## What is/are Randomized Measurements?

Randomized Measurements - Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements by fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one.^{[1]}First, we find the optimal criteria for different forms of multiparticle entanglement in three-qubit systems using the second moments of randomized measurements.

^{[2]}The fast compressed sensing (CS) reconstruction for natural image processing aims to infer the original pixel vector from randomized measurements as correctly as possible.

^{[3]}In this context, it has been shown that locally randomized measurements on a multiparticle quantum system can be used to obtain valuable information on the so-called moments of the partially transposed quantum state.

^{[4]}Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wave function.

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