Decoherence without entanglement and Quantum Darwinism

Abstract: 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.