纠缠动力学在监测量子电路中的三重方式
Three-fold way of entanglement dynamics in monitored quantum circuits
AI总结：
本研究通过对比三种圆系综下的量子电路，揭示了测量诱导纠缠相变中门纠缠产生与测量纠缠减少的相互作用，提出了基于KAK分解的统计纠缠能力高效表述及CSE反对称矩阵特征值统计的一般结果。
摘要：
我们研究了基于Dyson三种圆系综（圆酉系综、圆正交系综和圆辛系综；CUE、COE和CSE）构建的量子电路中的测量诱导纠缠相变。我们利用一维电路的既定模型，该电路在交替的局部随机酉门和以可调速率执行的投影测量下演化，对于从CUE中抽取的门，已知该模型在测量速率增加时表现出从广延纠缠标度到集约纠缠标度的转变。通过将此情况与COE和CSE进行对比，我们深入了解了门的局部纠缠产生与测量导致的纠缠减少之间的相互作用。为此，我们结合了不同系综中单个门产生的纠缠的精确解析随机矩阵结果，以及完整量子电路的数值结果。这些考虑包括将统计纠缠能力高效地重新表述为特征纠缠矩阵，该矩阵捕捉了Cartan的KAK分解的本质，以及一个关于与CSE相关的反对称矩阵特征值统计的一般结果。
英文摘要：
We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles (circular unitary, orthogonal, and symplectic ensembles; CUE, COE and CSE). We utilise the established model of a one-dimensional circuit evolving under alternating local random unitary gates and projective measurements performed with tunable rate, which for gates drawn from the CUE is known to display a transition from extensive to intensive entanglement scaling as the measurement rate is increased. By contrasting this case to the COE and CSE, we obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements. For this, we combine exact analytical random-matrix results for the entanglement generated by the individual gates in the different ensembles, and numerical results for the complete quantum circuit. These considerations include an efficient rephrasing of the statistical entangling power in terms of a characteristic entanglement matrix capturing the essence of Cartan's KAK decomposition, and a general result for the eigenvalue statistics of antisymmetric matrices associated with the CSE.
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