Informational correlation between two parties of a quantum system: spin-1/2 chains

We introduce the informational correlation \(E^{AB}\) between two interacting quantum subsystems \(A\) and \(B\) of a quantum system as the number of arbitrary parameters \(\varphi _i\) of a unitary transformation \(U^A\) (locally performed on the subsystem \(A\) ) which may be detected in the subsystem \(B\) by the local measurements. This quantity indicates whether the state of the subsystem \(B\) may be effected by means of the unitary transformation applied to the subsystem \(A\) . Emphasize that \(E^{AB}\ne E^{BA}\) in general. The informational correlations in systems with tensor product initial states are studied in more details. In particular, it is shown that the informational correlation may be changed by the local unitary transformations of the subsystem \(B\) . However, there is some non-reducible part of \(E^{AB}(t)\) which may not be decreased by any unitary transformation of the subsystem \(B\) at a fixed time instant \(t\) . Two examples of the informational correlations between two parties of the four-node spin-1/2 chain with mixed initial states are studied. The long chains with a single initially excited spin (the pure initial state) are considered as well.