We propose and experimentally demonstrate a universal quantum averaging process implementing the harmonic mean of quadrature variances. The harmonic mean protocol can be used to efficiently stabilize a set of fragile squeezed light sources with statistically fluctuating noise levels. The averaged variances are prepared probabilistically by means of linear optical interference and measurement induced conditioning. We verify that the implemented harmonic mean outperforms the standard arithmetic mean strategy. The effect of quantum averaging is experimentally tested both for uncorrelated and partially correlated noise sources with sub-Poissonian shot noise or super-Poissonian shot noise characteristics.
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