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Bloch-sphere approach to correlated noise in coupled qubits

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.