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Constructing multipartite Bell inequalities from stabilizers

Qi Zhao1,2,* and You Zhou3,4,†

  • 1QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
  • 2Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
  • 3Key Laboratory for Information Science of Electromagnetic Waves (Ministry of Education), Fudan University, Shanghai 200433, China
  • 4Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

  • *zhaoq@cs.hku.hk
  • †you_zhou@fudan.edu.cn
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Phys. Rev. Research 4, 043215 – Published 26 December, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.043215

Abstract

Bell inequality with a self-testing property has played an important role in quantum information processing with both fundamental and practical significance. However, it is generally challenging to find Bell inequalities used for self-testing multipartite states, and actually, there are not many known candidates. In this work we propose a systematic framework to construct Bell inequalities from stabilizers which are maximally violated by general stabilizer states, with two observables for each local party. We show that the constructed Bell inequalities can self-test any stabilizer state if and only if these stabilizers can uniquely determine the state in a device-dependent manner. This bridges the gap between device-independent and device-dependent verification methods. Our framework can provide plenty of Bell inequalities for self-testing N-party stabilizer states. Among them, we give two families of Bell inequalities with different advantages: (1) a family of Bell inequalities with a constant ratio of quantum and classical bounds using 2N correlations, and (2) single pair inequalities improving on all previous robustness self-testing bounds using N+1 correlations, which are both efficient and robust for realizations in multipartite systems.

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Phys. Rev. Research 4, 043215– Published 26 December, 2022
  • Received 20 March 2022
  • Accepted 2 December 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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