  We study time dependence of exchange symmetry properties of Bell states when
two qubits interact with local baths having identical parameters. In case of
classical noise, we consider a decoherence Hamiltonian which is invariant under
swapping the first and second qubits. We find that as the system evolves in
time, two of the three symmetric Bell states preserve their qubit exchange
symmetry with unit probability, whereas the symmetry of the remaining state
survives with a maximum probability of 0.5 at the asymptotic limit. Next, we
examine the exchange symmetry properties of the same states under local,
quantum mechanical noise which is modeled by two identical spin baths. Results
turn out to be very similar to the classical case. We identify decoherence as
the main mechanism leading to breaking of qubit exchange symmetry.
