Self-testing of quantum states using symmetric local hidden state model

TL;DR

This paper introduces a symmetric local hidden state model, derives a new inequality revealing a broader class of quantum correlations, and demonstrates its violation on IBM quantum computers, enabling device-independent self-testing of Bell states.

Contribution

The paper proposes a novel symmetric local hidden state model and an associated inequality, expanding the understanding of quantum nonlocality and enabling self-testing in a device-independent manner.

Findings

Derived a new inequality based on the symmetric local hidden state model.

Experimental violation demonstrated on IBM quantum computer for two qubits.

Maximal violation enables self-testing of Bell states and measurement bases.

Abstract

We introduce a symmetric local hidden state $(slhs)$ model in a scenario, where two spacially separated parties receive quantum states from an unknown source. We derive an inequality based on the model. A completely new form of nonlocality emerges from the resource theoretic point of view. The inequality singles out a larger set of quantum correlated states in the higher dimensional scenarios $(d> 2 $ X $2)$ than what is predicted by the existing $lhs$ model, opening a new front for the experimentalists to test the accuracy of the prediction. We propose an experiment to show the experimental violation of the inequality in the two qubit scenario and perform the experiment on the IBM quantum computer. However, the experimental method adopted for the two-qubit scenario does not naturally generalize in the higher dimensional scenarios and leaves the experimental verification of the claim open. We also show that the maximal violation of the inequality can be used to self-test the Bell state and measurement bases, leading to complete device-independence.