Device-independent parallel self-testing of two singlets

TL;DR

This paper demonstrates methods for device-independent verification of two entangled qubit pairs without assuming local structure, using specific Bell inequalities and games, with practical noise tolerance.

Contribution

It introduces criteria for parallel self-testing of two singlets without assuming local tensor product structure, using CHSH and Magic Square game.

Findings

Double CHSH inequality certifies two singlets.

Magic Square game uniquely identifies two singlets.

Noise tolerance is feasible with current technology.

Abstract

Device-independent self-testing is the possibility of certifying the quantum state and the measurements, up to local isometries, using only the statistics observed by querying uncharacterized local devices. In this paper, we study parallel self-testing of two maximally entangled pairs of qubits: in particular, the local tensor product structure is not assumed but derived. We prove two criteria that achieve the desired result: a double use of the Clauser-Horne-Shimony-Holt inequality and the $3\times 3$ Magic Square game. This demonstrate that the magic square game can only be perfectly won by measureing a two-singlets state. The tolerance to noise is well within reach of state-of-the-art experiments.