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math.OA2023
Positivity is undecidable in tensor products of free algebras
Arthur Mehta, William Slofstra, Yuming Zhao
It is well known that an element of the algebra of noncommutative *-polynomials is positive in all *-representations if and only if it is a sum of squares. This provides an effecti…
quant-ph2023
New Approaches to Complexity via Quantum Graphs
Eric Culf, Arthur Mehta
Problems based on the structure of graphs -- for example finding cliques, independent sets, or colourings -- are of fundamental importance in classical complexity. Defining well-fo…