Geometric phase and Quantum Correlations for a bipartite two-level system

FERNANDO C. LOMBARDO; PAULA I. VILLAR

Castiglioncello (Toscana)

Workshop; DICE 2014: Spacetime-Matter-Quantum Mechanics; 2014

We calculate the geometric phase of a bipartite two-level system coupled to an external environment. We compute the correction to the unitary geometric phase through a kinematic approach. To this end, we analyze the reduced density matrix of the bipartite system after tracing over the environmental degrees of freedom, for arbitrary initial states of the composite system. In all cases considered, the correction to the unitary phase has a similar structure as a function of the degree of the entanglement of the initial state. In the case of a maximally entangled state (MES), the survival phase is only the topological phase, and there is no correction induced by the environments. Further, we compute the quantum discord and concurrence of the bipartite state and analyze possible relations among these quantities and the geometric phase acquired during the non-unitary system?s evolution.