State polynomials: positivity, optimization and nonlinear Bell inequalities

This paper introduces state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. A state analog of Artin’s solution to Hilbert’s 17th problem is proved showing that state polynomials, positive over all matrices and matricial states, are sums of squares with d...

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Bibliographic Details
Published in:	Mathematical programming Vol. 207; no. 1-2; pp. 645 - 691
Main Authors:	Klep, Igor, Magron, Victor, Volčič, Jurij, Wang, Jie
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024 Springer Springer Verlag
Subjects:	Algebra Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Functional Analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization and Control Physics Quantum Physics Theoretical Semidefinite programming Hilbert’s 17th problem State optimization State polynomial Network scenario 13J30 81-08 46L30 46N50 Noncommutative polynomial Polynomial Bell inequality Positivstellensatz 90C22
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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