Counterexamples in self-testing

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt


  • Fulltext

    Forlagets udgivne version, 626 KB, PDF-dokument

In the recent years self-testing has grown into a rich and active area of study with applications ranging from practical verification of quantum devices to deep complexity theoretic results. Self-testing allows a classical verifier to deduce which quantum measurements and on what state are used, for example, by provers Alice and Bob in a nonlocal game. Hence, self-testing as well as its noise-tolerant cousin—robust self-testing—are desirable features for a nonlocal game to have. Contrary to what one might expect, we have a rather incomplete understanding of if and how self-testing could fail to hold. In particular, could it be that every 2-party nonlocal game or Bell inequality with a quantum advantage certifies the presence of a specific quantum state? Also, is it the case that every self-testing result can be turned robust with enough ingeniuty and effort? We answer these questions in the negative by providing simple and fully explicit counterexamples. To this end, given two nonlocal games G1 and G2, we introduce the (G1 ∨ G2)-game, in which the players get pairs of questions and choose which game they want to play. The players win if they choose the same game and win it with the answers they have given. Our counterexamples are based on this game and we believe this class of games to be of independent interest.

Sider (fra-til)1-22
StatusUdgivet - 2023

Bibliografisk note

Funding Information:
The authors thank the referees for useful comments and suggestions. S.S. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 101030346. L.M. is funded by the European Union under the Grant Agreement No 101078107, QInteract and VILLUM FONDEN via the QMATH Centre of Excellence (Grant No 10059) and Villum Young Investigator grant (No 37532). This project was funded within the QuantERA II Programme that has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No 101017733.

Publisher Copyright:
© 2023 Authors.

ID: 390577992