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This paper explores the use of 2-categorical technology for describing andreasoning about complex quantum procedures. We give syntactic definitions of afamily of complementary measurements, and of quantum key distribution, and showthat they are equivalent. We then show abstractly that either structure gives asolution to the Mean King problem, which we also formulate 2-categorically.

A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem