Volume 5
Summer 2012
Number 1

Quantum error correction for diagonal channels

Samuel D. Arnold

Abstract: The properties of quantum channels with diagonal Kraus operators are examined. These are exactly the channels which allow full transmission of classical information.
The condensed matrix is presented. The quantum channel has capacity zero iff the condensed matrix has full rank, otherwise it can transmit at least 1 qubit per use.
A tight bound on the number of error operators a random quantum channel may have and still be correctable is given for both real and complex diagonal channels.