Quantum error correcting codes from the compression formalism

@article{Choi2006QuantumEC,
  title={Quantum error correcting codes from the compression formalism},
  author={M. Choi and D. Kribs and K. Zyczkowski},
  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
75 Citations

Figures from this paper

Nuclear numerical range and quantum error correction codes for non-unitary noise models
  • 2
  • PDF
Entropy of a Quantum Error Correction Code
  • 5
  • PDF
Private quantum codes: introduction and connection with higher rank numerical ranges
  • 3
  • PDF
Quantum error correction and generalized numerical ranges
  • 6
  • PDF
Elliptical range theorems for generalized numerical ranges of quadratic operators
  • 15
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 23 REFERENCES
A nonadditive quantum code
  • 85
  • PDF
Theory of quantum error-correcting codes
  • 708
  • PDF
Operator quantum error correction
  • 121
  • PDF
Error Correcting Codes in Quantum Theory.
  • Steane
  • Physics, Medicine
  • Physical review letters
  • 1996
  • 1,652
  • PDF
Class of quantum error-correcting codes saturating the quantum Hamming bound.
  • Gottesman
  • Physics, Medicine
  • Physical review. A, Atomic, molecular, and optical physics
  • 1996
  • 824
  • PDF
Unified and generalized approach to quantum error correction.
  • 177
  • PDF
Quantum shadow enumerators
  • E. Rains
  • Mathematics, Physics
  • IEEE Trans. Inf. Theory
  • 1999
  • 70
  • PDF
Quantum Computation and Quantum Information
  • 12,027
  • PDF
...
1
2
3
...