A 2-Categorical Analysis of Complementary Families, Quantum Key   Distribution and the Mean King Problem
  This paper explores the use of 2-categorical technology for describing and reasoning about complex quantum procedures. We give syntactic definitions of a family of complementary measurements, and of quantum key distribution, and show that they are equivalent. We then show abstractly that either structure gives a solution to the Mean King problem, which we also formulate 2-categorically. 
Krzysztof Bar (Department of Computer Science, University of Oxford),   Jamie Vicary (Department of Computer Science, Univer...
cs.LO quant-ph