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Non-commutative optimization problems with differential constraints
Mateus Araújo, Andrew J. P. Garner, Miguel Navascues
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all st…
Introducing Moment: A toolkit for semi-definite programming with moment matrices
Andrew J. P. Garner, Mateus Araújo
Non-commutative polynomial optimization is a powerful technique with numerous applications in quantum nonlocality, quantum key distribution, causal inference, many-body physics, am…
First-order optimality conditions for non-commutative optimization problems
Mateus Araújo, Igor Klep, Andrew J. P. Garner +2
We consider the problem of optimizing the state average of a polynomial of non-commuting variables, over all states and operators satisfying a number of polynomial constraints, and…