We develop a theoretical scheme to perform a readout of the properties of a quasiperiodic system by coupling it to one or two qubits. We show that the decoherence dynamics of a single qubit coupled via a pure dephasing type term to a one-dimensional quasiperiodic system with a potential given by the André-Aubry-Harper (AAH) model and its generalized versions (GAAH model) is sensitive to the nature of the single-particle eigenstates (SPEs). More specifically, we can use the non-Markovianity of the qubit dynamics as quantified by the backflow of information to clearly distinguish the localized, delocalized, and mixed regimes with a mobility edge of the AAH and GAAH models and evidence the transition between them. By attaching two qubits at distinct sites of the system, we demonstrate that the transport property of the quasiperiodic system is encoded in the scaling of the threshold time to develop correlations between the qubits with the distance between the qubits. This scaling can also be used to distinguish and infer different regimes of transport such as ballistic, diffusive, and no transport engendered by SPEs that are delocalized, critical, and localized respectively. In addition, the localization length of the SPEs can also be gleaned from the exponential decay of correlations at long times as a function of distance between qubits. When there is a mobility edge allowing the coexistence of different kinds of SPEs in the spectrum, such as the coexistence of localized and delocalized states in the GAAH models, we find that the transport behavior and the scaling of the threshold time with qubit separation are governed by the fastest spreading states.

中文翻译：

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使用量子位读出准周期系统

我们开发了一种理论方案，通过将准周期系统的性质耦合到一个或两个量子位来进行读出。我们表明，通过纯相移类型项耦合到一维拟周期系统的单个量子比特的退相干动力学具有由André-Aubry-Harper（AAH）模型及其广义版本（GAAH模型）给出的势能单粒子本征态（SPE）的性质。更具体地说，我们可以使用通过信息回流量化的量子位动力学的非马尔可夫性来清楚地区分具有AAH和GAAH模型的移动性边缘的局部，非局部和混合状态，并证明它们之间的过渡。通过在系统的不同位置附加两个量子比特，我们证明准周期系统的输运性质是在阈值时间的标度中编码的，以发展量子位之间与量子位之间的距离的相关性。此缩放比例还可用于区分和推断不同的传输方式，例如弹道，扩散和分别由非本地化，临界和本地化的SPE引起的传输。另外，还可以根据量子位之间的距离，根据长时间的相关性指数衰减来收集SPE的定位长度。当存在移动性边缘时，可以允许频谱中不同种类的SPE共存，例如GAAH模型中本地化和非本地化状态的共存，