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Article Dans Une Revue Journal of Mathematical Physics Année : 2023

Polytope compatibility—From quantum measurements to magic squares


Several central problems in quantum information theory (such as measurement compatibility and quantum steering) can be rephrased as membership in the minimal matrix convex set corresponding to special polytopes (such as the hypercube or its dual). In this article, we generalize this idea and introduce the notion of polytope compatibility, by considering arbitrary polytopes. We find that semiclassical magic squares correspond to Birkhoff polytope compatibility. In general, we prove that polytope compatibility is in one-to-one correspondence with measurement compatibility, when the measurements have some elements in common and the post-processing of the joint measurement is restricted. Finally, we consider how much tuples operators with appropriate joint numerical range have to be scaled in the worst case in order to become polytope compatible and give both analytical sufficient conditions and numerical ones based on linear programming.
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Dates et versions

hal-04082901 , version 1 (26-04-2023)



Andreas Bluhm, Ion Nechita, Simon Schmidt. Polytope compatibility—From quantum measurements to magic squares: from quantum measurements to magic squares. Journal of Mathematical Physics, 2023, 64 (12), pp.122201. ⟨10.1063/5.0165424⟩. ⟨hal-04082901⟩
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