Characterizing correlation within multipartite quantum systems via local randomized measurements

Abstract

Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics, plays an important role in understanding multipartite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be non-linear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography and obviates the need to coherently interfere multiple copies of a given state. Thus, we provide a tool for proving multipartite correlations that can be applied to near-term quantum devices.

28 pages, 8 figures. Comments are welcome

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• Collective randomized measurements in quantum information processing
• Quantum separability criteria based on realignment moments
• Quantifying multiparticle entanglement with randomized measurements
• Robust ultra-shallow shadows
• Local measurement strategies for multipartite entanglement quantification
• Generating quantum dissonance via local operations
• Detecting high-dimensional entanglement by randomized product projections
• Investigating the effect of noise channels on the quality of unitary t-designs