  By use of a generalized Bloch vector construction, we study the decoherence
of a system composed of two interacting qubits in a general noisy environment.
In particular, we investigate the effects of correlations in the noise acting
on distinct qubits. Our treatment of the two-qubit system by use of the
generalized Bloch vector leads to tractable analytic equations for the dynamics
of the 4-level Bloch vector and allows for the application of geometrical
concepts from the well known 2-level Bloch sphere. We find that in the presence
of correlated or anticorrelated noise, the rate of decoherence is very
sensitive to the initial two-qubit state, as well as to the symmetry of the
Hamiltonian. In the absence of symmetry in the Hamiltonian, correlations only
weakly impact the decoherence rate.
