We extend the deterministic-control quantum Turing machine (dcq-TM) model to incorporate mixed state inputs and outputs. Moreover, we define dcq-computable states as those that can be accurately approximated by a dcq-TM, and we introduce (conditional) Kolmogorov complexity of quantum states. We show that this notion is machine independent and that the set of dcq-computable states coincides with states having computable classical representations. Furthermore, we prove an algorithmic information version of the no-cloning theorem stating that cloning most quantum states is as difficult as creating them. Finally, we also propose a correlation-aware definition for algorithmic mutual information and shown that it satisfies symmetry of information property.

翻译：我们将确定性控制量子图灵机（dcq-TM）模型扩展到包含混合态输入与输出。此外，我们将dcq可计算状态定义为能被dcq-TM精确逼近的状态，并引入量子状态的（条件）科尔莫戈罗夫复杂度。我们证明这一概念与机器无关，且dcq可计算状态集合等价于具有可计算经典表示的状态集合。更进一步，我们给出一个关于量子不可克隆定理的算法信息版本，该版本表明克隆大多数量子态的难度等同于创造这些态。最后，我们提出一个面向关联的算法互信息定义，并证明其满足信息对称性。