Complete characterization of quantum correlations by randomized measurements

Abstract

The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as quantum key distribution or quantum teleportation, but characterizing these correlations in an experimental setting is a formidable task, especially in scenarios where no shared reference frames are available. By definition, quantum correlations are reference-frame independent, i.e., invariant under local transformations; this physically motivated invariance implies, however, a dedicated mathematical structure and, therefore, constitutes a roadblock for an efficient analysis of these correlations in experiments. Here we provide a method to directly measure any locally invariant property of quantum states using locally randomized measurements, and we present a detailed toolbox to analyze these correlations for two quantum bits. We implement these methods experimentally using pairs of entangled photons, characterizing their usefulness for quantum teleportation and their potential to display quantum nonlocality in its simplest form. Our results can be applied to various quantum computing platforms, allowing simple analysis of correlations between arbitrary distant qubits in the architecture.

5 pages + 15 pages of appendix, 4 figures

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• On the connection between least squares, regularization, and classical shadows
• Detection of entanglement via moments of positive maps
• Corrupted sensing quantum state tomography
• Detecting high-dimensional entanglement by randomized product projections
• Hamiltonian Learning via Inverse Physics-Informed Neural Networks
• Classification of quantum states of light using random measurements through a multimode fiber
• Dephasing-Induced Distribution of Entanglement in Tripartite Quantum Systems
• Reference-frame-independent quantum metrology
• Bargmann-invariant framework for local unitary equivalence and entanglement