title: Arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality.
abstract: The use of Bell's theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest Bell test-one involving 2 parties each performing 2 binary-outcome measurements-an arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality. To this end, we introduce the notion of measurement dependent locality and show that the corresponding correlations form a convex polytope. These correlations can thus be characterized efficiently, e.g., using a finite set of Bell-like inequalities-an observation that enables the systematic study of quantum nonlocality and related applications under limited measurement independence.
authors.affiliation: Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland.
authors.forename: Gilles
authors.initials: G
authors.lastname: Pütz
authors.affiliation: Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland.
authors.forename: Denis
authors.initials: D
authors.lastname: Rosset
authors.affiliation: Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland.
authors.forename: Tomer Jack
authors.initials: TJ
authors.lastname: Barnea
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland.
authors.forename: Yeong-Cherng
authors.initials: YC
authors.lastname: Liang
authors.affiliation: Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Gisin