  It is commonly believed that decoherence arises as a result of the entangling
interaction between a quantum system and its environment, as a consequence of
which the environment effectively measures the system, thus washing away its
quantum properties. Moreover, this interaction results in the emergence of a
classical objective reality, as described by Quantum Darwinism. In this Letter,
we show that the widely believed idea that entanglement is needed for
decoherence is imprecise. We propose a new mechanism, dynamical mixing, capable
of inducing decoherence dynamics on a system without creating any entanglement
with its quantum environment. We illustrate this mechanism with a simple and
exactly solvable collision model. Interestingly, we find that Quantum Darwinism
does not occur if the system undergoes entanglement-free decoherence and, only
when the effect of a super-environment introducing system-environment
entanglement is taken into account, the emergence of an objective reality takes
place. Our results lead to the unexpected conclusion that system-environment
entanglement is not necessary for decoherence or information back-flow, but
plays a crucial role in the emergence of an objective reality.
