Quantum error correction and entanglement spectrum in tensor networks

TL;DR

This paper explores how tensor networks with specific constraints can model holography, analyze quantum error correction, and entanglement spectrum properties through geometric structures called critical protection tensor chains.

Contribution

It introduces the notion of critical protection in tensor networks and links geometric structures to quantum error correction and entanglement spectrum features.

Findings

Quantum error correction ability is quantified by CP tensor chain geometry.

Entanglement spectrum non-flatness is related to tensor network structure.

Correlation functions match conformal field theory results.

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), the non-flatness of entanglement spectrum (ES) and the correlation function can be quantitatively evaluated by the geometric structure of CP tensor chain. Four classes of tensor networks with different properties of entanglement is discussed. Thanks to tensor constraints and CP, the correlation function is reduced into a bracket of Matrix Production State and the result agrees with the one in conformal field theory.