Unified Quantum Convolutional Coding

Abstract

We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum channel for sending classical and quantum information simultaneously. Our method incorporates several resources for quantum redundancy: fresh ancilla qubits, entangled bits, and gauge qubits. The use of these diverse resources gives our technique the benefits of both active and passive quantum error correction. We can encode a classical-quantum bit stream with periodic quantum gates because our codes possess a convolutional structure. We end with an example of a ``grandfather'' quantum convolutional code that protects one qubit and one classical bit per frame by encoding them with one fresh ancilla qubit, one entangled bit, and one gauge qubit per frame. We explicitly provide the encoding and decoding circuits for this example.

5 pages, 1 figure, Accepted for publication in the Proceedings of the 2008 IEEE International Symposium on Information Theory (ISIT 2008)

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Cited by in corpus (10)

• Entanglement-assisted communication of classical and quantum information
• Entanglement-assisted quantum turbo codes
• Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
• On Classical and Quantum MDS-Convolutional BCH Codes
• Nonlocal quantum information in bipartite quantum error correction
• Minimal-memory, non-catastrophic, polynomial-depth quantum convolutional encoders
• Quantum Convolutional Coding with Shared Entanglement: General Structure
• Protecting Quantum Information with Entanglement and Noisy Optical Modes
• Minimal memory requirements for pearl-necklace encoders of quantum convolutional codes
• Examples of minimal-memory, non-catastrophic quantum convolutional encoders