通过几次局域测量检测度量学上有用的非对称性和纠缠
Detecting metrologically useful asymmetry and entanglement by a few local measurements
摘要：
量子系统的重要性质不能直接测量，但它们可以通过系统在受控扰动下的变化速度来揭示。特别是，不对称性和纠缠可以通过重建量子系统的状态来验证。然而，这通常需要实验和计算资源，这些资源随着系统规模呈指数级增加。在这里，我们展示了如何检测计量有用的不对称性和纠缠的有限数量的测量。这是通过研究它们如何影响系统在幺正变换下的演化速度来实现的。我们表明，多量子比特系统的速度可以通过测量一组局部可观测量来评估，相对于状态层析成像提供指数优势。事实上，所提出的方法既不需要对所有组成子系统进行的状态和参数编码哈密顿量的知识，也不需要对所有组成子系统进行全局测量。我们在全光实验中实现了该检测方案。
英文摘要：
Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the state of a quantum system. Yet, this usually requires experimental and computational resources which increase exponentially with the system size. Here we show how to detect metrologically useful asymmetry and entanglement by a limited number of measurements. This is achieved by studying how they affect the speed of evolution of a system under a unitary transformation. We show that the speed of multiqubit systems can be evaluated by measuring a set of local observables, providing exponential advantage with respect to state tomography. Indeed, the presented method requires neither the knowledge of the state and the parameter-encoding Hamiltonian nor global measurements performed on all the constituent subsystems. We implement the detection scheme in an all-optical experiment.
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