Due to M\"{u}ller's theorem, the Kolmogorov complexity of a string was shown to be equal to its quantum Kolmogorov complexity. Thus there are no benefits to using quantum mechanics to compress classical information. The quantitative amount of information in classical sources is invariant to the physical model used. These consequences make this theorem arguably the most important result in the intersection of algorithmic information theory and physics. The original proof is quite extensive. This paper contains two simple proofs of this theorem. This paper also contains new bounds for quantum Kolmogorov complexity with error.

翻译：根据穆勒定理，字符串的柯尔莫哥洛夫复杂度被证明等于其量子柯尔莫哥洛夫复杂度。因此，利用量子力学压缩经典信息并无优势。经典信源的信息量不随所用物理模型改变。这些推论使得该定理堪称算法信息论与物理学交叉领域最重要的成果。原始证明相当冗长。本文提出了该定理的两个简洁证明，同时给出了含误差量子柯尔莫哥洛夫复杂度的新界。