Knill-Laflamme Conditions

The Knill-Laflamme conditions characterize when a quantum error-correcting code corrects a set of error operators ${E_a}$ . If is the orthogonal projection onto , the conditions are

for all and , where the are scalars. Equivalently, the operators cannot distinguish states within the code subspace.

See also

Orthogonal Projection, Quantum Error-Correcting Code, Stabilizer Code

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References

Knill, E. and Laflamme, R. "Theory of Quantum Error-Correcting Codes." Phys. Rev. A 55, 900-911, 1997. https://doi.org/10.1103/PhysRevA.55.900.

Cite this as:

Weisstein, Eric W. "Knill-Laflamme Conditions." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Knill-LaflammeConditions.html

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