General entanglement-assisted quantum error-correcting codes

TL;DR

This paper introduces a unified framework called EAOQEC that combines entanglement-assisted and operator quantum error correction, enabling more flexible and powerful quantum error correction methods.

Contribution

It presents the formalism of EAOQEC, demonstrating its generality and advantages over previous quantum error correction schemes.

Findings

EAOQEC is the most general quantum error correction method known.

It can be constructed from any classical linear code.

Examples illustrate the flexibility of the new formalism.

Abstract

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-existing entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs which can only be constructed from dual-containing codes. Operator quantum error-correcting codes (OQECCs) allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement-assisted quantum error correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction (EAOQEC), is the most general and powerful quantum error-correcting technique known, retaining the advantages of both entanglement-assistance and passive correction. We present the formalism, show the considerable freedom in constructing EAOQECCs from classical codes, and demonstrate the construction with examples.