On the comparison of volumes of quantum states
Quantum Physics
2010-07-09 v2 Information Theory
Mathematical Physics
Functional Analysis
math.IT
math.MP
Abstract
This paper aims to study the -volume of , an arbitrary subset of the set of density matrices. The -volume is a generalization of the Hilbert-Schmidt volume and the volume induced by partial trace. We obtain two-side estimates for the -volume of in terms of its Hilbert-Schmidt volume. The analogous estimates between the Bures volume and the -volume are also established. We employ our results to obtain bounds for the -volume of the sets of separable quantum states and of states with positive partial transpose (PPT). Hence, our asymptotic results provide answers for questions listed on page 9 in \cite{K. Zyczkowski1998} for large in the sense of -volume. \vskip 3mm PACS numbers: 02.40.Ft, 03.65.Db, 03.65.Ud, 03.67.Mn
Keywords
Cite
@article{arxiv.1003.0727,
title = {On the comparison of volumes of quantum states},
author = {Deping Ye},
journal= {arXiv preprint arXiv:1003.0727},
year = {2010}
}