Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This finding motivates us to introduce measurement-only models, in which the “scrambling” and “unscrambling” effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. These models represent a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is frustration, or mutual incompatibility, of the measurements. Surprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local ($\gtrsim 3$-body) operators. We identify a class of exceptions to this behavior (“bipartite ensembles”) which cannot sustain an entangling phase but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light cone, despite the nonlocality inherent to quantum measurements.

中文翻译：

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仅测量动力学中的纠缠相变

经受重复投影测量的measurements电路可能会发生纠缠相变（EPT），这是测量速率的函数。通常根据单一动力学的扰动效应与测量的解缠结效应之间的竞争来理解这种过渡。我们发现，令人惊讶的是，即使没有加扰的单一动力学，EPT也是可能的，最好将其理解为仅由测量产生。这一发现激励我们引入仅测量模型，其中驱动EPT的“加扰”和“不加扰”效应从根本上交织在一起，不能归因于物理上不同的过程。这些模型代表了EPT的一种新颖形式，在概念上不同于混合式-射电路。我们探索了其中一些仅测量模型的纠缠相图，临界点和量子代码属性。我们发现，驱动这些模型中的EPT的原理是测量的挫败感或相互不兼容。令人惊讶的是，当测量足够长但仍局部的时，纠缠（体积定律）阶段是一般的结果（$\gtrsim 3$-body）运算符。我们确定了这种行为的一类例外（“二合体”），它们无法维持纠缠相，但显示出可能具有不同量子级的双重面积定律相，并被自我对偶临界点隔开。最后，尽管引入了量子测量固有的非局限性，我们还是通过测量引入了一种信息在动力学中的传播度量，并用它来证明统计光锥的出现。