We show that errors are not generated correlatedly provided that quantum bi
ts do not directly interact with (or couple to) each other. Generally, this
no-qubit-interaction condition is assumed except for the case where two-qu
bit gate operation is being performed. In particular, the no-qubit-interact
ion condition is satisfied in the collective decoherence models. Thus, erro
rs are not correlated in the collective decoherence. Consequently, we can s
ay that current quantum error correcting codes that correct single-qubit er
rors will work in most cases including the collective decoherence.