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.

4 pages, 1 figure, published version

References in corpus (8)

• Nonlocality of Einstein-Podolsky-Rosen State in Wigner Representation
• Maximal Violation of Bell's Inequalities for Continuous Variable Systems
• The conditions for quantum violation of macroscopic realism
• Good dynamics versus bad kinematics. Is entanglement needed for quantum computation?
• Classical model for bulk-ensemble NMR quantum computation
• Optimal States for Bell inequality Violations using Quadrature Phase Homodyne Measurements
• Multipartite Bell-type inequalities for arbitrary numbers of settings and outcomes per site
• On the probabilistic description of a multipartite correlation scenario with arbitrary numbers of settings and outcomes per site

Cited by in corpus (8)

• Observing Dirac's classical phase space analog to the quantum state
• Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
• Continuous-variable entanglement distillation and non-commutative central limit theorems
• Tunable non-Gaussian resources for continuous-variable quantum technologies
• Proposal for a macroscopic test of local realism with phase-space measurements
• Violation of multipartite Bell inequalities with classical subsystems via operationally local transformations
• The Interplay between Quantum Contextuality and Wigner Negativity
• In the Kreisgang between classical and quantum physics