  Entangled qubit pairs can serve as a quantum memory or as a resource for
quantum communication. The utility of such pairs is measured by how long they
take to disentangle or decohere. To answer the question of whether qubit-qubit
interactions can prolong entanglement, we calculate the dissipative dynamics of
a pair of qubits coupled via the exchange interaction in the presence of random
telegraph noise and $1/f$ noise. We show that for maximally entangled (Bell)
states, the exchange interaction generally suppresses decoherence and
disentanglement. This suppression is more apparent for random telegraph noise
if the noise is non-Markovian, whereas for $1/f$ noise the exchange interaction
should be comparable in magnitude to strongest noise source. The entangled
singlet-triplet superposition state of 2 qubits ($\psi_{\pm}$ Bell state) can
be protected by the interaction, while for the triplet-triplet state
($\phi_{\pm}$ Bell state), it is less effective. Thus the former is more
suitable for encoding quantum information.
