Noise-Tolerant Testing of High Entanglement of Formation

Authors Rotem Arnon-Friedman, Henry Yuen

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Rotem Arnon-Friedman
  • ETH Zürich, Switzerland,
Henry Yuen
  • UC Berkeley, USA,

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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)


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.

Subject Classification

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


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