Optimization Over Trace Polynomials

Motivated by recent progress in quantum information theory, this article aims at optimizing trace polynomials, i.e., polynomials in noncommuting variables and traces of their products. A novel Positivstellensatz certifying positivity of trace polynomials subject to trace constraints is presented, an...

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Bibliographic Details
Published in:	Annales Henri Poincaré Vol. 23; no. 1; pp. 67 - 100
Main Authors:	Klep, Igor, Magron, Victor, Volčič, Jurij
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.01.2022 Springer Nature B.V Springer Verlag
Subjects:	Bell's inequality Classical and Quantum Gravitation Convergence Dynamical Systems and Ergodic Theory Elementary Particles Functional Analysis Information theory Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical Physics Mathematics Operators (mathematics) Optimization Optimization and Control Physics Physics and Astronomy Polynomials Quantum Field Theory Quantum phenomena Quantum Physics Relativity Theory Theoretical 81-08 (Pure) trace polynomial 46N50 Semidefinite programming Von Neumann algebra Noncommutative polynomial Trace optimization Positivstellensatz 90C22 Semialgebraic set 47N10 13J30
ISSN:	1424-0637, 1424-0661
Online Access:	Get full text
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