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.
 Charles-Edwourd Bardyn, Timothy C. H. Liew, Serge Massar, Matthew McKague, and Valerio Scarani. Device-independent state estimation based on Bell's inequalities. Physical Review A (Atomic, Molecular, and Optical Physics), 80(6):062327, 2009. 10.1103/PhysRevA.80.062327. arXiv:0907.2170.
 John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 23(15):880-884, Oct 1969. 10.1103/PhysRevLett.23.880.
 Richard Cleve, William Slofstra, Falk Unger, and Sarvagya Upadhyay. Perfect parallel repetition theorem for quantum XOR proof systems. Computational Complexity, 17(2):282-299, 2008. 10.1007/s00037-008-0250-4. arXiv:quant-ph/0608146v2.
 Matthew McKague. Interactive proofs for BQP via self-tested graph states. Theory of Computing, 12(3):1-42, 2013. 10.4086/toc.2016.v012a003. arxiv:1309.5675.
 Matthew McKague. Self-testing in parallel. New Journal of Physics, 18(4):045013, 2016. 10.1088/1367-2630/18/4/045013. arXiv:1511.04194.
 Frédéric Magniez, Dominic Mayers, Michele Mosca, and Harold Ollivier. Self-testing of quantum circuits. In M Bugliesi et al., editor, Proceedings of the 33rd International Colloquium on Automata, Languages and Programming, number 4052 in Lecture Notes in Computer Science, pp. 72-83, 2006. 10.1007/11786986_8. arXiv:quant-ph/0512111v1.
 Carl A. Miller and Yaoyun Shi. Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices. J. ACM, 63(4):33:1-33:63, October 2016. 10.1145/2885493. arXiv:1402.0489.
 Matthew McKague, Tzyh Haur Yang, and Valerio Scarani. Robust self-testing of the singlet. Journal of Physics A: Mathematical and Theoretical, 45(45):455304, 2012. 10.1088/1751-8113/45/45/455304. arXiv:1203.2976.
 Sandu Popescu and Daniel Rohrlich. Which states violate Bell's inequality maximally? Physics Letters A, 169(6):411 - 414, 1992. 10.1016/0375-9601(92)90819-8.
 Umesh Vazirani and Thomas Vidick. Fully device-independent quantum key distribution. Physical review letters, 113(14):140501, 2014. 10.1103/PhysRevLett.113.140501.
 Xingyao Wu, Jean-Daniel Bancal, Matthew McKague, and Valerio Scarani. Device-independent parallel self-testing of two singlets. Phys. Rev. A, 93:062121, Jun 2016. 10.1103/PhysRevA.93.062121. arXiv:1512.02074.
 Jedrzej Kaniewski, "Self-testing of binary observables based on commutation", Physical Review A 95 6, 062323 (2017).
 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).
 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).
 Amir Kalev and Carl A Miller, "Rigidity of the magic pentagram game", Quantum Science and Technology 3 1, 015002 (2018).
The above citations are from Crossref's cited-by service (last updated 2019-05-21 06:41:31) and SAO/NASA ADS (last updated 2019-05-21 06:41:32). The list may be incomplete as not all publishers provide suitable and complete citation data.
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.