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Noise-Tolerant Testing of High Entanglement of Formation

Authors Rotem Arnon-Friedman, Henry Yuen

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ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • device independence
  • quantum games
  • entanglement testing
  • noise tolerance

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Abstract

In this work we construct tests that allow a classical user to certify high dimensional entanglement in uncharacterized and possibly noisy quantum devices. We present a family of non-local games {G_n} that for all n certify states with entanglement of formation Omega(n). These tests can be derived from any bipartite non-local game with a classical-quantum gap. Furthermore, our tests are noise-tolerant in the sense that fault tolerant technologies are not needed to play the games; entanglement distributed over noisy channels can pass with high probability, making our tests relevant for realistic experimental settings. This is in contrast to, e.g., results on self-testing of high dimensional entanglement, which are only relevant when the noise rate goes to zero with the system's size n. As a corollary of our result, we supply a lower-bound on the entanglement cost of any state achieving a quantum advantage in a bipartite non-local game. Our proof techniques heavily rely on ideas from the work on classical and quantum parallel repetition theorems.

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Rotem Arnon-Friedman and Henry Yuen. Noise-Tolerant Testing of High Entanglement of Formation. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 11:1-11:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ICALP.2018.11

Author Details

Rotem Arnon-Friedman
  • ETH Zürich, Switzerland, http://rotemaf.info
Henry Yuen
  • UC Berkeley, USA, http://www.henryyuen.net

Funding

  • Arnon-Friedman, Rotem: RAF is supported by the Swiss National Science Foundation (grant No. 200020-135048) via the National Centre of Competence in Research "Quantum Science and Technolog" and by the US Air Force Office of Scientific Research (grant No. FA9550-16-1-0245)
  • Yuen, Henry: HY is supported by ARO Grant W911NF-12-1-0541 and NSF Grant CCF-1410022.

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