On the Algorithmic Information Between Probabilities

03/13/2023

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by   Samuel Epstein, et al.

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We extend algorithmic conservation inequalities to probability measures. The amount of self information of a probability measure cannot increase when submitted to randomized processing. This includes (potentially non-computable) measures over finite sequences, infinite sequences, and T_0, second countable topologies. One example is the convolution of signals over real numbers with probability kernels. Thus the smoothing of any signal due We show that given a quantum measurement, for an overwhelming majority of pure states, no meaningful information is produced.