Norm Bounds on Sums of Positive Operators with Applications to Monogamy Games and Quantum Key Distribution

arXiv:2611.05943v1 Announce Type: new Abstract: Bounding the acceptance probabilities of quantum measurements is a recurring task in quantum information theory. An acceptance probability averaged over a random measurement setting can be bounded uniformly over the input state by the operator norm of an average of positive semidefinite operators. We prove a general inequality for such norms, valid for arbitrary finite families of positive semidefinite operators and averaging distributions. We give two applications of our operator-norm inequality. First, we determine the sharp robustness threshold for the parallel BB84 monogamy-of-entanglement game.