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Inverting the central limit theorem

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Loosely speaking, the Central Limit Theorem states that the sum of N independently distributed n-tuples of real variables tends to a multivariate gaussian distribution for large N; in a sense, the CLT maps microscopic distributions to macroscopic probability densities. Here we propose to invert this mapping: given a set of n correlated experimental gaussian variables, we try to infer information about the (discrete) spectrum of the microscopic variables whose sum generated such macroscopic statistics. The techniques developed along the research are applied to prove that the classical description of certain macroscopic optical experiments is infinitely more complex than the quantum one.

This talk is part of the CQIF Seminar series.

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