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A Single Entangled System Is an Unbounded Source of Nonlocal Correlations and of Certified Random Numbers

Research output: Chapter in Book/Report/Conference proceedingConference contribution

  • Florian J. Curchod
  • Markus Johansson
  • Remigiusz Augusiak
  • Matty J. Hoban
  • Peter Wittek
  • Antonio Acín

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Original languageEnglish
Title of host publication12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)
EditorsMark M. Wilde
Place of PublicationDagstuhl, Germany
PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany
Number of pages23
ISBN (Print)978-3-95977-034-7
Publication statusPublished - 1 Feb 2018
Event 12th Conference on the Theory of Quantum Computation, Communication, and Cryptography - Université Pierre et Marie Curie, Paris, France
Duration: 14 Jun 201716 Jun 2017

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik
ISSN (Print)1868-896


Conference 12th Conference on the Theory of Quantum Computation, Communication, and Cryptography
Abbreviated titleTQC 2017
Internet address


The outcomes of local measurements made on entangled systems can be certified to be random provided that the generated statistics violate a Bell inequality. This way of producing randomness relies only on a minimal set of assumptions because it is independent of the internal functioning of the devices generating the random outcomes. In this context it is crucial to understand both qualitatively and quantitatively how the three fundamental quantities - entanglement, nonlocality and randomness – relate to each other. To explore these relationships, we consider the case where repeated (non projective) measurements are made on the physical systems, each measurement being made on the post-measurement state of the previous measurement. In this work, we focus on the following questions: Given a single entangled system, how many nonlocal correlations in a sequence can we obtain? And from this single entangled system, how many certified random numbers is it possible to generate? In the standard scenario with a single measurement in the sequence, it is possible to generate non-local correlations between two distant observers only and the amount of random numbers is very limited. Here we show that we can overcome these limitations and obtain any amount of certified random numbers from a single entangled pair of qubit in a pure state by making sequences of measurements on it. Moreover, the state can be arbitrarily weakly entangled. In addition, this certification is achieved by nearmaximal violation of a particular Bell inequality for each measurement in the sequence. We also present numerical results giving insight on the resistance to imperfections and on the importance of the strength of the measurements in our scheme.

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