NMR Analog of Bell's Inequalities Violation Test

TL;DR

This paper develops an NMR-based analog test for Bell's inequalities involving multiple qubits, demonstrating a simulation of CHSH inequality violation consistent with quantum mechanics and local hidden variables models.

Contribution

It introduces a novel NMR simulation scheme for Bell's inequalities with multiple qubits, enabling tests of quantum nonlocality in NMR systems.

Findings

Experimental results match quantum mechanics predictions

Results are also compatible with local hidden variables models due to detection loophole

Discussion on future tests with highly polarized spins

Abstract

In this paper we present an analog of the Bell's inequalities violation test for $N$ qubits to be performed in a nuclear magnetic resonance (NMR) quantum computer. This can be used to simulate or predict results for different Bell's inequalities tests, with distinct configurations and larger number of qubits. To demonstrate our scheme, we implemented a simulation of the violation of Clauser, Horne, Shimony and Holt (CHSH) inequality using a two qubit NMR system and compared the results to those of a photon experiment. The experimental results are well described by Quantum Mechanics theory and a Local Realistic Hidden Variables model which was specially developed for NMR. That is why we refer to this experiment as a {\it simulation} of the Bell's inequality violation. Our result shows explicitly how both theories can be compatible to each other due the detection loophole. In the last part of this work we discuss the possibility of testing fundamental features of quantum mechanics using NMR with highly polarized spins, where a strong discrepancy between quantum mechanics and hidden variables models can be expected.