Mathematical foundations of quantum information: Measurement and foundations
Abstract
The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum measurement theory based on completely positive map-valued measures, a universally valid new formulation of the uncertainty principle for error and disturbance in quantum measurements, the Wigner-Araki-Yanase limit of quantum measurements, the accuracy limit of quantum computing based on conservation laws, and a quantum interpretation based on quantum set theory.
Keywords
Cite
@article{arxiv.1201.5334,
title = {Mathematical foundations of quantum information: Measurement and foundations},
author = {Masanao Ozawa},
journal= {arXiv preprint arXiv:1201.5334},
year = {2014}
}
Comments
30 pages, Latex. To appear in the December 2014 issue of "Sugaku Expositions," American Mathematical Society. Originally published in Japanese as: Masanao Ozawa, Mathematical Foundations of Quantum Information (in Japanese), Sugaku 61 (2), 113--132 (2009); doi:10.11429/sugaku.0612113. Based on a Plenary Address at the 2008 Mathematical Society of Japan Autumn Meeting, Tokyo, September 25, 2008