Hardy nonlocality for entangled pairs in a four-particle system

TL;DR

This paper explores Hardy's nonlocality in a four-particle cyclic entanglement system, revealing more conditions for nonlocality than fully entangled states, through theoretical analysis and quantum circuit simulations on IBM hardware.

Contribution

It introduces a novel cyclic entanglement configuration for Hardy's nonlocality, expanding understanding beyond fully entangled systems with practical circuit implementation.

Findings

Larger set of nonlocality conditions identified

Simulation results show correlation patterns consistent with theory

Experimental implementation on IBM Brisbane shows deviations from ideal predictions

Abstract

Nonlocality can be studied through different approaches, such as Bell's inequalities, and it can be found in numerous quantum states, including GHZ states or graph states. Hardy's paradox, or Hardy-type nonlocality, provides a way to investigate nonlocality for entangled states of particles without using inequalities. Previous studies of Hardy's nonlocality have mostly focused on the fully entangled systems, while other entanglement configurations remain less explored. In this work, the system under investigation consists of four particles arranged in a cyclic entanglement configuration, where each particle forms entangled pairs with two neighbors, while non-neighboring particles remain unentangled. We found that this entanglement structure offers a larger set of conditions that lead to the contradiction with the LHV model, compared to the fully entangled systems. This enhancement can be attributed to the presence of multiple excluded states and correlations, in which the measurement result of a particle only influences the result of its paired partners. We implement quantum circuits compatible with the cyclic entanglement structure, and through simulation, the correlation patterns and the states of interest are identified. We further execute the proposed circuits on IBM Brisbane, a practical backend; however, the results show considerable deviations from the simulation counterparts.