标题： 混合随机电路中的无序纯化相变 显示英文标题

标题： Disordered purification phase transition in hybrid random circuits

摘要： 噪声在现实的量子电路中是不可避免的。 它在空间中随机出现。 受噪声空间非均匀性的启发，我们研究了空间调制对混合随机 Clifford 电路中纯化相变的影响。 作为提取混合态中量子纠缠的有效可观测量，我们采用了多体否定性。 多体否定性的行为很好地表征了纯化相变及其临界性的存在。 我们发现了测量概率的空间非均匀性对纯化相变的影响。 纯化相变的临界性从均匀概率的情况发生了变化，这通过哈里斯准则的论证得到了阐明。 临界关联长度指数$\nu$从均匀概率下的$\nu < 2$变为空间调制概率下的$\nu > 2$。 我们进一步研究了一个设置，在该设置中，两比特随机 Clifford 门变为空间（准）调制的。 我们发现调制引起了一种相变，导致一种不同的纯相，在该相中短程量子纠缠仍然存在。 显示英文摘要

摘要： Noise is inevitable in realistic quantum circuits. It arises randomly in space. Inspired by spatial non-uniformity of the noise, we investigate the effects of spatial modulation on purification phase transitions in a hybrid random Clifford circuit. As an efficient observable for extracting quantum entanglement in mixed states, we employ many-body negativity. The behavior of the many-body negativity well characterizes the presence of the purification phase transitions and its criticality. We find the effect of spatial non-uniformity in measurement probability on purification phase transition. The criticality of the purification phase transition changes from that of uniform probability, which is elucidated from the argument of the Harris criterion. The critical correlation length exponent $\nu$ changes from $\nu < 2$ for uniform probability to $\nu > 2$ for spatially modulated probability. We further investigate a setting where two-site random Clifford gate becomes spatially (quasi-)modulated. We find that the modulation induces a phase transition, leading to a different pure phase where a short-range quantum entanglement remains.