A Moment for Random Measurements

Abstract

Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements. Although this approach might seem inefficient at first, sampling correlations in various random directions is a powerful tool to study properties which are invariant under local-unitary transformations. Based on random measurements, entanglement can be detected and characterized without a shared reference frame between the observers or even if local reference frames cannot be defined. This overview article discusses different methods using random measurements to detect genuine multipartite entanglement and to distinguish SLOCC classes. Furthermore, it reviews how measurement directions can efficiently be obtained based on spherical designs.

8 pages, 7 figures. Written as Perspective for Quantum Journal on Ketterer et al., Quantum 4, 325 (2020), arXiv:2004.08402

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Cited by in corpus (10)

• The randomized measurement toolbox
• Theoretical and Experimental Perspectives of Quantum Verification
• Bound entanglement from randomized measurements
• Analysing quantum systems with randomised measurements
• Complete characterization of quantum correlations by randomized measurements
• Statistically significant tests of multiparticle quantum correlations based on randomized measurements
• Correlation constraints and the Bloch geometry of two qubits
• Quantifying multiparticle entanglement with randomized measurements
• Classification of quantum states of light using random measurements through a multimode fiber
• Inter-qubit correlation dynamics driven by mutual interactions