Conditions for the approximate correction of algebras
C\'edric B\'eny
TL;DR
This paper investigates the conditions under which algebras of observables, representing hybrid quantum-classical information, can be approximately corrected, extending quantum error correction theory with dimension-independent error estimates.
Contribution
It generalizes the Knill-Laflamme conditions for approximate correctability to algebras of observables, providing a dimension-independent estimate of the optimal reconstruction error.
Findings
Generalized Knill-Laflamme conditions for approximate correction
Derived a trace-norm based estimate of reconstruction error
Applicable to hybrid quantum-classical information systems
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.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum Mechanics and Applications