Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model
Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model
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DOI：
10.1038/s41467-019-09436-y
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发表时间：
2018-08
影响因子：
16.6
通讯作者：
R. J. Lewis-Swan;A. Safavi-Naini;J. J. Bollinger-J.;A. Rey
中科院分区：
文献类型：
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作者：
R. J. Lewis-Swan;A. Safavi-Naini;J. J. Bollinger-J.;A. Rey
量子信息的加扰是一个过程，通过这个过程，最初存储在量子多体系统的局部自由度中的信息在其多体自由度上传播，变得无法被局部探测器访问，因此显然丢失了。扰乱和纠缠是调和看似无关的行为的关键概念，包括孤立量子系统的热化和黑洞中的信息丢失，并且彻底改变了我们对非平衡现象的理解。在这里，我们证明了一个家庭的保真度的时间顺序外扰子（FOTOC），最近测量的捕获离子量子模拟器通过时间反演的多体动力学，其次是保真度测量，可以作为一个统一的诊断工具，阐明了快速加扰，体积定律纠缠，遍历性，量子混沌，以及系统半经典动力学中的蝴蝶效应。我们证明了FOTOC的效用，通过计算它们在迪凯模型，一个标志性的模型，在量子光学，最近实施的原子和捕获离子设置。该模型描述了大自旋与振子的耦合，并具有丰富的行为，包括量子相变和混沌。在这里，我们表明，FOTOC提供了一个直接的测量自旋-声子Renyi熵和量子热化。此外，我们连接的FOTOC简单的运营商的方差，使我们能够观察到快速扰频的参数制度，系统的经典轨迹是混乱的，并明确涉及量子和经典的李雅普诺夫指数在一个真正的量子多体系统。我们的研究结果为实验使用FOTOC量化快速置乱，确定量子信息处理的界限以及识别可控量子系统中黑洞类似物的可能候选者开辟了一条道路。
Scrambling of quantum information is the process by which information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom, becoming inaccessible to local probes and thus apparently lost. Scrambling and entanglement are key concepts reconciling seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes, and have revolutionized our understanding of non-equilibrium phenomena. Here, we demonstrate that a family of fidelity out-of-time-order correlators (FOTOCs), recently measured in a trapped-ion quantum simulator via time reversal of the many-body dynamics followed by a fidelity measurement, can serve as a unifying diagnostic tool that elucidates the intrinsic connection between fast scrambling, volume law entanglement, ergodicity, quantum chaos, and the associated butterfly effect in the semiclassical dynamics of the system. We demonstrate the utility of FOTOCs by computing them in the Dicke model, an iconic model in quantum optics, recently implemented in atomic and trapped-ion setups. This model describes the coupling of a large spin to an oscillator and features rich behaviors, including a quantum phase transition and chaos. Here, we show that FOTOCs provide a direct measure of the spin-phonon Renyi entropy and quantum thermalization. Moreover, we connect the FOTOCs to the variance of simple operators, allowing us to observe fast scrambling in the parameter regime where the system's classical trajectories are chaotic, and to explicitly relate the quantum and classical Lyapunov exponents in a truly quantum many-body system. Our results open a path for the experimental use of FOTOCs to quantify fast scrambling, determine bounds on quantum information processing and to identify possible candidates of black hole analogs in controllable quantum systems.