Quantifier elimination theory and maps which preserve semipositivity

被引：0

作者：

Pastuszak, Grzegorz ^{[1
]}

Skowyrski, Adam ^{[1
]}

Jamiolkowski, Andrzej ^{[2
]}

机构：

[1] Nicolaus Copernicus Univ, Fac Math & Comp Sci, Torun, Poland

[2] Nicolaus Copernicus Univ, Fac Phys Astron & Informat, Torun, Poland

来源：

QUANTUM INFORMATION PROCESSING | 2021年 / 20卷 / 03期

关键词：

Hermitian superoperators; Positive maps; Quantifier elimination; Sturm's theorem; COMMON INVARIANT SUBSPACES; COMPUTATIONAL-COMPLEXITY; DECISION PROBLEM; 1ST-ORDER THEORY; PRELIMINARIES; CRITERION; GEOMETRY; REALS;

D O I：

10.1007/s11128-021-03060-w

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

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

页数：14

共 50 条

[31] Linear quantifier elimination
Nipkow, Tobias
AUTOMATED REASONING, PROCEEDINGS, 2008, 5195 : 18 - 33
[32] Robust nonlinear feedback design via quantifier elimination theory
Dorato, P
Yang, W
Famularo, D
ROBUST CONTROL DESIGN (ROCODN'97): A PROCEEDINGS VOLUME FROM THE IFAC SYMPOSIUM, 1997, : 51 - 54
[33] Variant quantifier elimination
Hong, Hoon
El Din, Mohab Safey
JOURNAL OF SYMBOLIC COMPUTATION, 2012, 47 (07) : 883 - 901
[34] QUANTIFIER ELIMINATION IN SHEAVES
BOFFA, M
CHERLIN, G
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1980, 290 (08): : 355 - 357
[35] Quantifier elimination for quartics
Yang, Lu
Xia, Bican
ARTIFICIAL INTELLIGENCE AND SYMBOLIC COMPUTATION, PROCEEDINGS, 2006, 4120 : 131 - 145
[36] QUANTIFIER ELIMINATION AND NEARFIELDS
SCHULZ, K
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 1988, 58 : 169 - 174
[37] On holomorphic maps between Riemann surfaces which preserve BMO
Gotoh, Y
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1995, 35 (02): : 299 - 324
[38] Linear Quantifier Elimination
Nipkow, Tobias
JOURNAL OF AUTOMATED REASONING, 2010, 45 (02) : 189 - 212
[39] Tree-depth, quantifier elimination, and quantifier rank
Chen, Yijia
Flum, Joerg
LICS'18: PROCEEDINGS OF THE 33RD ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, 2018, : 225 - 234
[40] Quantifier elimination for the theory of algebraically closed valued fields with analytic structure
Celikler, Yahn R.
MATHEMATICAL LOGIC QUARTERLY, 2007, 53 (03) : 237 - 246

← 1 2 3 4 5 →