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Parallel Self-Testing of EPR Pairs Under Computational Assumptions

Authors Honghao Fu , Daochen Wang , Qi Zhao

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Author Details

Honghao Fu
  • CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA
Daochen Wang
  • QuICS, University of Maryland, College Park, MD, USA
Qi Zhao
  • QuICS, University of Maryland, College Park, MD, USA
  • QICI, The University of Hong Kong, China

Funding

  • Fu, Honghao: NSF QLCI program (grant OMA-2016245).
  • Wang, Daochen: Army Research Office (grant W911NF-20-1-0015); the Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing program; and the National Science Foundation (grant DMR-1747426).
  • Zhao, Qi: Department of Defense through the QuICS Hartree Postdoctoral Fellowship.

Acknowledgements

We especially thank Carl Miller, Tony Metger, and Thomas Vidick for many helpful discussions and correspondence. We also thank Nai-Hui Chia, Shih-Han Hung, Yi Lee, Atul Mantri, and Jiayu Zhang for helpful discussions.

Cite As Get BibTex

Honghao Fu, Daochen Wang, and Qi Zhao. Parallel Self-Testing of EPR Pairs Under Computational Assumptions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 64:1-64:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ICALP.2023.64

Abstract

Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Metger and Vidick, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ε must be poly(N,ε)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution [Metger et al., 2021] under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.

Subject Classification

ACM Subject Classification
  • Theory of computation → Interactive proof systems
Keywords
  • Quantum complexity theory
  • self-testing
  • LWE

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