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Articles

Quantum error correction for a subgroup of the Pauli group using higher rank numerical range

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Pages 68-77 | Received 30 Dec 2014, Accepted 02 Apr 2015, Published online: 07 May 2015

References

  • Gottesman D. Class of quantum error-correcting codes saturating the quantum hamming bound. Phys. Rev. A. 1996;54:1862.
  • Gottesman D. Stabilizer codes and quantum error-correction [PhD thesis]. Pasadena (CA): California Institute of Technology; 1997.
  • Kribs DW, Pasieka A, Laforest M, Ryan C, da Silva MP. Research problems on numerical ranges in quantum computing. Linear Multilinear Algebra. 2009;57:491–502.
  • Knill E, Laflamme R. Theory of quantum error-correcting codes. Phys. Rev. A. 1997;55:900–911.
  • Li CK, Nakahara M, Poon YT, Sze NS, Tomita H. Efficient quantum error correction for fully correlated noise. Phys. Lett. A. 2011;375:3255–3258.
  • Li CK, Poon YT. Generalized numerical ranges and quatum error correction. J. Operator Theory. 2011;66:335–351.
  • Mousavi SA, Salemi A. Joint higher rank numerical range of Pauli group. Linear Multilinear Algebra. 2015;63:439–454.
  • Johnston N, Kribs DW, Teng CW. Operator algebraic formulation of the stabilizer formalism for quantum error correction. Acta Appl. Math. 2009;108:687–696.
  • Li CK, Nakahara M, Poon YT, Sze NS, Tomita H. Recovery in quantum error correction for general noise without measurement. Quantum Inf. Comput. 2012;12:149–158.

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