Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. This can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments. Crucially, unlike symmetry-blind randomized measurement protocols, these latter tasks can be performed without relearning symmetries via full reconstruction of the density matrix.

中文翻译：

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晶格规范理论的随机测量协议

随机测量协议，包括经典阴影、纠缠断层扫描和随机基准测试，是估计可观测值、执行状态断层扫描或提取量子态纠缠特性的强大技术。虽然解开量子态的复杂结构通常很困难并且需要大量资源，但自然界中的量子系统通常受到对称性的严格约束。我们提出的对称意识随机测量方案可以利用这一点，与对称盲随机化相比具有明显的优势，例如降低测量成本，在实验中实现基于对称性的误差减轻，允许（晶格）规范理论纠缠结构的差异化测量，并且有可能在现有和近期实验中验证拓扑有序状态。至关重要的是，与对称盲随机测量协议不同，后面这些任务可以在不通过密度矩阵的完全重建重新学习对称性的情况下执行。