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QI: Fachverband Quanteninformation

QI 24: Verification and Benchmarking of Quantum Systems

QI 24.1: Hauptvortrag

Donnerstag, 21. März 2024, 09:30–10:00, HFT-TA 441

Verification of quantum measurements via self-testing — •Laura Mančinska — QMATH, Department of Mathematical Sciences, University of Copenhagen, Denmark

Self-testing is the strongest form of quantum functionality verification which allows a classical user to deduce the quantum state and measurements used to produce measurement statistics. While self-testing of quantum states is well-understood, self-testing of measurements, especially in high dimensions, has remained more elusive. We demonstrate the first general result in this direction by showing that every real projective measurement can be self-tested in the 2-party Bell scenario. The standard definition of self-testing only allows for the certification of real measurements. Therefore, our work effectively broadens the scope of self-testable projective measurements to their full potential. To reach this result, we employ the idea that existing self-tests can be extended to verify additional untrusted measurements. This is known as `post-hoc self-testing'. We formalize the method of post-hoc self-testing and establish a sufficient condition for its application.

We develop a new technique of iterative self-testing, which involves using post-hoc self-testing in a sequential manner. Starting from any established self-test, we fully characterize the set of measurements that can be verified via iterative self-testing. This provides a clear methodology for constructing new self-tests from pre-existing ones.

This talk is based on a joint work with Ranyiliu Chen and Jurij Volčič.

Keywords: entanglement; Bell scenario; self-testing; device-independent protocols; nonlocal games