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Kolmogorov Complexity (interpreted in terms of shortest program computing a string) and Shannon Entropy are quite similar. Since there is a quantum entropy is it reasonable to ask if there is quantum ...

Consider a collection of increasing positive integers $\{a_i\}_{i=1}^m$ and the distribution $p_i=\frac{a_i}{\sum_{i=1}^ma_i}$. Let entropy of $\mathcal{A}=\{a_i\}_{i=1}^m$ be given by $$H(\mathcal{A}...