  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.
