Counterexamples in self-testing
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-07-01
|
| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-07-11-1051/pdf/ |
| _version_ | 1797783226718093312 |
|---|---|
| author | Laura Mančinska Simon Schmidt |
| author_facet | Laura Mančinska Simon Schmidt |
| author_sort | Laura Mančinska |
| collection | DOAJ |
| description | 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 $\mathcal{G}_1$ and $\mathcal{G}_2$, we introduce the $(\mathcal{G}_1 \lor \mathcal{G}_2)$-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. |
| first_indexed | 2024-03-13T00:23:03Z |
| format | Article |
| id | doaj.art-4585a30274e340809681377f5a4b7857 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-13T00:23:03Z |
| publishDate | 2023-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-4585a30274e340809681377f5a4b78572023-07-11T09:47:53ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-07-017105110.22331/q-2023-07-11-105110.22331/q-2023-07-11-1051Counterexamples in self-testingLaura MančinskaSimon SchmidtIn 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 $\mathcal{G}_1$ and $\mathcal{G}_2$, we introduce the $(\mathcal{G}_1 \lor \mathcal{G}_2)$-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.https://quantum-journal.org/papers/q-2023-07-11-1051/pdf/ |
| spellingShingle | Laura Mančinska Simon Schmidt Counterexamples in self-testing Quantum |
| title | Counterexamples in self-testing |
| title_full | Counterexamples in self-testing |
| title_fullStr | Counterexamples in self-testing |
| title_full_unstemmed | Counterexamples in self-testing |
| title_short | Counterexamples in self-testing |
| title_sort | counterexamples in self testing |
| url | https://quantum-journal.org/papers/q-2023-07-11-1051/pdf/ |
| work_keys_str_mv | AT lauramancinska counterexamplesinselftesting AT simonschmidt counterexamplesinselftesting |