Proposal for a macroscopic test of local realism with phase-space measurements

Abstract

We propose a new test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representation of these observables are bounded in phase space, and therefore, the associated inequality holds for any state described by a non-negative Wigner function. This agrees with Bell's remark that positive Wigner functions, serving as a valid probability distribution over local (hidden) phase space coordinates, do not reveal non-locality. We construct a class of entangled states resulting in a violation of the inequality, and thus truly demonstrate non-locality in phase space. The states can be realized through grating techniques in space-like separated interferometric setups. The non-locality is verified from the spatial correlation data, collected from the screens.

9 pages, 3 figures; Minor changes made in the title, references added, typographical errors fixed

References in corpus (7)

• Detecting entanglement in spatial interference
• State-independent quantum contextuality for continuous variables
• Contextuality in phase space
• Testing quantum nonlocality by generalized quasiprobability functions
• Quantum Information Processing by Weaving Quantum Talbot Carpets
• Maximal violation of tight Bell inequalities for maximal high-dimensional entanglement
• Positive phase space transformation incompatible with classical physics

Cited by in corpus (10)

• Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator
• Quantum information processing in phase space: A modular variables approach
• Testing macroscopic local realism using cat-states and Bell inequalities in time
• General conditions for maximal violation of non-contextuality in discrete and continuous variables
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Weak versus deterministic macroscopic realism, and Einstein-Podolsky-Rosen's elements of reality
• Tomographic entanglement indicators in frequency combs and Talbot carpets
• Non-classical Correlations in n-Cycle Setting
• Cat-state-like non-Gaussian entanglement in magnon systems
• Arbitrarily large violations of non-contextuality in single mode photon states with positive Wigner function