28 citations · 197 across the 30 of their papers we have counts for
37 papers
Hereditary NC Polynomials & Positivity Domains
Abdellah Islam, Jurij Volčič, Hugo J. Woerdeman
Noncommutative polynomials, elements of the free algebra generated by several noncommuting variables , are of importance in noncommutative algebra, fre…
Addendum to "Factoring non-negative operator valued trigonometric polynomials in two variables"
Michael A. Dritschel, Igor Klep, Scott McCullough +1
Factorization for positive semidefinite matrix-valued polynomials over a nonsingular compact affine real surface is established. Corollaries include Fejér-Riesz factorization for b…
Global structure behind pointwise equivalences of noncommutative polynomials
Eli Shamovich, Jurij Volčič
This paper investigates the interplay between local and global equivalences on noncommutative polynomials, the elements of the free algebra. When the latter are viewed as functions…
Quantum Max d-Cut via qudit swap operators
Igor Klep, Tea Štrekelj, Jurij Volčič
Quantum Max Cut (QMC) problem for systems of qubits is an example of a 2-local Hamiltonian problem, and a prominent paradigm in computational complexity theory. This paper investig…
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…
Constant-sized self-tests for maximally entangled states and single projective measurements
Jurij Volčič
Self-testing is a powerful certification of quantum systems relying on measured, classical statistics. This paper considers self-testing in bipartite Bell scenarios with small numb…
Sums of squares certificates for polynomial moment inequalities
Igor Klep, Victor Magron, Jurij Volčič
This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their posi…
All Real Projective Measurements Can be Self-tested
Ranyiliu Chen, Laura Mančinska, Jurij Volčič
Self-testing is the strongest form of quantum functionality verification which allows a classical user to deduce the quantum state and measurements used to produce measurement stat…
State polynomials: positivity, optimization and nonlinear Bell inequalities
Igor Klep, Victor Magron, Jurij Volčič +1
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 probl…
Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem
Igor Klep, Claus Scheiderer, Jurij Volčič
A noncommutative (nc) polynomial is called (globally) trace-positive if its evaluation at any tuple of operators in a tracial von Neumann algebra has nonnegative trace. Such polyno…
Ranks of linear matrix pencils separate simultaneous similarity orbits
Harm Derksen, Igor Klep, Visu Makam +1
This paper solves the two-sided version and provides a counterexample to the general version of the 2003 conjecture by Hadwin and Larson. Consider evaluations of linear matrix penc…
Dimension-free entanglement detection in multipartite Werner states
Felix Huber, Igor Klep, Victor Magron +1
Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. This paper gives a complete characterization of their ent…
Norms on complex matrices induced by complete homogeneous symmetric polynomials
Konrad Aguilar, Ángel Chávez, Stephan Ramon Garcia +1
We introduce a remarkable new family of norms on the space of complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their c…
Hilbert's 17th problem in free skew fields
Jurij Volčič
This paper solves the rational noncommutative analog of Hilbert's 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of hermitian matrices i…
Positive univariate trace polynomials
Igor Klep, James Eldred Pascoe, Jurij Volčič
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(x^j). Such an expression can be naturally evaluated on matrices, where the trace symbols a…
Optimization over trace polynomials
Igor Klep, Victor Magron, Jurij Volčič
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 produ…
Noncommutative rational functions invariant under the action of a finite solvable group
Igor Klep, James Eldred Pascoe, Gregor Podlogar +1
This paper describes the structure of invariant skew fields for linear actions of finite solvable groups on free skew fields in generators. These invariant skew fields are alwa…
Free Bertini's theorem and applications
Jurij Volčič
The simplest version of Bertini's irreducibility theorem states that the generic fiber of a non-composite polynomial function is an irreducible hypersurface. The main result of thi…
Plurisubharmonic Noncommutative Rational Functions
Harry Dym, J. William Helton, Igor Klep +2
A noncommutative (nc) function in is called plurisubharmonic (plush) if its nc complex Hessian takes only positive semidefinite values on an nc neig…
Factorization of noncommutative polynomials and Nullstellensätze for the free algebra
J. William Helton, Igor Klep, Jurij Volčič
This article gives a class of Nullstellensätze for noncommutative polynomials. The singularity set of a noncommutative polynomial is , where $…