Counterexamples In Self-testing

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Counterexamples in self-testing PlatoBlockchain Data Intelligence. Vertical Search. Ai.

Laura Mančinska and Simon Schmidt

QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark

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Abstract

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.

► BibTeX data

@article{Mancinska2023counterexamplesin, doi = {10.22331/q-2023-07-11-1051}, url = {https://doi.org/10.22331/q-2023-07-11-1051}, title = {Counterexamples in self-testing}, author = {Man{v{c}}inska, Laura and Schmidt, Simon}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1051}, month = jul, year = {2023}<br /> }

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Cited by

[1] Connor Paddock, William Slofstra, Yuming Zhao, and Yangchen Zhou, “An operator-algebraic formulation of self-testing”, arXiv:2301.11291, (2023).

[2] Pavel Sekatski, Jean-Daniel Bancal, Marie Ioannou, Mikael Afzelius, and Nicolas Brunner, “Towards the device-independent certification of a quantum memory”, arXiv:2304.10408, (2023).

[3] Anne Broadbent, Arthur Mehta, and Yuming Zhao, “Quantum delegation with an off-the-shelf device”, arXiv:2304.03448, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-07-14 10:01:30). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-07-14 10:01:28).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2023-07-11-1051/

Time Stamp: July 11, 2023

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Counterexamples in self-testing

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Abstract

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