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The geometric phase is of fundamental interest and plays an important role inquantum information processing. However, the definition and calculation of thisphase for open systems remains a problem due to the lack of agreement ongeneralizations of the parallel transport condition to mixed state nonunityevolutions. Here we tackle this problem by associating the open systemgeometric phase with the parallel transport of the joint system-reservoirstate. Our approach not only provides a way around the nonunitary evolutionobstacle, but also sheds light on the relation between the geometric phase andthe system-reservoir entanglement, which has not been investigated. Based onthis approach, we calculate the geometric phase of different quantum systemssubject to energy decay, showing that it is robust against decoherence, whichis in distinct contrast with previous results.

Open system geometric phase based on system-reservoir joint state evolution