Entanglement renormalization, quantum error correction, and bulk causality

TL;DR

This paper explores how entanglement renormalization acts as a quantum error correction mechanism in critical systems, revealing emergent bulk causality and operator locality properties akin to holographic codes.

Contribution

It demonstrates that entanglement renormalization encodes approximate quantum error correcting codes with emergent bulk causality in critical quantum systems.

Findings

Approximate holographic quantum error correcting code emerges at low energy.

Operators separated in scale behave as spatially separated under local Hamiltonian evolution.

Entanglement renormalization enhances protection of logical information against errors.

Abstract

Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated bya local Hamiltonian.