Self-testing in parallel with CHSH

TL;DR

This paper extends a framework for parallel self-testing to include the CHSH test, enabling verification of multiple entangled qubit pairs simultaneously with polynomial error bounds.

Contribution

It introduces a method to perform parallel self-testing for the CHSH test across any number of qubit pairs, which was not previously possible.

Findings

Achieves polynomial error bounds in the number of qubit pairs tested.

Extends the parallel self-testing framework to include CHSH.

Enables scalable verification of multiple entangled qubits.

Abstract

Self-testing allows classical referees to verify the quantum behaviour of some untrusted devices. Recently we developed a framework for building large self-tests by repeating a smaller self-test many times in parallel. However, the framework did not apply to the CHSH test, which tests a maximally entangled pair of qubits. CHSH is the most well known and widely used test of this type. Here we extend the parallel self-testing framework to build parallel CHSH self-tests for any number of pairs of maximally entangled qubits. Our construction achieves an error bound which is polynomial in the number of tested qubit pairs.