Quantifier elimination theory and maps which preserve semipositivity

被引：0
作者：
Grzegorz Pastuszak
Adam Skowyrski
Andrzej Jamiołkowski
机构：
[1] Nicolaus Copernicus University,Faculty of Mathematics and Computer Science
[2] Nicolaus Copernicus University,Faculty of Physics, Astronomy and Informatics
来源：
Quantum Information Processing | 2021年 / 20卷
关键词：
Hermitian superoperators; Positive maps; Quantifier elimination; Sturm’s theorem;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We give an algorithm determining whether a hermiticity-preserving superoperator is positive. In our approach we apply techniques of quantifier elimination theory for real numbers. Furthermore, we argue that quantifier elimination theory should play more significant role in quantum information theory and other areas as well.
引用
收藏
相关论文
共 33 条
[1]  
Alpin Yu(2000)Solving the two dimensional CIS problem by a rational algorithm Linear Algebra Appl. 312 115-123
[2]  
George A(2003)Rational procedures in the problem of common invariant subspaces of two matrices J. Math. Sci. 114 1757-1764
[3]  
Ikramov Kh(1988)Geometric reasoning with logic and algebra Artif. Intell. 31 37-60
[4]  
Alpin Yu(1988)On mechanical quantifier elimination for elementary algebra and geometry J. Symbolic Comput. 5 237-259
[5]  
Ikramov Kh(1989)On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines Bull. Am. Math. Soc. 21 1-46
[6]  
Arnon D(1975)Positive semidefinite biquadratic forms Linear Algebra Appl. 12 95-100
[7]  
Arnon DS(1996)Irreducible positive linear maps on operator algebras Proc. Am. Math. Soc. 124 3381-3390
[8]  
Mignotte M(1999)Common invariant subspaces of two matrices Linear Algebra Appl. 287 171-179
[9]  
Blum L(1983)Definability and fast quantifier elimination in algebraically closed fields Theoret. Comput. Sci. 24 239-277
[10]  
Shub M(1974)An effective method of investigation of positive maps on the set of positive definite operators Rep. Math. Phys. 5 415-424
1234