  The concept of multiple particle interference is discussed, using insights
provided by the classical theory of error correcting codes. This leads to a
discussion of error correction in a quantum communication channel or a quantum
computer. Methods of error correction in the quantum regime are presented, and
their limitations assessed. A quantum channel can recover from arbitrary
decoherence of x qubits if K bits of quantum information are encoded using n
quantum bits, where K/n can be greater than 1-2 H(2x/n), but must be less than
1 - 2 H(x/n). This implies exponential reduction of decoherence with only a
polynomial increase in the computing resources required. Therefore quantum
computation can be made free of errors in the presence of physically realistic
levels of decoherence. The methods also allow isolation of quantum
communication from noise and evesdropping (quantum privacy amplification).
