All Real Projective Measurements Can be Self-tested

• URL: http://arxiv.org/abs/2302.00974v2
• Date: Sat, 8 Jul 2023 10:37:55 GMT
• Title: All Real Projective Measurements Can be Self-tested
• Authors: Ranyiliu Chen, Laura Man\v{c}inska, Jurij Vol\v{c}i\v{c}
• Abstract summary: We show that every real projective measurement can be self-tested. We employ the idea that existing self-tests can be extended to verify additional untrusted measurements. We develop a new technique of iterative self-testing, which involves using post-hoc self-testing in a sequential manner.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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. 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. Using this condition we construct self-tests for all real projective measurements. Inspired by our construction, 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.

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