Comparing Singlet Testing Schemes

• URL: http://arxiv.org/abs/2211.13750v2
• Date: Mon, 12 Jun 2023 17:30:15 GMT
• Title: Comparing Singlet Testing Schemes
• Authors: George Cowperthwaite, Adrian Kent
• Abstract summary: We compare schemes for testing whether two parties share a two-qubit singlet state. The first, standard, scheme tests Braunstein-Caves 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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