entanglement spectrum in tensor networks

Abstract

A sort of planar tensor networks with tensor constraints is investigated as a model for holography. We study the greedy algorithm generated by tensor constraints and propose the notion of critical protection (CP) against the action of greedy algorithm. For given tensor constraints, a CP tensor chain can be defined. We further find that the ability of quantum error correction (QEC) and the non-flatness of entanglement spectrum (ES) can be quantitatively evaluated by the geometric structure of CP tensor chain. Our work provides a strategy for constructing tensor networks which capture the desirable holographic aspects of AdS space.