Hardy's Test versus the CHSH Test of Quantum Non-Locality: Fundamental and Practical Aspects

Abstract

We compare two different tests of quantum non-locality, both in theoretical terms and with respect to a possible implementation in a mesoscopic circuit: Hardy's test [Hardy, Phys. Rev. Lett. \textbf{68}, 2981 (1992)] and the CHSH test, the latter including a recently discovered inequality relevant for experiments with three possible outcomes [Collins and Gisin, J. Phys. A \textbf{37}, 1775 (2004)]. We clarify the geometry of the correlations defined by Hardy's equations with respect to the polytope of causal correlations, and show that these equations generalize to the CHSH inequality if the slightest imperfections in the setup need to be taken into account. We propose a mesoscopic circuit consisting of two interacting Mach-Zehnder interferometers in a Hall bar system for which both Hardy's test and the CHSH test can be realized with a simple change of gate voltages, and evaluate the robustness of the two tests in the case of fluctuating experimental parameters. The proposed setup is remarkably robust and should work for fluctuations of beam splitter angles or phases up to the order of one radian, or single particle loss rates up to about 15%.

arXiv comment26 pages; 3 EPS figures; typos corrected; references added/corrected

References in corpus (24)

• Hidden Variables and the Two Theorems of John Bell
• Bell inequalities for arbitrarily high dimensional systems
• An Electronic Mach-Zehnder Interferometer
• Non-local correlations as an information theoretic resource
• An On-Demand Coherent Single Electron Source
• An experimental test of non-local realism
• Bell inequality violation with two remote atomic qubits
• A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
• Quantum non-locality in two three-level systems
• Two-particle Aharonov-Bohm effect and Entanglement in the electronic Hanbury Brown Twiss setup
• Orbital entanglement and violation of Bell inequalities in mesoscopic conductors
• Bell inequalities and entanglement in solid state devices
• Current measurement by real-time counting of single electrons
• Production and detection of entangled electron-hole pairs in a degenerate electron gas
• Experimental Falsification of Leggett's Non-Local Variable Model
• Experimental test of nonlocal realistic theories without the rotational symmetry assumption
• Proofs of nonlocality without inequalities revisited
• Entanglement in a Noninteracting Mesoscopic Structure
• Full Counting Statistics with Spin-sensitive Detectors reveals Spin-singlets
• Entanglement in Mesoscopic Structures: Role of Projection
• Realisation of Hardy's Thought Experiment
• Hardy's criterion of nonlocality for mixed states
• Hardy's proof of nonlocality in the presence of noise
• Nonlocality without inequalities for almost all entangled states of any quantum system

Cited by in corpus (9)

• Tsirelson's problem and Kirchberg's conjecture
• The Inflation Technique for Causal Inference with Latent Variables
• Device-independent bounds for Hardy's experiment
• Measuring Which-Path Information with Coupled Electronic Mach-Zehnder Interferometers
• Increased success probability in Hardy's nonlocality: Theory and demonstration
• Persistence of nonlocality for bipartite quantum spin systems
• A unified view on Hardy's paradox and the CHSH inequality
• Characterizing quantum correlations in the nonsignaling framework
• The Hardy's nonlocality argument