Unitary-projective entanglement dynamics
Unitary-projective entanglement dynamics
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DOI：
10.1103/physrevb.99.224307
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发表时间：
2019-06-24
影响因子：
3.7
通讯作者：
Smith, Graeme
中科院分区：
文献类型：
--
作者：
Chan, Amos;Nandkishore, Rahul M.;Smith, Graeme
局部幺正时间演化从低量子纠缠态出发，增加了量子多体系统的纠缠态。相反，局部投影测量解除了纠缠度并减少了纠缠。我们通过考虑时间演化来结合统一动力学和射影动力学来研究这些竞争趋势的相互作用。我们首先构建一个贝尔对动力学的玩具模型，该模型表明测量可以使系统保持在低状态，即面积律纠缠，而不是由一般纯幺正时间演化产生的体积律纠缠。虽然最简单的贝尔对模型具有任何测量速率的面积律纠缠，如在某些非相互作用系统中所见，但我们表明，更一般的纠缠模型可以在测量速率的临界值处具有面积-体积律转变，这与最近的数值研究一致。作为这些思想的一个具体例子，我们分析研究了可以表现出纠缠跃迁的量子比特系统中的Clifford进化。我们能够确定稳定剂的尺寸分布特征的面积规律，体积规律，和关键的“固定点”。我们还讨论了一个Floquet随机酉电路，其答案依赖于极限的阶数——对于任何非零测量速率，一个阶数的极限产生面积律纠缠，而不同阶数的极限允许面积律-体积律跃迁。最后，我们提供了一个严格的论点，即如果一个系统也具有子导校正项，那么它只能表现出体积律纠缠熵，这为高纠缠阶段的射影动力学提供了普遍的特征。
Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many-body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study the interplay of these competing tendencies by considering time evolution combining both unitary and projective dynamics. We begin by constructing a toy model of Bell pair dynamics which demonstrates that measurements can keep a system in a state of low, i.e., area-law, entanglement, in contrast with the volume-law entanglement produced by generic pure unitary time evolution. While the simplest Bell pair model has area-law entanglement for any measurement rate, as seen in certain noninteracting systems, we show that more generic models of entanglement can feature an area-to-volume law transition at a critical value of the measurement rate, in agreement with recent numerical investigations. As a concrete example of these ideas, we analytically investigate Clifford evolution in qubit systems which can exhibit an entanglement transition. We are able to identify stabilizer size distributions characterizing the area law, volume law, and critical "fixed points." We also discuss a Floquet random unitary circuit, where the answers depend on the order of limits-one order of limits yields area-law entanglement for any nonzero measurement rate, whereas a different order of limits allows for an arealaw-volumelaw transition. Finally, we provide a rigorous argument that a system subjected to projective measurements can only exhibit a volume-law entanglement entropy if it also features a subleading correction term, which provides a universal signature of projective dynamics in the high-entanglement phase.