  The recently introduced detected-jump correcting quantum codes are capable of
stabilizing qubit-systems against spontaneous decay processes arising from
couplings to statistically independent reservoirs. These embedded quantum codes
exploit classical information about which qubit has emitted spontaneously and
correspond to an active error-correcting code embedded in a passive
error-correcting code. The construction of a family of one detected jump-error
correcting quantum codes is shown and the optimal redundancy, encoding and
recovery as well as general properties of detected jump-error correcting
quantum codes are discussed. By the use of design theory multiple jump-error
correcting quantum codes can be constructed. The performance of one jump-error
correcting quantum codes under non-ideal conditions is studied numerically by
simulating a quantum memory and Grover's algorithm.
