Nonseparability tests by noncommutativity of excitations

Elementary quantum mechanical principles are applied to bipartite or multipartite systems to test the nonseparability of subsystems (or nonadditivity in the system Hamiltonian) through interchanging the ordering of subsystem (local) operators that cause transitions between energy eigenstates, whether applied to pure or mixed states. A tentative measure for quantifying nonseparability is proposed, based on complete sets of subsystem transition operators. This serves as an upper bound for experimental determinations of the intersubsystem coupling. Two- and three-qubit systems are numerically tested to establish criteria for the noninvariance of transition probabilities in them with respect to the sequence of excitations, and it is conjectured that sequence noninvariance can be used as a probe for subsystems' nonseparability.