Some applications of hypercontractive inequalities in quantum information theory
Ashley Montanaro · 2016
Hypercontractive inequalities have become important tools in theoretical computer science and have recently found applications in quantum computation. In this note we discuss how hy-percontractive inequalities, in various settings, can be used to obtain (fairly) concise proofs of several results in quantum information theory: a recent lower bound of Lancien and Winter on the bias achievable by local measurements which are 4-designs; spectral concentration bounds for k-local Hamiltonians; and a recent result of Pellegrino and Seoane-Sepúlveda giving general lower bounds on the classical bias obtainable in multiplayer XOR games. 1