Quantum Coding with Entanglement Mark M. Wilde Communication Sciences Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089 Quantum Lunch, Los Alamos National Lab (April 24, 2008)
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Quantum Coding with Entanglement Mark M. Wilde Communication Sciences Institute, Ming Hsieh Department of Electrical Engineering, University of Southern.
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Quantum Coding withEntanglement
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
Quantum Lunch, Los Alamos National Lab (April 24, 2008)
Outline•Review techniques for Quantum Error Correction
2) Finite-depth and infinite-depth encoding circuit, and Finite-depth decoding circuit
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:
Unified Quantum Convolutional CodingResources for Quantum Redundancy
Ancillas (Active and Passive)
Ebits (Active)
Gauge qubits (Passive)
Encoded Information
Quantum
Classical (Additional Passive)
Goal of Unified QCC
Approach optimal rates in the following “grandfather” resource inequality:
Forms a portion of thethree-dimensional capacity region where the protocolconsumes nE ebits and n channel usesto send nQ noiseless qubits and nR noiseless classical bits.
Devetak et al., In preparation, 2008.
Example of a [5,1,1;1,1] Unified QCC
Wilde and Brun, arXiv:0801.0821, Accepted for ISIT, Toronto, July 2008.
Current Work on EAQCCDeriving methods for general (non-CSS) entanglement-assisted quantum convolutional codes.
Important Technique
Equivalent Code
Wilde and Brun, In preparation (2008).
Current Work on EAQCC
•Have finished Alice’s encoding for a general EAQCC
•Have finished Bob’s decoding circuit method.
Quantum Check Matrix
Shifted Symplectic Product Matrix
(special form)
Three-Party EA Codes
Non-Additive EA Codes
Unencoded Subspaces
Ground Subspace
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).
Conclusion and Future Work
•Importing classical convolutional coding theory produces high-performance quantum codes
•Can convolutional quantum key distribution improve the Shor-Preskill noise threshold for BB84?
•Entanglement-assisted convolutional coding exploits entanglement to encode a stream of qubits