Robust performance of control schemes for open quantum systems is investigated under classical uncertainties in the generators of the dynamics and nonclassical uncertainties due to decoherence and initial state preparation errors. A formalism is developed to measure performance based on the transmission of a dynamic perturbation or initial state preparation error to the quantum state error. This makes it possible to apply tools from classical robust control, such as structured singular value analysis. A difficulty arising from the singularity of the closed-loop Bloch equations for the quantum state is overcome by introducing the #-inversion lemma, a specialized version of the matrix inversion lemma. Under some conditions, this guarantees continuity of the structured singular value at $s = 0$ . Additional difficulties occur when symmetry gives rise to multiple open-loop poles, which under symmetry-breaking unfold into single eigenvalues. The concepts are applied to systems subject to pure decoherence and a general dissipative system example of two qubits in a leaky cavity under laser driving fields and spontaneous emission. A nonclassical performance index, steady-state entanglement quantified by the concurrence, a nonlinear function of the system state, is introduced. Simulations confirm a conflict between entanglement, its log-sensitivity and stability margin under decoherence.

中文翻译：

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开放量子系统的稳健控制性能

在动力学生成器的经典不确定性和退相干和初始状态准备误差引起的非经典不确定性下，研究了开放量子系统控制方案的鲁棒性能。基于动态扰动或初始状态准备误差到量子态误差的传输，开发了一种形式来测量性能。这使得应用来自经典鲁棒控制的工具成为可能，例如结构化奇异值分析。通过引入 #-inversion 引理（矩阵反转引理的一个特殊版本）克服了由量子态闭环 Bloch 方程的奇异性引起的困难。在某些条件下，这保证了结构化奇异值在$s = 0$ . 当对称性产生多个开环极点时，会出现额外的困难，这些极点在对称性破坏下展开为单个特征值。这些概念适用于受纯退相干影响的系统和在激光驱动场和自发发射下泄漏腔中的两个量子位的一般耗散系统示例。介绍了一种非经典性能指标，即由并发量化的稳态纠缠，它是系统状态的非线性函数。模拟证实了纠缠、其对数灵敏度和退相干下的稳定性裕度之间的冲突。