1 / 28

Quantum Coding with Entanglement

Quantum Coding with Entanglement. Communication Sciences Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089. Mark M. Wilde. Quantum Lunch, Los Alamos National Lab (April 24, 2008).

connie
Télécharger la présentation

Quantum Coding with Entanglement

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Quantum CodingwithEntanglement Communication Sciences Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089 Mark M. Wilde Quantum Lunch, Los Alamos National Lab (April 24, 2008)

  2. Review techniques for Quantum Error Correction (Including Entanglement-Assisted Coding) • Entanglement-Assisted Quantum Convolutional Coding arXiv:0712.2223 ?? • Unified Quantum Convolutional Coding • Hint at new directions arXiv:0801.0821 arXiv:08??.???? arXiv:09??.???? Outline

  3. Quantum Block Code Perform measurements that learn only about errors Encode qubits with ancillas Shor, PRA 52, pp. R2493-R2496 (1995).

  4. Unencoded Stabilizer Encoded Stabilizer Example Stabilizer for a Block Code Laflamme et al., Physical Review Letters 77, 198-201 (1996).

  5. Entanglement-Assisted Quantum Block Code Brun, Devetak, Hsieh, Science 314, 436-439 (2006).

  6. Unencoded Stabilizer Encoded Stabilizer Example Stabilizer for an EA Code Brun, Devetak, Hsieh, Science 314, 436-439 (2006).

  7. Given a set of generators H with good error-correcting properties The minimum number of ebits the quantum code needs is CSS code imported from 2 classical codes Quantum code imported from classical GF(4) code Minimum Ebit Formulae for EA Coding Wilde and Brun, arXiv:0804.1404 (2008).

  8. Convolutional Coding techniques have application in cellular and deep space communication ViterbiAlgorithmis most popular technique for determining errors Classical Convolutional Coding

  9. FIR Encoding Circuits Finite-durationinput streams producefinite-durationoutput streams (corresponding to finite polynomials)

  10. IIR Encoding Circuits Finite-durationinput streams can produceinfinite-durationoutput streams (corresponding to rational polynomials)

  11. 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).

  12. Unencoded Stabilizer Encoded Stabilizer Example Stabilizer for a QCC Forney, Grassl, Guha, IEEE Trans. Inf. Theory 53, 865-880 (2007).

  13. Entanglement-Assisted Quantum Convolutional Coding Wilde and Brun, arXiv:0712.2223 (2007).

  14. Unencoded Stabilizer Encoded Stabilizer Example Stabilizer for an EAQCC Wilde and Brun, arXiv:0712.2223 (2007).

  15. Classical conv. code EAQCC Encoding Circuit for Example EAQCC Rate (1/2,1/2) Wilde and Brun, arXiv:0712.2223 (2007).

  16. Implements Implements Infinite-Depth Operations

  17. Unencoded Stabilizer Encoded Stabilizer Example Stabilizer for another EAQCC Wilde and Brun, arXiv:0712.2223 (2007).

  18. Classical conv. code EAQCC EAQCC Example 2 Rate (1/2,1/2)

  19. Classes of EAQCCs 1) Finite-depth encoding and decoding circuits 2) Finite-depth and infinite-depth encoding circuit, and Finite-depth decoding circuit

  20. 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 => high-performance quantum codes)

  21. Ancillas (Active and Passive) Ebits (Active) Gauge qubits (Passive) Quantum Classical (Additional Passive) Unified Quantum Convolutional Coding Resources for Quantum Redundancy Encoded Information

  22. Goal of Unified QCC Approach optimal rates in the following “grandfather” resource inequality: Forms a portion of the three-dimensional capacity region where the protocol consumes nE ebits and n channel uses to send nQ noiseless qubits and nR noiseless classical bits. Devetak et al., In preparation, 2008.

  23. Example of a [5,1,1;1,1] Unified QCC Wilde and Brun, arXiv:0801.0821, Accepted for ISIT, Toronto, July 2008.

  24. Important Technique Equivalent Code Current Work on EAQCC Deriving methods for general (non-CSS) entanglement-assisted quantum convolutional codes. Wilde and Brun, In preparation (2008).

  25. Quantum Check Matrix Shifted Symplectic Product Matrix (special form) • Have finished Alice’s encoding for a general EAQCC • Have finished Bob’s decoding circuit method. Current Work on EAQCC

  26. Three-Party EA Codes

  27. Ground Subspace Unencoded Subspaces Non-Additive EA Codes Have encoding circuit for classical indices j and one to encode the stabilizer (similar to Grassl and Roetteler) Grassl and Roetteler, arXiv:0801.2144 (2008).

  28. Conclusion and Future Work • Entanglement-assisted convolutional codingexploits entanglementto encode a stream of qubits • Importing classical convolutional coding theory produceshigh-performance quantum codes • Can convolutional quantum key distributionimprove the Shor-Preskill noise threshold for BB84?

More Related