Quantum Convolutional Coding with Entanglement Assistance
Mark M. WildeCommunication Sciences Institute,
Ming Hsieh Department of Electrical Engineering,
University of Southern California,
Los Angeles, California 90089
Communication Sciences Institute,
Ming Hsieh Department of Electrical Engineering,
University of Southern California,
Los Angeles, California 90089
QEC07, Los Angeles, California (December 2007)
Summary
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arXiv:0708.3699arXiv:0712.2223
with Hari Krovi and Todd Brunwith Todd Brun
Classical Convolutional Coding
Convolutional Coding techniques have application in
cellular deep space communicationand
Viterbi Algorithm is most popular technique for determining errors
FIR Encoding Circuits
Finite-duration input streams produce finite-duration output streams
IIR Encoding Circuits
Finite-duration input streams can produce infinite-duration output streams
Quantum Block Code
Perform measurements that learn only about errorsEncode qubits with ancillas
Entanglement-Assisted Quantum Block Code
Brun, Devetak, Hsieh, Science 314, 436-439 (2006).
Quantum Convolutional Coding
Ollivier, Tillich, PRL 91, 177902 (2003).Forney, Grassl, Guha, IEEE Trans. Inf. Theory 53, 865-880 (2007).Grassl, Rötteler, In proceedings of ISIT (2005,2006,2007).
Entanglement-Assisted Quantum Convolutional Coding
Wilde and Brun, arXiv:0712.2223 (2007).
EAQCC Example 1
Infinite-Depth Operations
Implements[ 1+D-1 | 1/(1+D) ]
Implements[ 1+D-1+D-3 | 1/(1+D+D3) ]
EAQCC Example 2
Classes of EAQCCs
1) Finite-depth encoding and decoding circuits
2) Finite-depth and infinite-depth encoding circuit Finite-depth decoding circuit
3) Finite-depth and infinite-depth encoding circuit Finite-depth and infinite-depth decoding circuit (infinite-depth operations only on Bob’s half of the ebits)
Advantages of EAQCC
The rate and error-correcting properties of the classical codes translate to the EAQCC.(high-performance classical codes => high-performance quantum codes)
Produce an EAQCC from two arbitrary classical binary convolutional codes:
Block Entanglement Distillation
Convolutional Entanglement Distillation
Wilde, Krovi, Brun, arXiv:0708.3699 (2007).
Conclusion
• Entanglement-assisted convolutional coding exploits entanglement to encode a stream of qubits
• Importing classical convolutional coding theory should produce high-performance quantum codes
• Explore the connection to quantum key distribution in more detailThere is still much to explore in these areas
(QEC07@USC)
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