Classical Enhancement of Quantum Error-Correcting Codes

TL;DR

This paper introduces a unified formalism for quantum error-correcting codes that encode both classical and quantum information, combining entanglement-assisted and classical error correction methods.

Contribution

It develops a comprehensive framework for quantum codes that handle classical and quantum data simultaneously, including stabilizer and symplectic formalism, with new error-correcting conditions.

Findings

Formalism unifies classical and quantum error correction

Provides stabilizer and symplectic descriptions of codes

Includes examples demonstrating code construction

Abstract

We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and includes encoding, error correction, and decoding steps such that the encoded quantum and classical information can be correctly recovered by the receiver. We formally define this kind of quantum code using both stabilizer and symplectic language, and derive the appropriate error-correcting conditions. We give several examples to demonstrate the construction of such codes.