Quantum Kolmogorov complexity based on classical descriptions

Author

Vitányi, Paul M B

Author_Institution

Centrum voor Wiskunde en Inf., Amsterdam, Netherlands

Volume

47

Issue

6

fYear

2001

fDate

9/1/2001 12:00:00 AM

Firstpage

2464

Lastpage

2479

Abstract

We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity coincides with the classical Kolmogorov complexity on the classical domain. Quantum Kolmogorov complexity is upper-bounded and can be effectively approximated from above under certain conditions. With high probability, a quantum object is incompressible. Upper and lower bounds of the quantum complexity of multiple copies of individual pure quantum states are derived and may shed some light on the no-cloning properties of quantum states. In the quantum situation complexity is not subadditive. We discuss some relations with “no-cloning” and “approximate cloning” properties

Keywords

Turing machines; computational complexity; information theory; quantum computing; algorithmic information; approximate cloning; classical Kolmogorov complexity; classical descriptions; lower bounds; no-cloning properties; pure quantum state; quantum Kolmogorov complexity; quantum complexity; quantum object; quantum situation complexity; upper-bound; Algorithm design and analysis; Cloning; Combinatorial mathematics; Computational complexity; Information theory; Pattern analysis; Pattern recognition; Quantum computing; Quantum mechanics; Turing machines;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.945258

Filename

945258