  The concept of relative state is used to introduce geometric phases that
originate from correlations in states of composite quantum systems. In
particular, we identify an entanglement-induced geometric phase in terms of a
weighted average of geometric phase factors associated with a decomposition
that define the entanglement of formation. An explicit procedure to calculate
the entanglement-induced geometric phase for qubit pairs is put forward. We
illustrate it for maximally entangled mixed states (MEMS) of two qubits.
