Uhlmann phase in composite systems with entanglement

We study the geometric Uhlmann phase of entangled mixed states in a composite system made of two coupled spin-\frac 1 2particles with a magnetic field acting on one of them. Within a depolarizing channel setup, an exact analytical expression for such a phase in each subsystem is derived. We find an explicit connection to the concurrence of the depolarizing channel density matrix, which allows to characterize the features of the Uhlmann phase...