Physics – Quantum Physics
Scientific paper
2012-02-23
Physics
Quantum Physics
9 pages
Scientific paper
Operator quantum error correction extends the standard formalism of quantum error correction (QEC) to codes in which only a subsystem within a subspace of states is used to store information in a noise-resilient fashion. Motivated by recent work on approximate QEC, which has opened up the possibility of constructing subspace codes beyond the framework of perfect error correction, we investigate the problem of {\it approximate} operator quantum error correction (AOQEC). We demonstrate easily checkable sufficient conditions for the existence of AOQEC codes. Furthermore, for certain classes of noise processes, we prove the efficacy of the transpose channel as a simple-to-construct recovery map that works nearly as well as the optimal recovery channel, with optimality defined in terms of worst-case fidelity over all code states. This work generalizes our earlier approach \cite{aqecPRA} of using the transpose channel for approximate correction of subspace codes to the case of subsystem codes, and brings us closer to a unifying framework for approximate quantum error correction.
Mandayam Prabha
Ng Hui Khoon
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