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.
We investigate the nonseparability of multipartite bosonic and fermionic
GHZ and
W states in a causal diamond spacetime using the Abe-Rajagopal (AR)
q-conditional entropy. The finite lifetime of the observer gives rise to a causal diamond horizon, which induces an Unruh-like thermal effect and leads to a nontrivial restructuring of nonseparability in
N-partite systems. Our main result is that the thermal effect can enhance a net nonseparability of fermionic
W states, in sharp contrast to the general expectation that relativistic thermalization leads to a monotonic degradation of bosonic nonseparability. In addition, we find that fermionic nonseparability is generally more robust than its bosonic counterpart under causal diamond restrictions. Among different entangled resources,
GHZ states exhibit stronger nonseparability and greater robustness than
W states under identical causal conditions. We further show that the nonseparability of
W states decreases with increasing particle number
N, whereas that of
GHZ states remains independent of
N in causal diamond spacetime. These results demonstrate that particle statistics, entanglement structure, and observer lifetime jointly determine the persistence of nonseparability in causally restricted spacetimes, providing insights for relativistic quantum information processing.