Approximate quantum error correction can lead to better codes
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We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single amplitude damping error. This code violates the usual Hamming bound calculated for a Pauli description of the error process, and does not fit into the GF(4) classification.
7 pages, 2 figures, submitted to Phys. Rev. A
7 pages, 2 figures, submitted to Phys. Rev. A