title: Positive phase space transformation incompatible with classical physics.
abstract: Bell conjectured that a positive Wigner function does not allow violation of the inequalities imposed by local hidden variable theories. A requirement for this conjecture is "when phase space measurements are performed." We introduce the theory-independent concept of "operationally local transformations" which refers to the change of the switch on a local measurement apparatus. We show that two separated parties, performing only phase space measurements on a composite quantum system with a positive Wigner function and performing only operationally local transformations that preserve this positivity, can nonetheless violate Bell's inequality. Such operationally local transformations are realized using entangled ancillae.
authors.affiliation: The School of Physics and Astronomy, University of Leeds, LS2 9JT Leeds, United Kingdom.
authors.forename: Wonmin
authors.initials: W
authors.lastname: Son
authors.forename: Johannes
authors.initials: J
authors.lastname: Kofler
authors.forename: M S
authors.initials: MS
authors.lastname: Kim
authors.forename: Vlatko
authors.initials: V
authors.lastname: Vedral
authors.forename: Caslav
authors.initials: C
authors.lastname: Brukner