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，对一般量子态的Kolmogorov复杂性进行了研究。我们扩展了dcq-TM模型以涵盖混合态输入与输出，并将dcq可计算状态定义为能够被dcq-TM近似逼近的状态。进一步，我们引入了量子态的（条件）Kolmogorov复杂性，并利用该概念从三个特定维度探讨量子态中包含的算法信息：将量子态信息与其经典表示（实数数组）中的信息进行比较；在算法复杂性框架下探索量子态复制的局限性；以及研究量子系统中关联的复杂性，最终提出一种满足对称性信息性质的、具有关联感知的算法互信息定义。