Self-testing in parallel with CHSH

Matthew McKague

Department of Electrical Engineering and Computer Science, Queensland University of Technology

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Self-testing allows classical referees to verify the quantum behaviour of some untrusted devices. Recently we developed a framework for building large self-tests by repeating a smaller self-test many times in parallel. However, the framework did not apply to the CHSH test, which tests a maximally entangled pair of qubits. CHSH is the most well known and widely used test of this type. Here we extend the parallel self-testing framework to build parallel CHSH self-tests for any number of pairs of maximally entangled qubits. Our construction achieves an error bound which is polynomial in the number of tested qubit pairs.

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► References

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[1] Joseph Bowles, Ivan Šupić, Daniel Cavalcanti, and Antonio Acín, "Self-testing of Pauli observables for device-independent entanglement certification", Physical Review A 98 4, 042336 (2018).

[2] Iris Agresti, Davide Poderini, Leonardo Guerini, Michele Mancusi, Gonzalo Carvacho, Leandro Aolita, Daniel Cavalcanti, Rafael Chaves, and Fabio Sciarrino, "Experimental device-independent certified randomness generation with an instrumental causal structure", Communications Physics 3 1, 110 (2020).

[3] Jędrzej Kaniewski, "Weak form of self-testing", arXiv:1910.00706, Physical Review Research 2 3, 033420 (2020).

[4] Tim Coopmans, Jędrzej Kaniewski, and Christian Schaffner, "Robust self-testing of two-qubit states", Physical Review A 99 5, 052123 (2019).

[5] Ivan Šupić and Joseph Bowles, "Self-testing of quantum systems: a review", Quantum 4, 337 (2020).

[6] Spencer Breiner, Amir Kalev, and Carl A. Miller, "Parallel Self-Testing of the GHZ State with a Proof by Diagrams", Electronic Proceedings in Theoretical Computer Science 287, 43 (2019).

[7] Qingshan Xu, Xiaoqing Tan, Rui Huang, and Xiaodan Zeng, "Parallel self‐testing for device‐independent verifiable blind quantum computation", Quantum Engineering 2 3(2020).

[8] Ivan Šupić, Daniel Cavalcanti, and Joseph Bowles, "Device-independent certification of tensor products of quantum states using single-copy self-testing protocols", Quantum 5, 418 (2021).

[9] Alex B. Grilo, William Slofstra, and Henry Yuen, 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) 611 (2019) ISBN:978-1-7281-4952-3.

[10] David Cui, Arthur Mehta, Hamoon Mousavi, and Seyed Sajjad Nezhadi, "A generalization of CHSH and the algebraic structure of optimal strategies", Quantum 4, 346 (2020).

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[12] Jedrzej Kaniewski, "Self-testing of binary observables based on commutation", Physical Review A 95 6, 062323 (2017).

The above citations are from Crossref's cited-by service (last updated successfully 2021-10-27 22:01:08) and SAO/NASA ADS (last updated successfully 2021-10-27 22:01:10). The list may be incomplete as not all publishers provide suitable and complete citation data.