2005/11/30 by Man-Duen Choi, David W. Kribs, Karol Zyczkowski
Physics and Astronomy · Mathematics · #quant-ph #math.FA #math.OA
paper · pdf · doi:10.1016/s0034-4877(06)80041-8
published as Rep. Math. Phys., 58 (2006), 77-91. · 8 pages, 2 figures, Rep. Math. Phys., to appear
arxiv created 2006/05/12 · arxiv updated 2009/12/01
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and identify correctable codes for Pauli-error models not obtained by the stabilizer formalism. This is accomplished through an application of a new tool for error correction in quantum computing called the ``higher-rank numerical range''. We describe its basic properties and discuss possible further applications.