通过随机测量认证量子时间关联：理论与实验
Certifying Quantum Temporal Correlation via Randomized Measurements: Theory and Experiment
AI总结：
本研究提出一种基于随机测量和虚拟制备伪密度矩阵的高效协议，用于认证量子时间关联，仅需恒定测量基，并在核磁共振平台上实验验证，结果与理论一致。
摘要：
我们考虑使用伪密度矩阵（PDM）来认证时间量子关联，PDM是密度矩阵在时间域上的扩展，其中负特征值是时间关联的关键指标。检测这些关联的传统方法依赖于PDM层析成像，这通常涉及过多的冗余信息并需要指数级资源。在本工作中，我们开发了一种高效的时间关联检测协议，通过在单个时间片内虚拟制备PDM，并使用随机测量估计其二阶矩。通过样本复杂度分析，我们证明我们的协议仅需要恒定数量的测量基，这使得它特别适用于利用系综平均测量的系统，因为无论量子比特数量如何，它都保持恒定的运行时复杂度。我们在核磁共振平台上实验验证了我们的协议，这是一个典型的热力学量子系统，实验结果与理论预测紧密吻合，确认了我们协议的有效性。
英文摘要：
We consider the certification of temporal quantum correlations using the pseudo-density matrix (PDM), an extension of the density matrix to the time domain, where negative eigenvalues are key indicators of temporal correlations. Conventional methods for detecting these correlations rely on PDM tomography, which often involves excessive redundant information and requires exponential resources. In this work, we develop an efficient protocol for temporal correlation detection by virtually preparing the PDM within a single time slice and estimating its second-order moments using randomized measurements. Through sample complexity analysis, we demonstrate that our protocol requires only a constant number of measurement bases, making it particularly advantageous for systems utilizing ensemble average measurements, as it maintains constant runtime complexity regardless of the number of qubits. We experimentally validate our protocol on a nuclear magnetic resonance platform, a typical thermodynamic quantum system, where the experimental results closely align with theoretical predictions, confirming the effectiveness of our protocol.
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