A new error-modeling of Hardy's paradox for superconducting qubits and its experimental verification

TL;DR

This paper introduces a novel error-modeling approach for Hardy's paradox tailored to superconducting qubits, experimentally verifies non-locality, and discusses practical implementation challenges and solutions.

Contribution

It proposes a new error-modeling method specific to superconducting qubits and experimentally verifies Hardy's paradox in this system for the first time.

Findings

Non-maximally entangled states violate Hardy's equations

Maximally entangled and product states do not exhibit Hardy's non-locality

Identified practical challenges and proposed remedies for Hardy's protocol implementation

Abstract

Hardy's paradox (equivalently, Hardy's non-locality or Hardy's test) [\href{https://link.aps.org/doi/10.1103/PhysRevLett.68.2981}{L. Hardy, Phys. Rev. Lett. \textbf{68}, 2981 (1992)}] is used to show non-locality without inequalities and it has been tested several times using optical circuits. We, for the first time, experimentally test Hardy's paradox of non-locality in superconducting qubits. For practical verification of Hardy's paradox, we argue that the error-modeling used in optical circuits is not useful for superconducting qubits. So, we propose a new error-modeling for Hardy's paradox and a new method to estimate the lower bound on Hardy's probability (i.e., the probability of a specific event in Hardy's test) for superconducting qubits. Our results confirmed the theory that any non-maximally entangled state of two qubits violates Hardy's equations; whereas, any maximally entangled state and product state of two qubits do not exhibit Hardy's non-locality. Further, we point out the difficulties associated with the practical implementation of quantum protocols based on Hardy's paradox and propose possible remedies. We also propose two performance measures for any two qubits of any quantum computer based on superconducting qubits.