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

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