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Bloch-sphere approach to correlated noise in coupled qubits. (English) Zbl 1267.81053

Summary: 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 well-known 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 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.

MSC:

81P16 Quantum state spaces, operational and probabilistic concepts
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P40 Quantum coherence, entanglement, quantum correlations
81S22 Open systems, reduced dynamics, master equations, decoherence
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