Continuous Variable Quantum Error Correction Coding

1
Continuous Variable Quantum Error Correction
Coding

• U.L. Andersen, M. Lassen, J. Niset, M. Sabuncu,
  A. Huck, N.J. Cerf and G. Leuchs

Technical University of Denmark, Department of
Physics Max Planck Institute for the Science of
Light, Germany Université Libre de Bruxelles,
Belgium
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Lossy transmission
Norm. intensity
Time
3
Quantum error correction coding
Syndrome diagnosis and recovery
Channel
Encoding
Qubits P.W. Shor, PRA 52,2493,1995 A.
Steane, PRL 77, 793, 1996 Cont. Var Lloyd and
Slotine, PRL 80, 4088, 1998, Braunstein PRL 80,
4084, 1998.
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Error correction and filtration
Deterministic Detect and Correct
Probabilistic Detect and Select
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Building our Scheme
Output
Fidelity
1
0.4
0.5
Probability pE
Output
Manipulation
J.Niset, U. Andersen, N. Cerf, PRL 101, 130503
(2008)
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Experimental setup
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Results - Deterministic
Input
8
Results - Probabilistic
PE25
Output
9
Results - Probabilistic
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Summary

• Demonstrated continuous variable quantum erasure
  correction.

• Two different methods Deterministic and
  probabilistic

11
Continuous Variable Quantum Error Correction
Coding

• U.L. Andersen, M. Lassen, J. Niset, M. Sabuncu,
  A. Huck, N.J. Cerf and G. Leuchs

Technical University of Denmark, Department of
Physics Max Planck Institute for the Science of
Light, Germany Université Libre de Bruxelles,
Belgium
12
Quantum erasure coding for qubits
Encoding
Syndrome diagnosis and recovery
Erasure channel
Encodes two logical qubits into four qubits
Grassl, Beth and Pellizzari, PRA 56, 33 1997
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Continuous variable erasure coding
Coherent states
Syndrome diagnosis and recovery
Erasure channel
CV quantum gates
CV operations and quadrature measurements
Two mode squeezed vacuum
J. Niset, U.L. Andersen and N. Cerf, PRL 101,
130503, 2008.
QND operation Yoshikawa, Miwa, Huck, Andersen,
Loock, Furusawa, PRL 2008