Characterizing multipartite entanglement with moments of random correlations

Abstract

The experimental detection of multipartite entanglement usually requires a number of appropriately chosen local quantum measurements which are aligned with respect to a previously shared common reference frame. The latter, however, can be a challenging prerequisite e.g. for satellite-based photonic quantum communication, making the development of alternative detection strategies desirable. One possibility for avoiding the distribution of classical reference frames is to perform a number of local measurements with settings distributed uniformly at random. In this work we follow such a treatment and show that an improved detection and characterization of multipartite entanglement is possible by combining statistical moments of different order. To do so, we make use of designs which are pseudo-random processes allowing to link the present entanglement criteria to ordinary reference frame independent ones. The strengths of our methods are illustrated in various cases starting with two qubits and followed by more involved multipartite scenarios.

15 pages, 5 figures, v2: revised Sec. "Moments from designs"

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• Symmetry-resolved dynamical purification in synthetic quantum matter
• Quantum Fisher information from randomized measurements
• Probing many-body quantum chaos with quantum simulators
• Optimal Entanglement Certification from Moments of the Partial Transpose
• Quantum scrambling with classical shadows
• Bound entanglement from randomized measurements
• Multipartite Entanglement Analysis From Random Correlations
• Deep learning of quantum entanglement from incomplete measurements
• Importance sampling of randomized measurements for probing entanglement
• Characterizing entanglement dimensionality from randomized measurements
• Work fluctuations and entanglement in quantum batteries
• Analysing quantum systems with randomised measurements
• Entanglement characterization using quantum designs
• Entropic uncertainty relations from quantum designs
• Performance analysis of multi-shot shadow estimation
• Complete characterization of quantum correlations by randomized measurements
• Characterizing quantum states via sector lengths
• Characterizing correlation within multipartite quantum systems via local randomized measurements
• A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator
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• Quantum verification and estimation with few copies
• Probing the geometry of correlation matrices with randomized measurements
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations
• Entanglement estimation in tensor network states via sampling
• Designs via Free Probability
• Enhanced estimation of quantum properties with common randomized measurements
• Collective randomized measurements in quantum information processing
• Randomness-enhanced expressivity of quantum neural networks
• Quantum separability criteria based on realignment moments
• Many-body entropies and entanglement from polynomially-many local measurements
• Rényi formulation of uncertainty relations for POVMs assigned to a quantum design
• Characterizing four-body indistinguishability via symmetries
• A Moment for Random Measurements
• Experimental certification of high-dimensional entanglement with randomized measurements
• Partial Transpose Moments, Principal Minors and Entanglement Detection
• Quantifying multiparticle entanglement with randomized measurements
• Approximate inverse measurement channel for shallow shadows
• Operational detection of entanglement via quantum designs
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