Decoherence without entanglement and quantum Darwinism

It is often assumed 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 Rapid Communication, we show that the idea that entanglement is needed for decoherence is imprecise. We propose a dynamical mixing mechanism capable of inducing decoherence dynamics on a system without creating any entanglement with its quantum environment. We illustrate this mechanism by introducing a simple and exactly solvable collisional model that combines both quantum and classical decoherence features. Interestingly, by tuning the model parameters, we can describe the same open system dynamics both with and without entanglement between system and environment. For a finite environment, we show that dynamical mixing can account for non-Markovian recoherence, even in the absence of entanglement. Our results highlight 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.

Figure 1

Sketch illustrating the model. The orange dots represent the system $\mathcal{S}$ colliding with different ancillae (white dots) at exponentially distributed random times, depicted as red vertical lines on the $t$ axis. During each collision, the system and the corresponding ancilla undergo a unitary transformation $U_{\theta }$. The set of all ancillae defines the environment $\mathcal{E}$, whereas ${\mathcal{E}}_f$ represents a randomly chosen fraction $f$ of the ancillae, to which an observer might have access in order to acquire information about the state of the system.

Figure 2

Coherence factor for the qubit, Eq. (3), as a function of time for different numbers of ancillae with nonentangling interaction strength, $\theta =\pi$ and $\lambda =1$. The vertical lines indicate the corresponding mixture time $t_m$, at which the coherence vanishes. As the number of ancillae increases, the coherence remains close to zero for longer periods of time. Notice that the final state depends on the parity of the number of ancillae.

Figure 3

Mutual information over system entropy as a function of environment fraction for the two settings at different times, for $n={10}^4$ ancillae and $\lambda =1$. To indicate the state of the system at the time to which each curve corresponds, they have been colored matching the corresponding dot in the inset, which shows the coherence factor as in Fig. 2. The times have been chosen to cover the different dynamical regimes undergone by the system. (a) The origin of the randomness in the collision times is not considered. The plateau in the mutual information occurs for $I_f=0$, meaning that the ancillae alone barely carry any information. (b) The emitters are part of the quantum state as well. The effect of the emitters is the appearance of QD while the system is in a highly mixed state.