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Abstract
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 postmeasurement 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 nonlocal 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.
Original language  English 

Title of host publication  12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017) 
Editors  Mark M. Wilde 
Place of Publication  Dagstuhl, Germany 
Publisher  Schloss Dagstuhl  LeibnizZentrum fuer Informatik, Germany 
Pages  1:11:23 
Number of pages  23 
ISBN (Print)  9783959770347 
DOIs  
Publication status  Published  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 2017 → 16 Jun 2017 http://tqc2017.lip6.fr/ http://tqc2017.lip6.fr/ 
Publication series
Name  Leibniz International Proceedings in Informatics (LIPIcs) 

Publisher  Schloss DagstuhlLeibnizZentrum fuer Informatik 
Volume  73 
ISSN (Print)  1868896 
Conference
Conference  12th Conference on the Theory of Quantum Computation, Communication, and Cryptography 

Abbreviated title  TQC 2017 
Country/Territory  France 
City  Paris 
Period  14/06/17 → 16/06/17 
Internet address 
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 1 Finished

UK Quantum Technology Hub: NQIT  Networked Quantum Information Technologies
1/12/14 → 30/11/19
Project: Research