Analysing quantum systems with randomised measurements

Abstract

Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum computing when dealing with noisy environments, and allow the estimation of properties of complex quantum systems in an easy and efficient manner. In this review, we present the advancements made in utilising randomised measurements in various scenarios of quantum information science. We describe how to detect and characterise different forms of entanglement, including genuine multipartite entanglement and bound entanglement. Bell inequalities are discussed to be typically violated even with randomised measurements, especially for a growing number of particles and settings. Furthermore, we also present an overview on the estimation of non-linear functions of quantum states and shadow tomography from randomised measurements. Throughout the review, we complement the description of theoretical ideas by explaining key experiments.

review paper, 56 pages, 9 figures, P. Cieśliński and S. Imai contributed equally as co-first authors

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Cited by in corpus (23)

• Krylov shadow tomography: Efficient estimation of quantum Fisher information
• Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps
• Experimental certification of high-dimensional entanglement with randomized measurements
• Metrological usefulness of entanglement and nonlinear Hamiltonians
• Approximate inverse measurement channel for shallow shadows
• Real randomized measurements for analyzing properties of quantum states
• Detecting genuine multipartite entanglement using moments of positive maps
• Entanglement dynamics and Page curves in random permutation circuits
• Geometry of two-body correlations in three-qubit states
• Protecting entanglement witnesses with randomized measurements
• Detecting high-dimensional entanglement by randomized product projections
• Variational-toolbox-based separability detection of multiqubit states
• Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
• How Likely Are You to Observe Non-locality with Imperfect Detection Efficiency and Random Measurement Settings?
• Absolutely maximally entangled pure states of multipartite quantum systems
• Learning mixed quantum states in large-scale experiments
• Inter-qubit correlation dynamics driven by mutual interactions
• Multiqubit monogamy relations beyond shadow inequalities
• Optimal randomized measurements for a family of non-linear quantum properties
• Scalable protocol to coherence estimation from scarce data: Theory and experiment
• Certifying entanglement dimensionality by $k$-reduction moments
• Reference-frame-independent quantum metrology
• Classification of quantum states of light using random measurements through a multimode fiber