Bell and steering scenarios in terms of operator systems

Abstract

The aim of this paper is to indicate possible applications of operator systems in qualitative description of varoius scenarios while studying non-locality. To this end we study in details the notion of generalized non-commuting cube. Following ideas of Fritz and Farenick-Kavruk-Paulsen-Todorov we show in systematic way that various classes of Tsirelson's correlation boxes as well as NPA hierarchies can be described by using various operator system tensor products of generalized non-commuting cubes. Moreover, we show also that noncommuting cubes can be applied for the description of steering assemblages. Next we study some aproximation properties of noncommuting cubes by finite dimensional models. Finaly, we indicate possibility to use the framework operator systems for studying Bell and steering inequalities.

arXiv comment21 pages

References in corpus (8)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Negativity and steering: a stronger Peres conjecture
• Large violation of Bell inequalities with low entanglement
• More non-locality with less entanglement
• Extremal quantum correlations for N parties with two dichotomic observables per site
• Tsirelson's Problem
• The Weak Expectation Property and Riesz Interpolation
• Operator space approach to steering inequality