Abstract:

We show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes that do not require a measurement as part of the recovery process, the so-called unitarily correctable codes. Whereas in the arbitrary, not necessarily unital case they form a proper subset of unitarily correctable codes that can be computed from properties of the channel. As part of the analysis we derive a representation theoretic characterization of subsystem codes. We also present a number of illustrative examples.

Authors:

• Man-Duen Choi
• Nathaniel Johnston
• David Kribs

Download:

• Official publication from IOP [pdf]
• Preprint from arXiv:0811.0947v1 [quant-ph] [pdf]
• Local preprint [pdf]
• Poster presentation [pdf]
• Poster presentation [.zip of LaTeX files]
• Slideshow presentation [pdf]
• Slideshow presentation with audio from the Fields Institute’s website

Status:

• Published in Journal of Physics A: Mathematical and Theoretical in June 2009
  

Cite as:

• M.-D. Choi, N. Johnston, and D. W. Kribs, The Multiplicative Domain in Quantum Error Correction. Journal of Physics A: Mathematical and Theoretical 42, 245303 (2009).

Presentation Dates and Locations:

• Quantum Information & Geometric Statistics Seminar (QuIGS) – University of Guelph. July 2008
• Canadian Mathematical Society Winter 2008 Meeting – Ottawa, Ontario. December 2008
• Canadian Quantum Information Student Conference – Toronto, Ontario. August 2009

Supplementary Material:

• Generalized Multiplicative Domains and Quantum Error Correction (sequel publication)
• A Brief Introduction to the Multiplicative Domain and its Role in Quantum Error Correction (blog post)