The excitonic qubit on a star graph: dephasing-limited coherent motion

A phenomenological model is used for describing how a fluctuating bath modifies the way an exciton promotes quantum state transfer on a star graph. A markovian generalized master equation is first established. Then, it is solved exactly for studying specific elements of the exciton reduced density matrix. These elements, called coherences, characterize the ability of the exciton to develop qubit states that are superimpositions involving the vacuum and the local one-exciton states. Although dephasing-limited coherent motion is clearly evidenced, it is shown that both the decoherence and the information transfer are very sensitive to the number of branches that form the star. The larger the branch number is, the slower is the decoherence and the better is the efficiency of the transfer.