Quantum error correcting codes from the compression formalism

@article{Choi2006QuantumEC,
  title={Quantum error correcting codes from the compression formalism},
  author={Man-Duen Choi and D. Kribs and K. Życzkowski},
  journal={Reports on Mathematical Physics},
  year={2006},
  volume={58},
  pages={77-91}
}
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… Expand

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