We introduce quantum-K ($QK$), a measure of the descriptive complexity density matrices using classical prefix-free Turing machines and show that initial segments weak Solovay random quantum Schnorr states are incompressible in sense $QK$. Many properties enjoyed by Kolmogorov ($K$) have analogous versions for $QK$; notably counting condition. Several connections between randomness $K$, includi...

We continue an investigation into resource-bounded Kolmogorov complexity [ABK06], which highlights the close connections between circuit complexity and Levin’s time-bounded Kolmogorov complexity measure Kt (and other measures with a similar flavor), and also exploits derandomization techniques to provide new insights regarding Kolmogorov complexity. The Kolmogorov measures that have been introd...