Tomita-Takesaki Modular Theory vs. Quantum Information Theory
Mathematical Physics
2016-07-15 v2 math.MP
Operator Algebras
Quantum Physics
Abstract
In this paper, we will try to find out the relationship between separating and cyclic vectors in the theory of von Neumann algebra and entangled states in the theory of quantum information. The corresponding physical interpretation is presented as well.
Keywords
Cite
@article{arxiv.1301.1836,
title = {Tomita-Takesaki Modular Theory vs. Quantum Information Theory},
author = {Lin Zhang and Junde Wu},
journal= {arXiv preprint arXiv:1301.1836},
year = {2016}
}
Comments
v1: 29 pages, LaTeX, this review article is not completed and to be continued. The first goal of writing this topic is just to understand the notion of cyclic and separating vector in von Neumann algebra. The second goal is to apply Tomita-Takesaki modular theory in Quantum Information Theory. All comments are welcome!. v2: 41 pages, LaTeX, no figure. Expansion of previous version. arXiv admin note: text overlap with arXiv:0802.1234, arXiv:0906.3980 by other authors