We show how procedures which can correct phase and amplitude errors are in themselves sufficient to correct errors due to quantum entanglement, generalizing earlier results. We specify general criteria for quantum error correction, introduce quantum versions of the Hamming and the Gilbert-Varshamov bounds, and comment on the practical implementations of quantum codes. [S0031-9007 (96) 01212-4] PACS numbers: 89.70.+c, 02.50.-r, 03.65.-w, 89.80.+h Suppose we want to transmit a block of l qubits

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... .e., two-state quantum systems) in some unknown quantum state (pure or mixed) over a noisy quantum channel.