On the Algorithmic Information Between Probabilities

• URL: http://arxiv.org/abs/2303.07296v2
• Date: Wed, 11 Sep 2024 17:26:13 GMT
• Title: On the Algorithmic Information Between Probabilities
• Authors: Samuel Epstein,
• Abstract summary: We extend algorithmic conservation inequalities to probability measures. The amount of self information of a probability measure cannot increase when submitted to randomized processing. We show that given a quantum measurement, for an overwhelming majority of pure states, no meaningful information is produced.
• Score: 6.5268245109828005
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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