Comparing Singlet Testing Schemes

TL;DR

This paper compares two schemes for testing whether two parties share a singlet state, finding that the random measurement scheme generally outperforms the standard CHSH-based approach in various adversarial scenarios.

Contribution

It introduces and evaluates an alternative singlet testing scheme based on random measurements, demonstrating its superiority over the traditional CHSH inequality test in adversarial conditions.

Findings

Random measurement test outperforms CHSH test in most scenarios.

The schemes are formulated as hypothesis tests and evaluated under adversarial conditions.

The random measurement scheme shows higher test power against eavesdroppers.

Abstract

We compare schemes for testing whether two parties share a two-qubit singlet state. The first, standard, scheme tests Braunstein-Caves (or CHSH) inequalities, comparing the correlations of local measurements drawn from a fixed finite set against the quantum predictions for a singlet. The second, alternative, scheme tests the correlations of local measurements, drawn randomly from the set of those that are $\theta$-separated on the Bloch sphere, against the quantum predictions. We formulate each scheme as a hypothesis test and then evaluate the test power in a number of adversarial scenarios involving an eavesdropper altering or replacing the singlet qubits. We find the `random measurement' test to be superior in most natural scenarios.