The Multiplicative Domain in Quantum Error Correction

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.

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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:

Journal of Physics A: Mathematical and Theoretical {\bf 42} 245303 (2009)
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