Counterexamples in self-testing
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
Counterexamples in self-testing. / Mančinska, Laura; Schmidt, Simon.
In: Quantum, Vol. 7, 2023, p. 1-22.Research output: Contribution to journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Counterexamples in self-testing
AU - Mančinska, Laura
AU - Schmidt, Simon
N1 - Publisher Copyright: © 2023 Authors.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
U2 - 10.22331/Q-2023-07-11-1051
DO - 10.22331/Q-2023-07-11-1051
M3 - Journal article
AN - SCOPUS:85168385019
VL - 7
SP - 1
EP - 22
JO - Quantum
JF - Quantum
SN - 2521-327X
ER -
ID: 390577992