Researchers have established the precise threshold for using replicas in quantum state estimation. They proved that for estimating nonlinear moments of quantum states, a specific number of replicas, denoted as \lceil t/2\rceil, is the exact boundary between polynomial-sample estimation and a dimension-growing complexity barrier. This finding holds for both pure moments and a wider range of observable-weighted moments, indicating that coherent replicas are a discrete resource for nonlinear quantum-state estimation. AI
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RANK_REASON This is a research paper published on arXiv detailing theoretical findings in quantum physics.