Conditions for the Approximate Correction of Algebras
- Cite this paper as:
- Bény C. (2009) Conditions for the Approximate Correction of Algebras. In: Childs A., Mosca M. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2009. Lecture Notes in Computer Science, vol 5906. Springer, Berlin, Heidelberg
We study the approximate correctability of general algebras of observables, which represent hybrid quantum-classical information. This includes approximate quantum error correcting codes and subsystems codes. We show that the main result of  yields a natural generalization of the Knill-Laflamme conditions in the form of a dimension independent estimate of the optimal reconstruction error for a given encoding, measured using the trace-norm distance to a noiseless channel.
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