Positive phase space transformation incompatible with classical physics

TL;DR

This paper demonstrates that even with a positive Wigner function and local phase space measurements, Bell inequalities can be violated through specific local transformations involving entangled ancillae, challenging classical physics assumptions.

Contribution

It introduces the concept of operationally local transformations and shows they can lead to Bell inequality violations despite positive Wigner functions.

Findings

Bell inequality violations with positive Wigner functions

Operationally local transformations can involve entangled ancillae

Challenges Bell's conjecture on classical physics limits

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.