TY - JOUR

T1 - All real projective measurements can be self-tested

AU - Chen, Ranyiliu

AU - Mančinska, Laura

AU - Volčič, Jurij

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024

Y1 - 2024

N2 - Entangled quantum systems feature non-local correlations that are stronger than could be realized classically. This property makes it possible to perform self-testing, the strongest form of quantum functionality verification, which allows a classical user to deduce the quantum state and measurements used to produce a given set of measurement statistics. While self-testing of quantum states is well understood, self-testing of measurements, especially in high dimensions, remains relatively unexplored. Here we prove that every real projective measurement can be self-tested. Our approach employs the idea that existing self-tests can be extended to verify additional untrusted measurements, known as post-hoc self-testing. We formalize the method of post-hoc self-testing and establish the condition under which it can be applied. Using this condition, we construct self-tests for all real projective measurements. We build on this result to develop an iterative self-testing technique that provides a clear methodology for constructing new self-tests from pre-existing ones.

AB - Entangled quantum systems feature non-local correlations that are stronger than could be realized classically. This property makes it possible to perform self-testing, the strongest form of quantum functionality verification, which allows a classical user to deduce the quantum state and measurements used to produce a given set of measurement statistics. While self-testing of quantum states is well understood, self-testing of measurements, especially in high dimensions, remains relatively unexplored. Here we prove that every real projective measurement can be self-tested. Our approach employs the idea that existing self-tests can be extended to verify additional untrusted measurements, known as post-hoc self-testing. We formalize the method of post-hoc self-testing and establish the condition under which it can be applied. Using this condition, we construct self-tests for all real projective measurements. We build on this result to develop an iterative self-testing technique that provides a clear methodology for constructing new self-tests from pre-existing ones.

U2 - 10.1038/s41567-024-02584-z

DO - 10.1038/s41567-024-02584-z

M3 - Journal article

AN - SCOPUS:85200220264

JO - Nature Physics

JF - Nature Physics

SN - 1745-2473

ER -