That implies that a measurement of an observable that only pertains to the system plus the measurement device cannot discriminate between the total pure state and a mixed state. However, as it was extensively discussed by d’Espagnat the formal identity between the reduced density matrix and a mixed-state density matrix is frequently misinterpreted as implying that the system is in a mixed state. As the system is entangled with the environment the total system is still described by a pure state and no individual definite state or set of possible states may be attributed to a portion of the total system. As it is well known, measurements on the environment will always allow us, in principle, to distinguish between the reduced and mixed state density matrices.

The combined effect of these two forms of decoherence could allow to understand the physical transition from a reduced density matrix to a mixed state. In fact, the precise unitary evolution of the total system is broken by the clock-induced decoherence destroying the correlations. What remains to be studied is whether this effect is sufficiently fast to avoid any possibility of distinguishing, not only for all practical purposes but also on theoretical basis, between 