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Entanglement Boosts Quantum Turbo Codes

Overview. Brief review of quantum error correction (entanglement-assisted as well). Review of quantum convolutional codes and their properties. Adding entanglement assistance to quantum convolutional encoders. Review of quantum turbo codes and their decoding algorithm. Results of simulat

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Entanglement Boosts Quantum Turbo Codes

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Presentation Transcript

    3. Quantum Error Correction

    4. Stabilizer Formalism

    5. Distance of a Quantum Code

    6. Maximum Likelihood Decoding

    7. Entanglement-Assisted Quantum Error Correction

    8. Entanglement-Assisted Stabilizer Formalism

    9. Distance of an EA Quantum Code

    10. EA Maximum Likelihood Decoding

    11. Quantum Convolutional Codes

    12. State Diagram

    13. Catastrophicity

    14. Catastrophicity (ctd.)

    15. Recursiveness

    16. No-Go Theorem

    17. Idea: Add Entanglement

    18. State Diagram

    19. Catastrophicity

    20. Catastrophicity (ctd.)

    21. Recursiveness

    22. Non-Catastrophic and Recursive Encoder

    23. Quantum Turbo Codes

    24. How to decode a Quantum Turbo Code?

    25. Iterative Decoding

    26. Iterative Decoding (Backward Recursion)

    27. Iterative Decoding (Forward Recursion)

    28. Iterative Decoding (Local Update)

    29. Iterative Decoding of a Quantum Turbo Code

    30. Simulations

    31. Compare with the Hashing Bounds

    32. Unassisted Turbo Code

    33. Fully Assisted Turbo Code

    34. “Inner” Entanglement Assisted Turbo Code

    35. “Outer” Entanglement Assisted Turbo Code

    36. Adding Noise to Bob's Share of the Ebits

    37. No-Go Theorem for Subsystem or Classically-Enhanced Codes

    38. Conclusion

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