28 citations · 197 across the 30 of their papers we have counts for
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Maximal device-independent randomness in every dimension
Máté Farkas, Jurij Volčič, Sigurd A. L. Storgaard +2
Random numbers are used in a wide range of sciences. In many applications, generating unpredictable private random numbers is indispensable. Device-independent quantum random numbe…
Linear matrix pencils and noncommutative convexity
Jurij Volčič
Hermitian linear matrix pencils are ubiquitous in control theory, operator systems, semidefinite optimization, and real algebraic geometry. This survey reviews the fundamental feat…
Dimension-free matricial Nullstellensätze for noncommutative polynomials
Jurij Volčič
Hilbert's Nullstellensatz is one of the most fundamental correspondences between algebra and geometry, and has inspired a plethora of noncommutative analogs. In last two decades, t…
Upper bound hierarchies for noncommutative polynomial optimization
Igor Klep, Victor Magron, Gaël Massé +1
This work focuses on minimizing the eigenvalue of a noncommutative polynomial subject to a finite number of noncommutative polynomial inequality constraints. Based on the Helton-Mc…
Matrix evaluations of noncommutative rational functions and Waring problems
Matej Brešar, Jurij Volčič
Let be a nonconstant noncommutative rational function in variables over an algebraically closed field of characteristic 0. We show that for large enough, there exis…