标题： 单位和监控量子多体系统中非可稳定性的高效评估 显示英文标题

标题： Efficient evaluation of the nonstabilizerness in unitary and monitored quantum many-body systems

摘要： 我们考虑交错XXZ链的量子态扩散动力学，同时也关注其非相互作用紧束缚极限以及SYK模型。 我们通过量子轨迹描述该过程，并沿着轨迹评估非稳定化性（也称为“魔法”），通过稳定化Rényi熵（SRE）进行量化。 为此，我们引入了一种数值方法来计算SRE，比暴力方法更高效，该方法基于在经典自旋构型的计算基下对限制在子空间中的状态进行展开。 在没有测量的情况下，我们发现SYK模型是唯一一个时间平均SRE达到完全随机态界限且与系统大小相关的理论预测对于量子混沌系统有良好描述的模型。 在存在测量的情况下，我们数值发现渐近SRE与环境耦合强度的关系可以通过广义洛伦兹函数很好地拟合。 拟合参数与系统大小的标度表明，在所有考虑的情况下，渐近SRE随大小线性增加。 显示英文摘要

摘要： We consider the quantum-state-diffusion dynamics of the staggered XXZ chain, also focusing on its noninteracting tight-binding limit, and of the SYK model. We describe the process through quantum trajectories and evaluate the nonstabilizerness (also known as ``magic'') along the trajectories, quantified through the stabilizer R\'enyi entropy (SRE). To do that we introduce a numerical method to evaluate SRE, more efficient than the brute-force one, based on the expansion of the state restricted to a subspace in the computational basis of the classical spin configurations. In the absence of measurements, we find that the SYK model is the only one where the time-averaged SRE saturates the fully-random state bound and has a scaling with the system size that is well described by the theoretical prediction for quantum chaotic systems. In the presence of measurements, we numerically find that the asymptotic SRE versus the coupling strength to the environment is well fitted by a generalized Lorentzian function. The scaling of the fitting parameters with the system size suggests that the asymptotic SRE linearly increases with the size in all the considered cases.