Citations:hypercontractive


 * 2010 Nathan Keller, "A tight quantitative version of Arrow's impossibility theorem" arXiv
 * Our proof is based on the works of Kalai and Mossel, but uses also an additional ingredient: a combination of the Bonami-Beckner hypercontractive inequality with a reverse hypercontractive inequality due to Borell, applied to find simultaneously upper bounds and lower bounds on the "noise correlation" between Boolean functions on the discrete cube.
 * 2012 Ashley Montanaro, "Some applications of hypercontractive inequalities in quantum information theory" arXiv
 * In this note we discuss how hypercontractive inequalities, in various settings, can be used to obtain (fairly) concise proofs of several results in quantum information theory