Towards holography via quantum source-channel codes

TL;DR

This paper introduces quantum source-channel codes inspired by holography, combining lossy compression and quantum error correction, and demonstrates their potential for protecting critical quantum states like those in the Ising model.

Contribution

It presents the concept of quantum source-channel codes, linking quantum error correction with holography, and provides a concrete example with critical Gibbs states.

Findings

Gibbs states at criticality show protection from local erasure.

First interpretation of a conformal field theory as a quantum error correcting code.

Derived performance guarantees using entropic quantities.

Abstract

While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT), indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy-compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit non-trivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.