Quantum Kolmogorov Complexity Based on Classical Descriptions
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 sub-additive. We discuss some relations with ``no-cloning'' and ``approximate cloning'' properties.
Cite
@article{arxiv.quant-ph/0102108,
title = {Quantum Kolmogorov Complexity Based on Classical Descriptions},
author = {Paul M. B. Vitanyi},
journal= {arXiv preprint arXiv:quant-ph/0102108},
year = {2016}
}
Comments
17 pages, LaTeX, final and extended version of quant-ph/9907035, with corrections to the published journal version (the two displayed equations in the right-hand column on page 2466 had the left-hand sides of the displayed formulas erroneously interchanged)