Testing the Clauser-Horne-Shimony-Holt inequality using observables with arbitrary spectrum

Abstract

The Clauser-Horne-Shimony and Holt inequality applies when measurements with binary outcomes are performed on physical systems under the assumption of local realism. Testing such inequalities in the quantum realm usually involves either measurements of two--valued quantum observables or pre-defining a context dependent binning procedure. Here we establish the conditions to test the Clauser-Horne-Shimony and Holt inequality using any quantum observable. Our result applies to observables with an arbitrary spectrum and no prior knowledge of their underlying Hilbert space's dimension is required. Finally, we demonstrate the proposed general measurement strategy, that can be seen as positive operator valued measurements performed on the system, using the formalism of modular variables applied to the transverse degrees of freedom of single photons.

10 pages, 4 figures, including a new Sec. 4

References in corpus (7)

• Reconstruction of non-classical cavity field states with snapshots of their decoherence
• Bell inequalities for continuous-variable correlations
• Continuous variable quantum computation with spatial degrees of freedom of photons
• Experimental Violation of Bell's Inequality in Spatial-Parity Space
• Testing quantum nonlocality by generalized quasiprobability functions
• Maximal violation of tight Bell inequalities for maximal high-dimensional entanglement
• Ancilla-assisted measurement of photonic spatial correlations and entanglement

Cited by in corpus (10)

• Quantum information processing in phase space: A modular variables approach
• Experimental violation of a Bell-like inequality with optical vortex beams
• Modeling Leggett-Garg-inequality violation
• Testing macroscopic local realism using cat-states and Bell inequalities in time
• Proposal for a macroscopic test of local realism with phase-space measurements
• 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
• Periodic discretized continuous observables are neither continuous nor discrete
• Cat-state-like non-Gaussian entanglement in magnon systems