OPTIMAL QUANTUM CODES FOR PREVENTING COLLECTIVE AMPLITUDE DAMPING

Collective decoherence is possible if the distance between quantum bit s is smaller than the effective wavelength of the noise held. Collecti vity in the decoherence helps us to devise more efficient quantum code s. We present a class of optimal quantum codes for preventing collecti ve amplitude damping to a reservoir at zero temperature. It is shown t hat two quantum bits (qubits) are enough to protect one bit quantum in formation, and approximately L + 1/2 ln(2)(pi L/2) qubits are enough t o protect L-qubit information when L is large. For preventing collecti ve amplitude damping, these codes are much more efficient than the pre viously discovered quantum error correcting or avoiding codes. [S1050- 2947(98)08410-8].