1202.5139 (Prabha Mandayam et al.)

Towards a Unified Framework for Approximate Quantum Error Correction    [PDF]

Prabha Mandayam, Hui Khoon Ng

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.

View original: http://arxiv.org/abs/1202.5139