# Comparing Singlet Testing Schemes

## TL;DR

The paper compares two methods for testing if two parties share a quantum singlet state, finding that random measurement schemes are more effective in detecting eavesdropping.

## Contribution

The novel contribution is the proposal and evaluation of a random measurement scheme for singlet testing, which outperforms the standard fixed measurement approach.

## Key findings

- The random measurement scheme demonstrates higher test power in adversarial scenarios involving eavesdropping.
- Standard schemes using fixed measurement sets are less effective in detecting altered or replaced singlet qubits.
- The random scheme is superior in most natural eavesdropping situations.

## 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 θ-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.