Conditions for the approximate correction of algebras

Authors:
Cédric Bény
Affiliations:
Centre for Quantum Technologies, National University of Singapore
Venue:
TQC'09 Proceedings of the 4th international conference on Theory of Quantum Computation, Communication, and Cryptography
Year:
2009

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Abstract

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 [1] 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.