Entanglement-Assisted Quantum Convolutional Coding

TL;DR

This paper introduces a method for protecting quantum information during transmission by combining entanglement and convolutional coding, creating a new class of quantum error-correcting codes with practical encoding procedures.

Contribution

It develops a theory of entanglement-assisted quantum convolutional coding using classical convolutional codes, enabling improved quantum error correction with shared entanglement.

Findings

Constructs CSS entanglement-assisted quantum convolutional codes from classical codes

Establishes a direct link between classical convolutional code properties and quantum code performance

Provides encoding procedures for quantum streams using shared entanglement

Abstract

We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted quantum convolutional coding. Our construction produces a Calderbank-Shor-Steane (CSS) entanglement-assisted quantum convolutional code from two arbitrary classical binary convolutional codes. The rate and error-correcting properties of the classical convolutional codes directly determine the corresponding properties of the resulting entanglement-assisted quantum convolutional code. We explain how to encode our CSS entanglement-assisted quantum convolutional codes starting from a stream of information qubits, ancilla qubits, and shared entangled bits.