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

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.