  We consider the quantum dynamics of two spin-1/2 systems, each coupled to a
bath of oscillators, so that a bath-mediated coupling is generated between the
spins. We find that the interactions destroys any coherent motion of the 2
spins, even if the coupling of each spin to the bath is quite weak, unless the
interaction is extremely small. This is because the dynamic mutual bias between
the spins blocks any coherent transitions between nearly degenerate states. In
many quantum measurement operations this means that decoherence effects will be
much stonger during the actual measurement
