可调噪声强度下量子动力学的精确解析工具箱
Exact analytic toolbox for quantum dynamics with tunable noise strength
AI总结：
本研究提出一种可精确解析处理可调强度相干噪声下量子动力学的框架，以GUE为核心研究对象，推导了其谱形状因子、量子信道及方差的精确结果，揭示了GUE信道的非单调特性等特殊性质。
摘要：
我们提出了一个框架，可对受相干噪声影响的量子动力学进行精确解析处理。该噪声通过任意希尔伯特空间维度$N$下、取自随机矩阵系综的哈密顿量所主导的幺正演化来建模。我们开发的方法适用于所有具备旋转不变性的此类通用系综，但主要聚焦于高斯幺正系综（Gaussian unitary ensemble, GUE）。\n对“含噪”哈密顿量的系综求平均可产生一个有效量子信道，其性质可通过解析方式计算，且由相关系综的谱形状因子决定。我们精确计算了任意有限$N$下GUE的谱形状因子，以及对应的GUE量子信道及其方差。\n我们方法的核心优势包括：能够得到任意$N$下的精确解析结果，能够调节至无噪声极限（例如与Haar系综形成对比），以及能够解析获取方差之外的各阶矩。我们还指出了GUE信道的一些特殊性质，包括不同算符的系数随噪声强度变化的非单调性，以及即使在无限噪声强度下也无法达到Haar随机极限的特性。
英文摘要：
We introduce a framework that allows for the exact analytic treatment of quantum dynamics subject to coherent noise. The noise is modeled via unitary evolution under a Hamiltonian drawn from a random-matrix ensemble for arbitrary Hilbert-space dimension $N$. While the methods we develop apply to generic such ensembles with a notion of rotation invariance, we focus largely on the Gaussian unitary ensemble (GUE). Averaging over the ensemble of ''noisy'' Hamiltonians produces an effective quantum channel, the properties of which are analytically calculable and determined by the spectral form factors of the relevant ensemble. We compute spectral form factors of the GUE exactly for any finite $N$, along with the corresponding GUE quantum channel, and its variance. Key advantages of our approach include the ability to access exact analytic results for any $N$ and the ability to tune to the noise-free limit (in contrast, e.g., to the Haar ensemble), and analytic access to moments beyond the variance. We also highlight some unusual features of the GUE channel, including the nonmonotonicity of the coefficients of various operators as a function of noise strength and the failure to saturate the Haar-random limit, even with infinite noise strength.
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