Self-testing in parallel

TL;DR

This paper develops methods for self-testing multiple entangled qubit pairs simultaneously in a parallel setting, enhancing the ability to verify large quantum states efficiently.

Contribution

It introduces new sufficient conditions and constructions for parallel self-testing of many maximally entangled qubit pairs, extending previous sequential testing approaches.

Findings

Derived sufficient conditions for parallel self-testing.

Proposed two new constructions for simultaneous testing.

Enhanced robustness against dishonest players in multi-pair tests.

Abstract

Self-testing allows us to determine, through classical interaction only, whether some players in a non-local game share particular quantum states. Most work on self-testing has concentrated on developing tests for small states like one pair of maximally entangled qubits, or on tests where there is a separate player for each qubit, as in a graph state. Here we consider the case of testing many maximally entangled pairs of qubits shared between two players. Previously such a test was shown where testing is sequential, i.e., one pair is tested at a time. Here we consider the parallel case where all pairs are tested simultaneously, giving considerably more power to dishonest players. We derive sufficient conditions for a self-test for many maximally entangled pairs of qubits shared between two players and also two constructions for self-tests where all pairs are tested simultaneously.