Quantum Convolutional Coding with Entanglement Assistance

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Quantum Convolutional Coding with Entanglement
Assistance

• Mark M. Wilde

Communication Sciences Institute, Ming Hsieh
Department of Electrical Engineering, University
of Southern California, Los Angeles, California
90089
QEC07, Los Angeles, California (December 2007)
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Summary
arXiv0708.3699
arXiv0712.2223
with Hari Krovi and Todd Brun
with Todd Brun
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Classical Convolutional Coding
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FIR Encoding Circuits
Finite-duration input streams produce
finite-duration output streams
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IIR Encoding Circuits
Finite-duration input streams can produce
infinite-duration output streams
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Quantum Block Code
Perform measurements that learn only about errors
Encode qubits with ancillas
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Entanglement-Assisted Quantum Block Code
Brun, Devetak, Hsieh, Science 314, 436-439 (2006).
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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).
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Entanglement-Assisted Quantum Convolutional Coding
Wilde and Brun, arXiv0712.2223 (2007).
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EAQCC Example 1
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Infinite-Depth Operations
Implements 1D-1 1/(1D)
Implements 1D-1D-3 1/(1DD3)
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EAQCC Example 2
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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 Bobs half of the ebits)
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Advantages of EAQCC
Produce an EAQCC from two arbitrary classical
binary convolutional codes
The rate and error-correcting properties of the
classical codes translate to the
EAQCC.(high-performance classical codes gt
high-performance quantum codes)
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Block Entanglement Distillation
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Convolutional Entanglement Distillation
Wilde, Krovi, Brun, arXiv0708.3699 (2007).
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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 detail
• There is still much to explore in these areas
  (QEC07_at_USC)