On the Algorithmic Information Between Probabilities

Samuel Epstein

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arXiv · 2303.07296

On the Algorithmic Information Between Probabilities

Samuel Epstein

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Abstract

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.

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Samuel Epstein. 2023-03-13. On the Algorithmic Information Between Probabilities. https://arxiv.org/abs/2303.07296

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