Conditions for the approximate correction of algebras
arXiv:0907.4207
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 arXiv:quant-ph/0605009 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.
Related to a talk given at TQC 2009 in Waterloo
References in corpus (7)
- The structure of preserved information in quantum processes
- Generalization of Quantum Error Correction via the Heisenberg Picture
- Semidefinite programs for completely bounded norms
- Complementarity of Private and Correctable Subsystems in Quantum Cryptography and Error Correction
- Computing Stabilized Norms for Quantum Operations via the Theory of Completely Bounded Maps
- Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes
- Unsharp pointer observables and the structure of decoherence