Fidelity as a function of time for entangled states experiencing collective relaxation under different modulations compared to that of a single qubit without modulation (blue, dashed) (color online): bright-state, without modulation (red, dot-dashed); GHZ with without modulation (green, dotted); bright-state with under asymmetric modulation (black, solid). (a) Decoherence rates for with asymmetric modulation. Single-qubit decoherence rates, (black, solid), undergo oscillations then attain constant nonzero values at ; cross-decoherence rates (blue, dashed) also oscillate but then decay to zero at . (b) For qubits and , the overlap of the bath coupling spectrum (red area) and the modulation spectra and (green areas) determine the decoherence rate. If the qubits undergo (asymmetric) different modulations , their lack of overlap eliminates cross decoherence. (c) Addressing individual ions in a trap by different control fields with different amplitudes induces asymmetric Rabi flippings and thereby eliminates cross decoherence.