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

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

1999-07-09

arxiv.org/abs/quant-ph/9907035v3

In: Proc. 15th IEEE Conf. Computational Complexity, 2000

Physics

Quantum Physics

8 pages, LaTeX

Scientific paper

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.

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