Speaker:

Mark M. Wilde, University of Southern California

Date:

Tuesday, 11 November 08, 04:00 PM

Venue:

Dept of Mathematics, S14-03-10

Title

Entanglement-Assisted Quantum Error Correction

Abstract:

The entanglement-assisted communication paradigm assumes that a sender can exploit entanglement shared with a receiver when sending quantum information over a noisy quantum channel [1]. Using this entanglement-assisted paradigm, it is possible to import an arbitrary classical error-correction code for as a quantum error-correcting code.

A quantum convolutional code is a quantum error correction scheme that encodes a stream of quantum information [2]. The sender acts with the same unitary on a set of incoming qubits and a set of memory qubits. The sender then transmits some of the qubits and keeps others as part of the memory and repeats this procedure on the incoming stream of quantum information.

In this seminar, I discuss our recently developed techniques for entanglement-assisted quantum convolutional coding [3,4,5,6,7,8]. The benefit of these techniques is that we can produce an entanglement-assisted quantum convolutional code from an arbitrary classical convolutional code. The performance of the resulting quantum code depends on the performance of the imported classical convolutional code. I also give a conjecture for how to determine the optimal amount of entanglement that an entanglement-assisted quantum convolutional code requires.

[1] T. A. Brun, I. Devetak, and M.-H. Hsieh, "Correcting quantum errors with entanglement," Science, vol. 314, no. 5798, pp. pp. 436 – 439, October 2006.

[2] H. Ollivier and J.-P. Tillich, "Description of a quantum convolutional code," Phys. Rev. Lett., vol. 91, no. 17, p. 177902, October 2003.

[3] M. M. Wilde and T. A. Brun, "Optimal entanglement formulas for entanglement-assisted quantum coding," Physical Review A, vol. 77, p. 064302, 2008.

[4] M. M. Wilde, H. Krovi, and T. A. Brun, "Convolutional entanglement distillation," arXiv:0708.3699, 2007.

[5] M. M. Wilde and T. A. Brun, "Entanglement-assisted quantum convolutional coding," arXiv:0712.2223, 2007.

[6] M. M. Wilde and T. A. Brun, "Unified quantum convolutional coding," in IEEE International Symposium on Information Theory (arXiv:0801.0821), July 2008.

[7] M. M. Wilde and T. A. Brun, "Quantum Convolutional Coding with Shared Entanglement: General Structure," arXiv:0807.3803, 2008.

[8] M. M. Wilde, "Quantum Coding with Entanglement," arXiv:0806.4214, Ph.D. Thesis, University of Southern California, 2008.