Quantum quantities near the Grothendieck bound in a single quantum system

Abstract

The Grothendieck theorem considers a ‘classical’ quadratic form that uses complex scalars in the unit disc, and the corresponding ‘quantum’ quadratic form that replaces the scalars with vectors in the unit ball of a Hilbert space. It shows that when then might take values greater than 1, up to the complex Grothendieck constant kG . Previous work in a quantum context, used Grothendieck’s theorem with multipartite entangled systems, in contrast to the present work which uses it for a single quantum system. The emphasis in the paper is in examples with , which is a classically forbidden region in the sense that cannot take values in it.