Three Approaches to the Quantitative Definition of Information in an Individual Pure Quantum State

Abstract

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 approximated from above. With high probability a quantum object is incompressible. There are two alternative approaches possible: to define the complexity as the length of the shortest qubit program that effectively describes the object, and to use classical descriptions with computable real parameters.

arXiv comment8 pages, LaTeX

Cited by in corpus (3)

• Quantum Kolmogorov Complexity Based on Classical Descriptions
• The information-theoretical viewpoint on the physical complexity of classical and quantum objects and their dynamical evolution
• Classification of the automorphisms of the noncommutative torus among the (chaotic and non-chaotic) shallow ones and the non-chaotic complex ones