Nonlocal effect of a bipartite system induced by local cyclic operation

The state of a bipartite system may be changed by a cyclic operation applied on one of its subsystems. The change is a nonlocal effect, and can be detected only by measuring the two parts jointly. By employing the Hilbert-Schmidt metric, we can quantify such nonlocal effects via measuring the distance between the initial and final state. We show that this nonlocal property can be manifested not only by entangled states but also by the disentangled states which are classically correlated. Furthermore, we study the effect for the system of two qubits in detail. It is interesting that the nonlocal effect of disentangled states is limited by 1/root 2, while the entangled states can exceed this limit and reach 1 for maximally entangled states.