University of Cambridge > Talks.cam > CQIF Seminar > Compatibility of quantum measurements and inclusion constants for free spectrahedra

Compatibility of quantum measurements and inclusion constants for free spectrahedra

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In this talk, we establish a connection between two previously unrelated problems: the compatibility of measurements in quantum information theory and the inclusion problem for free spectrahedra in convex optimization. We show that compatibility of a tuple of binary measurements is equivalent to the inclusion of the matrix diamond inside a free spectrahedron defined by the effect operators of the measurements. We also relate the amount of noise necessary to render any tuple of binary measurements compatible to the inclusion constants for the matrix diamond. These connections allow us to largely improve known bounds for incompatibility robustness from quantum information theory. Finally, we will show how to extend our results to measurements with an arbitrary number of outcomes.

This talk is part of the CQIF Seminar series.

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