Improved local models and new Bell inequalities via Frank-Wolfe algorithms

Abstract

∞ 1979 Lower bounds 0.5 Werner [4] ∞ 1989 Table I. Successive refinements of the bounds on v Wer c , the nonlocality threshold of the two-qubit Werner states under projective measurements. Using m measurements to simulate all projective ones is denoted by m ∼ ∞.

Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant

“…Let us now recall the Grothendieck constant of order 3 22 , 25 , 26 , 32 , 33 , which is given by where the maximization is taken over real matrices M of arbitrary dimensions , q ( M ) is defined by ( 8 ) and L ( M ) is defined as follows where the maximum is taken over all . The value of in ( 16 ), according to the recent work of Designolle et al 34 , is bounded by where the lower bound is an improved version of that given in Ref. 35 and the upper bound is an improved version of that given in Refs.…”