Experimental Detection of Non-local Correlations using a Local Measurement-Based Hierarchy on an NMR Quantum Processor

TL;DR

This paper demonstrates an experimental method using a local measurement hierarchy on an NMR quantum processor to detect non-local correlations in tripartite entangled states, confirming their non-locality and entanglement.

Contribution

It introduces an experimental implementation of a local measurement hierarchy on NMR hardware to detect non-local correlations in multi-qubit states.

Findings

SDP failed to find a positive moment matrix for entangled states

Confirmed non-locality of GHZ, W, and graph states

Validated the method's effectiveness in detecting entanglement

Abstract

The non-local nature of the correlations possessed by quantum systems may be revealed by experimental demonstrations of the violation of Bell-type inequalities. Recent work has placed bounds on the correlations that quantum systems can possess in an actual experiment. These bounds were limited to a composite quantum system comprising of a few lower-dimensional subsystems. In a more general approach, it has been shown that fewer body correlations can reveal the non-local nature of the correlations arising from a quantum mechanical description of nature. Such tests on the correlations can be transformed to a semi-definite program (SDP). This study reports the experimental implementation of a local measurement-based hierarchy on the nuclear magnetic resonance (NMR) hardware utilizing three nuclear spins as qubits. The protocol has been experimentally tested on genuinely entangled tripartite states such as W state, GHZ state and a few graph states. In all the cases, the experimentally measured correlations were used to formulate the SDP, using linear constraints on the entries of the moment matrix. We observed that for each genuinely entangled state, the SDP failed to find a semi-definite positive moment matrix consistent with the experimental data. This implies that the observed correlations can not arise from local measurements on a separable state and are hence non-local in nature, and also confirms that the states being tested are indeed entangled.