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In order to demonstrate a generalized Bloch-sphere approach for the treatment of noise in coupled qubits, we perform a case study of the decoherence of a system composed of two interacting qubits in a 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 four-level Bloch vector and allows for the application of geometrical concepts from the wellknown two-level Bloch sphere. We find that in the presence of correlated or anticorrelated noise, the rate of decoherence is very sensitive to the initial twoqubit 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. [ABSTRACT FROM AUTHOR]

We study the domain of applicability of the classical telegraph noise model in the study of decoherence in qubits. We investigate the decoherence of a qubit coupled to either a quantum fluctuator, a quantum two-level system (TLS) again coupled to an environment, or to a classical fluctuator modeled by random telegraph noise. In order to do this, we construct a model for the quantum fluctuator where we can adjust the temperature of its environment, and the decoherence rate independently. The model has a well-defined classical limit at any temperature and this corresponds to the appropriate random telegraph process, which is symmetric at high temperatures and becomes asymmetric at low temperatures. We find that the difference in the qubit decoherence rates predicted by the two models depends on the ratio between the qubit-fluctuator coupling and the decoherence rate in the pointer basis of the fluctuator. This is then the relevant parameter, which determines whether the fluctuator, has to be treated quantum mechanically or can be replaced by a classical telegraph process. We also compare the mutual information between the qubit and the fluctuator in the classical and the quantum model. [ABSTRACT FROM AUTHOR]