This work presents a study of Kolmogorov complexity for general quantum states from the perspective of deterministic-control quantum Turing Machines (dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and outputs, and define dcq-computable states as those that can be approximated by a dcq-TM. Moreover, we introduce (conditional) Kolmogorov complexity of quantum states and use it to study three particular aspects of the algorithmic information contained in a quantum state: a comparison of the information in a quantum state with that of its classical representation as an array of real numbers, an exploration of the limits of quantum state copying in the context of algorithmic complexity, and study of the complexity of correlations in quantum systems, resulting in a correlation-aware definition for algorithmic mutual information that satisfies symmetry of information property.

翻译：本文从确定性控制量子图灵机(dcq-TM)的视角，研究了一般量子态的Kolmogorov复杂性。我们将dcq-TM模型扩展至包含混合态输入与输出，并定义dcq可计算态为可通过dcq-TM逼近的量子态。进一步地，我们引入量子态的(条件)Kolmogorov复杂性，并利用该概念研究量子态中算法信息的三个特定方面：比较量子态与其经典实数数组表示所包含的信息量、探索算法复杂性框架下量子态复制的极限，以及分析量子系统中的关联复杂性。基于此，我们提出了一种满足对称信息特性的关联感知算法互信息定义。