In analogy of classical Kolmogorov complexity we define a notion of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides with the new quantum Kolmogorov complexity restricted to the classical domain. Quantum Kolmogorov complexity is upper bounded and can be effectively approxim...

In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides with the new quantum Kolmogorov complexity restricted to the classical domain. Quantum Kolmogorov complexity is upper bounded and can be effectively approxi...